how to state a non directional hypothesis

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Hypotheses; directional and non-directional, what is the difference between an experimental and an alternative hypothesis.

Nothing much! If the study is a laboratory experiment then we can call the hypothesis “an experimental hypothesis”, where we make a prediction about how the IV causes an effect on the DV. If we have a non-experimental design, i.e. we are not able to manipulate the IV as in a natural or quasi-experiment , or if some other research method has been used, then we call it an “alternativehypothesis”, alternative to the null.

Directional hypothesis: A directional (or one tailed hypothesis) states which way you think the results are going to go, for example in an experimental study we might say…”Participants who have been deprived of sleep for 24 hours will have more cold symptoms in the following week after exposure to a virus than participants who have not been sleep deprived”; the hypothesis compares the two groups/conditions and states which one will ….have more/less, be quicker/slower, etc.

If we had a correlational study, the directional hypothesis would state whether we expect a positive or a negative correlation, we are stating how the two variables will be related to each other, e.g. there will be a positive correlation between the number of stressful life events experienced in the last year and the number of coughs and colds suffered, whereby the more life events you have suffered the more coughs and cold you will have had”. The directional hypothesis can also state a negative correlation, e.g. the higher the number of face-book friends, the lower the life satisfaction score “

Non-directional hypothesis: A non-directional (or two tailed hypothesis) simply states that there will be a difference between the two groups/conditions but does not say which will be greater/smaller, quicker/slower etc. Using our example above we would say “There will be a difference between the number of cold symptoms experienced in the following week after exposure to a virus for those participants who have been sleep deprived for 24 hours compared with those who have not been sleep deprived for 24 hours.”

When the study is correlational, we simply state that variables will be correlated but do not state whether the relationship will be positive or negative, e.g. there will be a significant correlation between variable A and variable B.

Null hypothesis The null hypothesis states that the alternative or experimental hypothesis is NOT the case, if your experimental hypothesis was directional you would say…

Participants who have been deprived of sleep for 24 hours will NOT have more cold symptoms in the following week after exposure to a virus than participants who have not been sleep deprived and any difference that does arise will be due to chance alone.

or with a directional correlational hypothesis….

There will NOT be a positive correlation between the number of stress life events experienced in the last year and the number of coughs and colds suffered, whereby the more life events you have suffered the more coughs and cold you will have had”

With a non-directional or  two tailed hypothesis…

There will be NO difference between the number of cold symptoms experienced in the following week after exposure to a virus for those participants who have been sleep deprived for 24 hours compared with those who have not been sleep deprived for 24 hours.

or for a correlational …

there will be NO correlation between variable A and variable B.

When it comes to conducting an inferential stats test, if you have a directional hypothesis , you must do a one tailed test to find out whether your observed value is significant. If you have a non-directional hypothesis , you must do a two tailed test .

Exam Techniques/Advice

• Remember, a decent hypothesis will contain two variables, in the case of an experimental hypothesis there will be an IV and a DV; in a correlational hypothesis there will be two co-variables
• both variables need to be fully operationalised to score the marks, that is you need to be very clear and specific about what you mean by your IV and your DV; if someone wanted to repeat your study, they should be able to look at your hypothesis and know exactly what to change between the two groups/conditions and exactly what to measure (including any units/explanation of rating scales etc, e.g. “where 1 is low and 7 is high”)
• double check the question, did it ask for a directional or non-directional hypothesis?
• if you were asked for a null hypothesis, make sure you always include the phrase “and any difference/correlation (is your study experimental or correlational?) that does arise will be due to chance alone”

Practice Questions:

• Mr Faraz wants to compare the levels of attendance between his psychology group and those of Mr Simon, who teaches a different psychology group. Which of the following is a suitable directional (one tailed) hypothesis for Mr Faraz’s investigation?

A There will be a difference in the levels of attendance between the two psychology groups.

B Students’ level of attendance will be higher in Mr Faraz’s group than Mr Simon’s group.

C Any difference in the levels of attendance between the two psychology groups is due to chance.

D The level of attendance of the students will depend upon who is teaching the groups.

2. Tracy works for the local council. The council is thinking about reducing the number of people it employs to pick up litter from the street. Tracy has been asked to carry out a study to see if having the streets cleaned at less regular intervals will affect the amount of litter the public will drop. She studies a street to compare how much litter is dropped at two different times, once when it has just been cleaned and once after it has not been cleaned for a month.

Write a fully operationalised non-directional (two-tailed) hypothesis for Tracy’s study. (2)

3. Jamila is conducting a practical investigation to look at gender differences in carrying out visuo-spatial tasks. She decides to give males and females a jigsaw puzzle and will time them to see who completes it the fastest. She uses a random sample of pupils from a local school to get her participants.

(a) Write a fully operationalised directional (one tailed) hypothesis for Jamila’s study. (2) (b) Outline one strength and one weakness of the random sampling method. You may refer to Jamila’s use of this type of sampling in your answer. (4)

4. Which of the following is a non-directional (two tailed) hypothesis?

A There is a difference in driving ability with men being better drivers than women

B Women are better at concentrating on more than one thing at a time than men

C Women spend more time doing the cooking and cleaning than men

D There is a difference in the number of men and women who participate in sports

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Non Directional Hypothesis

Ai generator.

In the realm of hypothesis formulation, non-directional hypotheses offer a distinct perspective. These hypotheses suggest a relationship between variables without specifying the nature or direction of that relationship. This guide delves into non-directional hypothesis examples across various fields, outlines a step-by-step approach to crafting them, and provides expert tips to ensure your non-directional hypotheses are robust and insightful. Explore the world of Thesis statement hypotheses that explore connections without predetermined expectations.

What is the Non-Directional Hypothesis? – Definition

A non-directional hypothesis, also known as a two tailed hypothesis , is a type of hypothesis that predicts a relationship between variables without specifying the direction of that relationship. Unlike directional hypotheses that predict a specific outcome, non-directional hypotheses simply suggest that a relationship exists without indicating whether one variable will increase or decrease in response to changes in the other variable.

What is an Example of a Non-Directional Hypothesis Statement?

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“An increase in exercise frequency is associated with changes in weight.”

In this non-directional hypothesis, the statement suggests that a relationship exists between exercise frequency and weight changes but doesn’t specify whether increased exercise will lead to weight loss or weight gain. It leaves the direction of the relationship open for empirical investigation and data analysis.

100 Non Directional Hypothesis Statement Examples

Non-directional hypotheses explore relationships between variables without predicting the specific outcome. These simple hypothesis offer flexibility, allowing researchers to uncover unforeseen connections. Discover a range of non-directional hypothesis examples that span disciplines, enabling empirical exploration and evidence-based conclusions.

• Impact of Stress on Sleep Quality : Stress levels are related to changes in sleep quality among college students.
• Relationship Between Social Media Use and Loneliness : Social media use is associated with variations in reported feelings of loneliness.
• Connection Between Parenting Styles and Adolescent Self-Esteem : Different parenting styles correlate with differences in adolescent self-esteem levels.
• Effects of Temperature on Productivity : Temperature variations affect productivity levels in office environments.
• Link Between Screen Time and Eye Strain : Screen time is related to variations in reported eye strain among digital device users.
• Influence of Study Techniques on Exam Performance : Study techniques correlate with differences in exam performance among students.
• Relationship Between Classroom Environment and Student Engagement : Classroom environment is associated with variations in student engagement levels.
• Impact of Music Tempo on Heart Rate : Music tempo relates to changes in heart rate during exercise.
• Connection Between Diet and Cholesterol Levels : Dietary choices are related to variations in cholesterol levels among adults.
• Effects of Outdoor Exposure on Mood : Outdoor exposure is associated with changes in reported mood among urban dwellers.
• Relationship Between Personality Traits and Leadership Styles : Personality traits are associated with differences in preferred leadership styles among professionals.
• Impact of Time Management Strategies on Academic Performance : Time management strategies correlate with variations in academic performance among college students.
• Connection Between Cultural Exposure and Empathy Levels : Cultural exposure relates to changes in reported empathy levels among individuals.
• Effects of Nutrition Education on Dietary Choices : Nutrition education is associated with variations in dietary choices among adolescents.
• Link Between Social Support and Stress Levels : Social support is related to differences in reported stress levels among working adults.
• Influence of Exercise Intensity on Mood : Exercise intensity correlates with variations in reported mood among fitness enthusiasts.
• Relationship Between Parental Involvement and Academic Achievement : Parental involvement is associated with differences in academic achievement among schoolchildren.
• Impact of Sleep Duration on Cognitive Function : Sleep duration is related to changes in cognitive function among older adults.
• Connection Between Environmental Factors and Creativity : Environmental factors correlate with variations in reported creative thinking abilities among artists.
• Effects of Communication Styles on Conflict Resolution : Communication styles are associated with differences in conflict resolution outcomes among couples.
• Relationship Between Social Interaction and Life Satisfaction : Social interaction is related to variations in reported life satisfaction among elderly individuals.
• Impact of Classroom Seating Arrangements on Participation : Classroom seating arrangements correlate with differences in student participation levels.
• Connection Between Smartphone Use and Sleep Quality : Smartphone use is associated with changes in reported sleep quality among young adults.
• Effects of Mindfulness Practices on Stress Reduction : Mindfulness practices relate to variations in reported stress levels among participants.
• Link Between Gender and Communication Styles : Gender is related to differences in communication styles among individuals in group discussions.
• Influence of Advertising Exposure on Purchase Decisions : Advertising exposure correlates with variations in reported purchase decisions among consumers.
• Relationship Between Job Satisfaction and Employee Productivity : Job satisfaction is associated with differences in employee productivity levels.
• Impact of Social Support on Coping Mechanisms : Social support relates to variations in reported coping mechanisms among individuals facing challenges.
• Connection Between Classroom Environment and Student Creativity : Classroom environment is related to changes in student creativity levels.
• Effects of Exercise on Mood : Exercise is associated with variations in reported mood levels among participants.
• Relationship Between Music Preferences and Stress Levels : Music preferences are related to variations in reported stress levels among individuals.
• Impact of Nutrition Education on Food Choices : Nutrition education correlates with differences in dietary food choices among adolescents.
• Connection Between Physical Activity and Cognitive Function : Physical activity is associated with changes in cognitive function among older adults.
• Effects of Color Exposure on Mood : Color exposure relates to variations in reported mood levels among participants.
• Link Between Personality Traits and Career Choice : Personality traits are related to differences in career choices among individuals.
• Influence of Outdoor Recreation on Mental Well-being : Outdoor recreation is associated with variations in reported mental well-being among participants.
• Relationship Between Social Media Use and Self-Esteem : Social media use correlates with changes in reported self-esteem levels among young adults.
• Impact of Parenting Styles on Adolescent Risk Behavior : Parenting styles are related to variations in reported risk behaviors among adolescents.
• Connection Between Sleep Quality and Cognitive Performance : Sleep quality relates to changes in cognitive performance among students.
• Effects of Art Exposure on Creativity : Art exposure is associated with differences in reported creative thinking abilities among participants.
• Relationship Between Social Support and Mental Health : Social support is related to variations in reported mental health outcomes among individuals.
• Impact of Technology Use on Interpersonal Communication : Technology use correlates with differences in reported interpersonal communication skills among individuals.
• Connection Between Parental Attachment and Romantic Relationships : Parental attachment is associated with variations in the quality of romantic relationships among adults.
• Effects of Environmental Noise on Concentration : Environmental noise relates to changes in reported concentration levels among students.
• Link Between Music Exposure and Memory Performance : Music exposure is related to differences in memory performance among participants.
• Influence of Nutrition on Physical Fitness : Nutrition choices correlate with variations in reported physical fitness levels among athletes.
• Relationship Between Stress and Health Outcomes : Stress levels are associated with changes in reported health outcomes among individuals.
• Impact of Workplace Environment on Job Satisfaction : Workplace environment relates to differences in reported job satisfaction among employees.
• Connection Between Humor and Stress Reduction : Humor is related to variations in reported stress reduction among participants.
• Effects of Social Interaction on Emotional Well-being : Social interaction correlates with changes in reported emotional well-being among participants.
• Relationship Between Cultural Exposure and Cognitive Flexibility : Cultural exposure is related to variations in reported cognitive flexibility among individuals.
• Impact of Parent-Child Communication on Academic Achievement : Parent-child communication correlates with differences in academic achievement levels among students.
• Connection Between Personality Traits and Prosocial Behavior : Personality traits are associated with variations in reported prosocial behaviors among individuals.
• Effects of Nature Exposure on Stress Reduction : Nature exposure relates to changes in reported stress reduction among participants.
• Link Between Sleep Duration and Cognitive Performance : Sleep duration is related to differences in cognitive performance among participants.
• Influence of Social Media Use on Body Image : Social media use correlates with variations in reported body image satisfaction among young adults.
• Relationship Between Exercise and Mental Well-being : Exercise levels are associated with changes in reported mental well-being among participants.
• Impact of Cultural Competency Training on Patient Care : Cultural competency training relates to differences in patient care outcomes among healthcare professionals.
• Connection Between Perceived Social Support and Resilience : Perceived social support is related to variations in reported resilience levels among individuals.
• Effects of Environmental Factors on Mood : Environmental factors correlate with changes in reported mood levels among participants.
• Relationship Between Cultural Diversity and Team Performance : Cultural diversity is related to variations in reported team performance outcomes among professionals.
• Impact of Parental Involvement on Academic Motivation : Parental involvement correlates with differences in academic motivation levels among schoolchildren.
• Connection Between Mindfulness Practices and Anxiety Reduction : Mindfulness practices are associated with changes in reported anxiety levels among participants.
• Effects of Nutrition Education on Eating Habits : Nutrition education relates to variations in dietary eating habits among adolescents.
• Link Between Personality Traits and Learning Styles : Personality traits are related to differences in preferred learning styles among students.
• Influence of Nature Exposure on Creativity : Nature exposure correlates with variations in reported creative thinking abilities among individuals.
• Relationship Between Extracurricular Activities and Social Skills : Extracurricular activities are associated with changes in reported social skills among adolescents.
• Impact of Cultural Awareness Training on Stereotypes : Cultural awareness training relates to differences in perceived stereotypes among participants.
• Connection Between Sleep Quality and Emotional Regulation : Sleep quality is related to variations in reported emotional regulation skills among individuals.
• Effects of Music Exposure on Mood : Music exposure correlates with changes in reported mood levels among participants.
• Relationship Between Cultural Sensitivity and Cross-Cultural Communication : Cultural sensitivity is related to variations in reported cross-cultural communication skills among professionals.
• Impact of Parent-Child Bonding on Emotional Well-being : Parent-child bonding correlates with differences in reported emotional well-being levels among individuals.
• Connection Between Personality Traits and Conflict Resolution Styles : Personality traits are associated with variations in preferred conflict resolution styles among individuals.
• Effects of Mindfulness Practices on Focus and Concentration : Mindfulness practices relate to changes in reported focus and concentration levels among participants.
• Link Between Gender Identity and Career Aspirations : Gender identity is related to differences in reported career aspirations among individuals.
• Influence of Art Exposure on Emotional Expression : Art exposure correlates with variations in reported emotional expression abilities among participants.
• Relationship Between Peer Influence and Risky Behavior : Peer influence is associated with changes in reported engagement in risky behaviors among adolescents.
• Impact of Diversity Training on Workplace Harmony : Diversity training relates to differences in perceived workplace harmony among employees.
• Connection Between Sleep Patterns and Cognitive Performance : Sleep patterns are related to variations in cognitive performance among students.
• Effects of Exercise on Self-Esteem : Exercise correlates with changes in reported self-esteem levels among participants.
• Relationship Between Social Interaction and Well-being : Social interaction is related to variations in reported well-being levels among individuals.
• Impact of Parenting Styles on Adolescent Peer Relationships : Parenting styles correlate with differences in peer relationship quality among adolescents.
• Connection Between Personality Traits and Communication Effectiveness : Personality traits are associated with variations in communication effectiveness among professionals.
• Effects of Outdoor Activities on Stress Reduction : Outdoor activities relate to changes in reported stress reduction among participants.
• Link Between Music Exposure and Emotional Regulation : Music exposure is related to differences in reported emotional regulation skills among individuals.
• Influence of Family Dynamics on Academic Achievement : Family dynamics correlate with variations in academic achievement levels among students.
• Relationship Between Cultural Engagement and Empathy : Cultural engagement is associated with changes in reported empathy levels among individuals.
• Impact of Conflict Resolution Strategies on Relationship Satisfaction : Conflict resolution strategies relate to differences in reported relationship satisfaction levels among couples.
• Connection Between Sleep Quality and Physical Health : Sleep quality is related to variations in reported physical health outcomes among individuals.
• Effects of Social Support on Coping with Stress : Social support correlates with changes in reported coping strategies for stress among participants.
• Relationship Between Cultural Sensitivity and Patient Care : Cultural sensitivity is related to variations in reported patient care outcomes among healthcare professionals.
• Impact of Family Communication on Adolescent Well-being : Family communication correlates with differences in reported well-being levels among adolescents.
• Connection Between Personality Traits and Leadership Styles : Personality traits are associated with variations in preferred leadership styles among professionals.
• Effects of Nature Exposure on Attention Span : Nature exposure relates to changes in reported attention span among participants.
• Link Between Music Preference and Emotional Expression : Music preference is related to differences in reported emotional expression abilities among individuals.
• Influence of Peer Support on Academic Success : Peer support correlates with variations in reported academic success levels among students.
• Relationship Between Cultural Engagement and Creativity : Cultural engagement is associated with changes in reported creative thinking abilities among individuals.
• Impact of Conflict Resolution Skills on Relationship Satisfaction : Conflict resolution skills relate to differences in reported relationship satisfaction levels among couples.
• Connection Between Sleep Patterns and Stress Levels : Sleep patterns are related to variations in reported stress levels among individuals.
• Effects of Social Interaction on Happiness : Social interaction correlates with changes in reported happiness levels among participants.

Non-Directional Hypothesis Statement Examples for Psychology

These examples pertain to psychological studies and cover various relationships between psychological hypothesis concepts. For instance, the first example suggests that attachment styles might be related to romantic satisfaction, but it doesn’t specify whether attachment styles would increase or decrease satisfaction.

• Relationship Between Attachment Styles and Romantic Satisfaction : Attachment styles are related to variations in reported romantic satisfaction levels among individuals in psychology studies.
• Impact of Personality Traits on Career Success : Personality traits correlate with differences in reported career success outcomes among psychology study participants.
• Connection Between Parenting Styles and Adolescent Self-Esteem : Parenting styles are associated with variations in reported self-esteem levels among adolescents in psychological research.
• Effects of Social Media Use on Body Image : Social media use relates to changes in reported body image satisfaction among young adults in psychology experiments.
• Link Between Sleep Patterns and Emotional Well-being : Sleep patterns are related to differences in reported emotional well-being levels among psychology research participants.
• Influence of Mindfulness Practices on Stress Reduction : Mindfulness practices correlate with variations in reported stress reduction among psychology study participants.
• Relationship Between Social Interaction and Mental Health : Social interaction is associated with changes in reported mental health outcomes among individuals in psychology studies.
• Impact of Parent-Child Bonding on Emotional Resilience : Parent-child bonding relates to differences in reported emotional resilience levels among psychology research participants.
• Connection Between Cultural Sensitivity and Empathy : Cultural sensitivity is related to variations in reported empathy levels among individuals in psychology experiments.
• Effects of Exercise on Mood : Exercise correlates with changes in reported mood levels among psychology study participants.

Non-Directional Hypothesis Statement Examples in Research

These research hypothesis examples focus on research studies in general, covering a wide range of topics and relationships. For instance, the second example suggests that employee training might be related to workplace productivity, without indicating whether the training would lead to higher or lower productivity.

• Relationship Between Time Management and Academic Performance : Time management is related to variations in academic performance levels among research participants.
• Impact of Employee Training on Workplace Productivity : Employee training correlates with differences in reported workplace productivity outcomes among research subjects.
• Connection Between Media Exposure and Political Knowledge : Media exposure is associated with variations in reported political knowledge levels among research participants.
• Effects of Environmental Factors on Children’s Cognitive Development : Environmental factors relate to changes in reported cognitive development among research subjects.
• Link Between Parental Involvement and Student Motivation : Parental involvement is related to differences in reported student motivation levels among research participants.
• Influence of Cultural Immersion on Language Proficiency : Cultural immersion correlates with variations in reported language proficiency levels among research subjects.
• Relationship Between Leadership Styles and Team Performance : Leadership styles are associated with changes in reported team performance outcomes among research participants.
• Impact of Financial Literacy Education on Savings Habits : Financial literacy education relates to differences in reported savings habits among research subjects.
• Connection Between Stress Levels and Physical Health : Stress levels are related to variations in reported physical health outcomes among research participants.
• Effects of Music Exposure on Concentration : Music exposure correlates with changes in reported concentration levels among research subjects.

Non-Directional Hypothesis Statement Examples for Research Methodology

These examples are specific to the methods used in conducting research. The eighth example states that randomization might relate to group equivalence, but it doesn’t specify whether randomization would lead to more equivalent or less equivalent groups.

• Relationship Between Sampling Techniques and Research Validity : Sampling techniques are related to variations in research validity outcomes in studies of research methodology.
• Impact of Data Collection Methods on Data Accuracy : Data collection methods correlate with differences in reported data accuracy in research methodology experiments.
• Connection Between Research Design and Study Reproducibility : Research design is associated with variations in reported study reproducibility in research methodology studies.
• Effects of Questionnaire Format on Response Consistency : Questionnaire format relates to changes in reported response consistency in research methodology research.
• Link Between Ethical Considerations and Research Credibility : Ethical considerations are related to differences in reported research credibility in studies of research methodology.
• Influence of Measurement Scales on Data Precision : Measurement scales correlate with variations in reported data precision in research methodology experiments.
• Relationship Between Experimental Controls and Internal Validity : Experimental controls are associated with changes in internal validity outcomes in research methodology studies.
• Impact of Randomization on Group Equivalence : Randomization relates to differences in reported group equivalence in research methodology research.
• Connection Between Qualitative Data Analysis Methods and Data Richness : Qualitative data analysis methods are related to variations in reported data richness in studies of research methodology.
• Effects of Hypothesis Formulation on Research Focus : Hypothesis formulation correlates with changes in reported research focus in research methodology experiments.

These non-directional hypothesis statement examples offer insights into the diverse array of relationships explored in psychology, research, and research methodology studies, fostering empirical discovery and contributing to the advancement of knowledge across various fields.

Difference between Directional & Non-Directional Hypothesis

Directional and non-directional hypotheses are distinct approaches used in formulating hypotheses for research studies. Understanding the differences between them is essential for researchers to choose the appropriate type of causal hypothesis based on their study’s goals and prior knowledge.

• Direction: Directional hypotheses predict a specific relationship direction, while non-directional hypotheses do not specify a direction.
• Specificity: Directional hypotheses are more specific, while non-directional hypotheses are more general.
• Flexibility: Non-directional hypotheses allow for open-ended exploration, while directional hypotheses focus on confirming or refuting specific expectations.

How to Write a Non-Directional Hypothesis Statement – Step by Step Guide

• Identify Variables: Clearly define the variables you’re investigating—usually, an independent variable (the one manipulated) and a dependent variable (the one measured).
• Indicate Relationship: State that a relationship exists between the variables without predicting a specific direction.
• Use General Language: Craft the statement in a way that encompasses various possible outcomes.
• Avoid Biased Language: Do not include words that suggest a stronger effect or specific outcome for either variable.
• Connect to Research: If applicable, link the hypothesis to existing research or theories that justify exploring the relationship.

Tips for Writing a Non-Directional Hypothesis

• Start with Inquiry: Frame your hypothesis as an answer to a research question.
• Embrace Openness: Non-directional hypotheses are ideal when no strong expectation exists.
• Be Succinct: Keep the hypothesis statement concise and clear.
• Stay Neutral: Avoid implying that one variable will have a stronger impact.
• Allow Exploration: Leave room for various potential outcomes without preconceived notions.
• Tailor to Context: Ensure the hypothesis aligns with your research context and goals.

Non-directional hypotheses are particularly useful in exploratory research, where researchers aim to discover relationships without imposing specific expectations. They allow for unbiased investigation and the potential to uncover unexpected patterns or connections.

Remember that whether you choose a directional or non-directional hypothesis, both play critical roles in shaping the research process, guiding study design, data collection, and analysis. The choice depends on the research’s nature, goals, and existing knowledge in the field.  You may also be interested in our  science hypothesis .

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Directional Hypothesis: Definition and 10 Examples

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Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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A directional hypothesis refers to a type of hypothesis used in statistical testing that predicts a particular direction of the expected relationship between two variables.

In simpler terms, a directional hypothesis is an educated, specific guess about the direction of an outcome—whether an increase, decrease, or a proclaimed difference in variable sets.

For example, in a study investigating the effects of sleep deprivation on cognitive performance, a directional hypothesis might state that as sleep deprivation (Independent Variable) increases, cognitive performance (Dependent Variable) decreases (Killgore, 2010). Such a hypothesis offers a clear, directional relationship whereby a specific increase or decrease is anticipated.

Global warming provides another notable example of a directional hypothesis. A researcher might hypothesize that as carbon dioxide (CO2) levels increase, global temperatures also increase (Thompson, 2010). In this instance, the hypothesis clearly articulates an upward trend for both variables. 

In any given circumstance, it’s imperative that a directional hypothesis is grounded on solid evidence. For instance, the CO2 and global temperature relationship is based on substantial scientific evidence, and not on a random guess or mere speculation (Florides & Christodoulides, 2009).

Directional vs Non-Directional vs Null Hypotheses

A directional hypothesis is generally contrasted to a non-directional hypothesis. Here’s how they compare:

• Directional hypothesis: A directional hypothesis provides a perspective of the expected relationship between variables, predicting the direction of that relationship (either positive, negative, or a specific difference). 
• Non-directional hypothesis: A non-directional hypothesis denotes the possibility of a relationship between two variables ( the independent and dependent variables ), although this hypothesis does not venture a prediction as to the direction of this relationship (Ali & Bhaskar, 2016). For example, a non-directional hypothesis might state that there exists a relationship between a person’s diet (independent variable) and their mood (dependent variable), without indicating whether improvement in diet enhances mood positively or negatively. Overall, the choice between a directional or non-directional hypothesis depends on the known or anticipated link between the variables under consideration in research studies.

Another very important type of hypothesis that we need to know about is a null hypothesis :

• Null hypothesis : The null hypothesis stands as a universality—the hypothesis that there is no observed effect in the population under study, meaning there is no association between variables (or that the differences are down to chance). For instance, a null hypothesis could be constructed around the idea that changing diet (independent variable) has no discernible effect on a person’s mood (dependent variable) (Yan & Su, 2016). This proposition is the one that we aim to disprove in an experiment.

While directional and non-directional hypotheses involve some integrated expectations about the outcomes (either distinct direction or a vague relationship), a null hypothesis operates on the premise of negating such relationships or effects.

The null hypotheses is typically proposed to be negated or disproved by statistical tests, paving way for the acceptance of an alternate hypothesis (either directional or non-directional).

Directional Hypothesis Examples

1. exercise and heart health.

Research suggests that as regular physical exercise (independent variable) increases, the risk of heart disease (dependent variable) decreases (Jakicic, Davis, Rogers, King, Marcus, Helsel, Rickman, Wahed, Belle, 2016). In this example, a directional hypothesis anticipates that the more individuals maintain routine workouts, the lesser would be their odds of developing heart-related disorders. This assumption is based on the underlying fact that routine exercise can help reduce harmful cholesterol levels, regulate blood pressure, and bring about overall health benefits. Thus, a direction – a decrease in heart disease – is expected in relation with an increase in exercise. 

2. Screen Time and Sleep Quality

Another classic instance of a directional hypothesis can be seen in the relationship between the independent variable, screen time (especially before bed), and the dependent variable, sleep quality. This hypothesis predicts that as screen time before bed increases, sleep quality decreases (Chang, Aeschbach, Duffy, Czeisler, 2015). The reasoning behind this hypothesis is the disruptive effect of artificial light (especially blue light from screens) on melatonin production, a hormone needed to regulate sleep. As individuals spend more time exposed to screens before bed, it is predictably hypothesized that their sleep quality worsens. 

3. Job Satisfaction and Employee Turnover

A typical scenario in organizational behavior research posits that as job satisfaction (independent variable) increases, the rate of employee turnover (dependent variable) decreases (Cheng, Jiang, & Riley, 2017). This directional hypothesis emphasizes that an increased level of job satisfaction would lead to a reduced rate of employees leaving the company. The theoretical basis for this hypothesis is that satisfied employees often tend to be more committed to the organization and are less likely to seek employment elsewhere, thus reducing turnover rates.

4. Healthy Eating and Body Weight

Healthy eating, as the independent variable, is commonly thought to influence body weight, the dependent variable, in a positive way. For example, the hypothesis might state that as consumption of healthy foods increases, an individual’s body weight decreases (Framson, Kristal, Schenk, Littman, Zeliadt, & Benitez, 2009). This projection is based on the premise that healthier foods, such as fruits and vegetables, are generally lower in calories than junk food, assisting in weight management.

5. Sun Exposure and Skin Health

The association between sun exposure (independent variable) and skin health (dependent variable) allows for a definitive hypothesis declaring that as sun exposure increases, the risk of skin damage or skin cancer increases (Whiteman, Whiteman, & Green, 2001). The premise aligns with the understanding that overexposure to the sun’s ultraviolet rays can deteriorate skin health, leading to conditions like sunburn or, in extreme cases, skin cancer.

6. Study Hours and Academic Performance

A regularly assessed relationship in academia suggests that as the number of study hours (independent variable) rises, so too does academic performance (dependent variable) (Nonis, Hudson, Logan, Ford, 2013). The hypothesis proposes a positive correlation , with an increase in study time expected to contribute to enhanced academic outcomes.

7. Screen Time and Eye Strain

It’s commonly hypothesized that as screen time (independent variable) increases, the likelihood of experiencing eye strain (dependent variable) also increases (Sheppard & Wolffsohn, 2018). This is based on the idea that prolonged engagement with digital screens—computers, tablets, or mobile phones—can cause discomfort or fatigue in the eyes, attributing to symptoms of eye strain.

8. Physical Activity and Stress Levels

In the sphere of mental health, it’s often proposed that as physical activity (independent variable) increases, levels of stress (dependent variable) decrease (Stonerock, Hoffman, Smith, Blumenthal, 2015). Regular exercise is known to stimulate the production of endorphins, the body’s natural mood elevators, helping to alleviate stress.

9. Water Consumption and Kidney Health

A common health-related hypothesis might predict that as water consumption (independent variable) increases, the risk of kidney stones (dependent variable) decreases (Curhan, Willett, Knight, & Stampfer, 2004). Here, an increase in water intake is inferred to reduce the risk of kidney stones by diluting the substances that lead to stone formation.

10. Traffic Noise and Sleep Quality

In urban planning research, it’s often supposed that as traffic noise (independent variable) increases, sleep quality (dependent variable) decreases (Muzet, 2007). Increased noise levels, particularly during the night, can result in sleep disruptions, thus, leading to poor sleep quality.

11. Sugar Consumption and Dental Health

In the field of dental health, an example might be stating as one’s sugar consumption (independent variable) increases, dental health (dependent variable) decreases (Sheiham, & James, 2014). This stems from the fact that sugar is a major factor in tooth decay, and increased consumption of sugary foods or drinks leads to a decline in dental health due to the high likelihood of cavities.

See 15 More Examples of Hypotheses Here

A directional hypothesis plays a critical role in research, paving the way for specific predicted outcomes based on the relationship between two variables. These hypotheses clearly illuminate the expected direction—the increase or decrease—of an effect. From predicting the impacts of healthy eating on body weight to forecasting the influence of screen time on sleep quality, directional hypotheses allow for targeted and strategic examination of phenomena. In essence, directional hypotheses provide the crucial path for inquiry, shaping the trajectory of research studies and ultimately aiding in the generation of insightful, relevant findings.

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Chang, A. M., Aeschbach, D., Duffy, J. F., & Czeisler, C. A. (2015). Evening use of light-emitting eReaders negatively affects sleep, circadian timing, and next-morning alertness. Proceeding of the National Academy of Sciences, 112 (4), 1232-1237. doi: https://doi.org/10.1073/pnas.1418490112  

Cheng, G. H. L., Jiang, D., & Riley, J. H. (2017). Organizational commitment and intrinsic motivation of regular and contractual primary school teachers in China. New Psychology, 19 (3), 316-326. Doi: https://doi.org/10.4103%2F2249-4863.184631  

Curhan, G. C., Willett, W. C., Knight, E. L., & Stampfer, M. J. (2004). Dietary factors and the risk of incident kidney stones in younger women: Nurses’ Health Study II. Archives of Internal Medicine, 164 (8), 885–891.

Florides, G. A., & Christodoulides, P. (2009). Global warming and carbon dioxide through sciences. Environment international , 35 (2), 390-401. doi: https://doi.org/10.1016/j.envint.2008.07.007

Framson, C., Kristal, A. R., Schenk, J. M., Littman, A. J., Zeliadt, S., & Benitez, D. (2009). Development and validation of the mindful eating questionnaire. Journal of the American Dietetic Association, 109 (8), 1439-1444. doi: https://doi.org/10.1016/j.jada.2009.05.006  

Jakicic, J. M., Davis, K. K., Rogers, R. J., King, W. C., Marcus, M. D., Helsel, D., … & Belle, S. H. (2016). Effect of wearable technology combined with a lifestyle intervention on long-term weight loss: The IDEA randomized clinical trial. JAMA, 316 (11), 1161-1171.

Khan, S., & Iqbal, N. (2013). Study of the relationship between study habits and academic achievement of students: A case of SPSS model. Higher Education Studies, 3 (1), 14-26.

Killgore, W. D. (2010). Effects of sleep deprivation on cognition. Progress in brain research , 185 , 105-129. doi: https://doi.org/10.1016/B978-0-444-53702-7.00007-5  

Marczinski, C. A., & Fillmore, M. T. (2014). Dissociative antagonistic effects of caffeine on alcohol-induced impairment of behavioral control. Experimental and Clinical Psychopharmacology, 22 (4), 298–311. doi: https://psycnet.apa.org/doi/10.1037/1064-1297.11.3.228  

Muzet, A. (2007). Environmental Noise, Sleep and Health. Sleep Medicine Reviews, 11 (2), 135-142. doi: https://doi.org/10.1016/j.smrv.2006.09.001  

Nonis, S. A., Hudson, G. I., Logan, L. B., & Ford, C. W. (2013). Influence of perceived control over time on college students’ stress and stress-related outcomes. Research in Higher Education, 54 (5), 536-552. doi: https://doi.org/10.1023/A:1018753706925  

Sheiham, A., & James, W. P. (2014). A new understanding of the relationship between sugars, dental caries and fluoride use: implications for limits on sugars consumption. Public health nutrition, 17 (10), 2176-2184. Doi: https://doi.org/10.1017/S136898001400113X  

Sheppard, A. L., & Wolffsohn, J. S. (2018). Digital eye strain: prevalence, measurement and amelioration. BMJ open ophthalmology , 3 (1), e000146. doi: http://dx.doi.org/10.1136/bmjophth-2018-000146

Stonerock, G. L., Hoffman, B. M., Smith, P. J., & Blumenthal, J. A. (2015). Exercise as Treatment for Anxiety: Systematic Review and Analysis. Annals of Behavioral Medicine, 49 (4), 542–556. doi: https://doi.org/10.1007/s12160-014-9685-9  

Thompson, L. G. (2010). Climate change: The evidence and our options. The Behavior Analyst , 33 , 153-170. Doi: https://doi.org/10.1007/BF03392211  

Whiteman, D. C., Whiteman, C. A., & Green, A. C. (2001). Childhood sun exposure as a risk factor for melanoma: a systematic review of epidemiologic studies. Cancer Causes & Control, 12 (1), 69-82. doi: https://doi.org/10.1023/A:1008980919928

Yan, X., & Su, X. (2009). Linear regression analysis: theory and computing . New Jersey: World Scientific.

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5.2 - writing hypotheses.

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

• At this point we can write hypotheses for a single mean (\(\mu\)), paired means(\(\mu_d\)), a single proportion (\(p\)), the difference between two independent means (\(\mu_1-\mu_2\)), the difference between two proportions (\(p_1-p_2\)), a simple linear regression slope (\(\beta\)), and a correlation (\(\rho\)). 
• The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
• The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., \(\mu_0\) and \(p_0\)). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., \(p\) and \(\mu\)).  The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

Directional and non-directional hypothesis: A Comprehensive Guide

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In the world of research and statistical analysis, hypotheses play a crucial role in formulating and testing scientific claims. Understanding the differences between directional and non-directional hypothesis is essential for designing sound experiments and drawing accurate conclusions. Whether you’re a student, researcher, or simply curious about the foundations of hypothesis testing, this guide will equip you with the knowledge and tools to navigate this fundamental aspect of scientific inquiry.

Understanding Directional Hypothesis

Understanding directional hypotheses is crucial for conducting hypothesis-driven research, as they guide the selection of appropriate statistical tests and aid in the interpretation of results. By incorporating directional hypotheses, researchers can make more precise predictions, contribute to scientific knowledge, and advance their fields of study.

Definition of directional hypothesis

Directional hypotheses, also known as one-tailed hypotheses, are statements in research that make specific predictions about the direction of a relationship or difference between variables. Unlike non-directional hypotheses, which simply state that there is a relationship or difference without specifying its direction, directional hypotheses provide a focused and precise expectation.

A directional hypothesis predicts either a positive or negative relationship between variables or predicts that one group will perform better than another. It asserts a specific direction of effect or outcome. For example, a directional hypothesis could state that “increased exposure to sunlight will lead to an improvement in mood” or “participants who receive the experimental treatment will exhibit higher levels of cognitive performance compared to the control group.”

Directional hypotheses are formulated based on existing theory, prior research, or logical reasoning, and they guide the researcher’s expectations and analysis. They allow for more targeted predictions and enable researchers to test specific hypotheses using appropriate statistical tests.

The role of directional hypothesis in research

Directional hypotheses also play a significant role in research surveys. Let’s explore their role specifically in the context of survey research:

• Objective-driven surveys : Directional hypotheses help align survey research with specific objectives. By formulating directional hypotheses, researchers can focus on gathering data that directly addresses the predicted relationship or difference between variables of interest.
• Question design and measurement : Directional hypotheses guide the design of survey question types and the selection of appropriate measurement scales. They ensure that the questions are tailored to capture the specific aspects related to the predicted direction, enabling researchers to obtain more targeted and relevant data from survey respondents.
• Data analysis and interpretation : Directional hypotheses assist in data analysis by directing researchers towards appropriate statistical tests and methods. Researchers can analyze the survey data to specifically test the predicted relationship or difference, enhancing the accuracy and reliability of their findings. The results can then be interpreted within the context of the directional hypothesis, providing more meaningful insights.
• Practical implications and decision-making : Directional hypotheses in surveys often have practical implications. When the predicted relationship or difference is confirmed, it informs decision-making processes, program development, or interventions. The survey findings based on directional hypotheses can guide organizations, policymakers, or practitioners in making informed choices to achieve desired outcomes.
• Replication and further research : Directional hypotheses in survey research contribute to the replication and extension of studies. Researchers can replicate the survey with different populations or contexts to assess the generalizability of the predicted relationships. Furthermore, if the directional hypothesis is supported, it encourages further research to explore underlying mechanisms or boundary conditions.

By incorporating directional hypotheses in survey research, researchers can align their objectives, design effective surveys, conduct focused data analysis, and derive practical insights. They provide a framework for organizing survey research and contribute to the accumulation of knowledge in the field.

Examples of research questions for directional hypothesis

Here are some examples of research questions that lend themselves to directional hypotheses:

• Does increased daily exercise lead to a decrease in body weight among sedentary adults?
• Is there a positive relationship between study hours and academic performance among college students?
• Does exposure to violent video games result in an increase in aggressive behavior among adolescents?
• Does the implementation of a mindfulness-based intervention lead to a reduction in stress levels among working professionals?
• Is there a difference in customer satisfaction between Product A and Product B, with Product A expected to have higher satisfaction ratings?
• Does the use of social media influence self-esteem levels, with higher social media usage associated with lower self-esteem?
• Is there a negative relationship between job satisfaction and employee turnover, indicating that lower job satisfaction leads to higher turnover rates?
• Does the administration of a specific medication result in a decrease in symptoms among individuals with a particular medical condition?
• Does increased access to early childhood education lead to improved cognitive development in preschool-aged children?
• Is there a difference in purchase intention between advertisements with celebrity endorsements and advertisements without, with celebrity endorsements expected to have a higher impact?

These research questions generate specific predictions about the direction of the relationship or difference between variables and can be tested using appropriate research methods and statistical analyses.

Definition of non-directional hypothesis

Non-directional hypotheses, also known as two-tailed hypotheses, are statements in research that indicate the presence of a relationship or difference between variables without specifying the direction of the effect. Instead of making predictions about the specific direction of the relationship or difference, non-directional hypotheses simply state that there is an association or distinction between the variables of interest.

Non-directional hypotheses are often used when there is no prior theoretical basis or clear expectation about the direction of the relationship. They leave the possibility open for either a positive or negative relationship, or for both groups to differ in some way without specifying which group will perform better or worse.

Advantages and utility of non-directional hypothesis

Non-directional hypotheses in survey s offer several advantages and utilities, providing flexibility and comprehensive analysis of survey data. Here are some of the key advantages and utilities of using non-directional hypotheses in surveys:

• Exploration of Relationships : Non-directional hypotheses allow researchers to explore and examine relationships between variables without assuming a specific direction. This is particularly useful in surveys where the relationship between variables may not be well-known or there may be conflicting evidence regarding the direction of the effect.
• Flexibility in Question Design : With non-directional hypotheses, survey questions can be designed to measure the relationship between variables without being biased towards a particular outcome. This flexibility allows researchers to collect data and analyze the results more objectively.
• Open to Unexpected Findings : Non-directional hypotheses enable researchers to be open to unexpected or surprising findings in survey data. By not committing to a specific direction of the effect, researchers can identify and explore relationships that may not have been initially anticipated, leading to new insights and discoveries.
• Comprehensive Analysis : Non-directional hypotheses promote comprehensive analysis of survey data by considering the possibility of an effect in either direction. Researchers can assess the magnitude and significance of relationships without limiting their analysis to only one possible outcome.
• S tatistical Validity : Non-directional hypotheses in surveys allow for the use of two-tailed statistical tests, which provide a more conservative and robust assessment of significance. Two-tailed tests consider both positive and negative deviations from the null hypothesis, ensuring accurate and reliable statistical analysis of survey data.
• Exploratory Research : Non-directional hypotheses are particularly useful in exploratory research, where the goal is to gather initial insights and generate hypotheses. Surveys with non-directional hypotheses can help researchers explore various relationships and identify patterns that can guide further research or hypothesis development.

It is worth noting that the choice between directional and non-directional hypotheses in surveys depends on the research objectives, existing knowledge, and the specific variables being investigated. Researchers should carefully consider the advantages and limitations of each approach and select the one that aligns best with their research goals and survey design.

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Understanding the fundamentals of a non-directional hypothesis

A crucial aspect of conducting research is formulating a hypothesis. In simple terms, a hypothesis is a statement that makes a prediction about the relationship between two or more variables. It serves as a guide for researchers to test their theories and draw conclusions. A non-directional hypothesis, also known as a two-tailed hypothesis, is a type of hypothesis that does not specify the direction of the predicted relationship between variables. This means that the researcher is not making a specific prediction and is open to the possibility of any outcome. In this article, we will delve into the fundamentals of a non-directional hypothesis and its significance in research studies.

The difference between directional and non-directional hypotheses

When conducting research, it is important to have a clear understanding of the different types of hypotheses. One key distinction to make is between directional and non-directional hypotheses.

A directional hypothesis, also known as a one-tailed hypothesis, predicts the direction of the relationship between variables. This means that the researcher has a specific prediction in mind. For example, a directional hypothesis might state that "increased exercise leads to improved cardiovascular health." In this case, the researcher is specifically predicting that increased exercise will have a positive effect on cardiovascular health.

On the other hand, a non-directional hypothesis, also known as a two-tailed hypothesis, does not specify the direction of the relationship between variables. This means that the researcher does not have a specific prediction in mind and is open to the possibility of any outcome. For example, a non-directional hypothesis might state that "there is a relationship between exercise and cardiovascular health." In this case, the researcher is simply predicting that there is some sort of relationship between the two variables, but is not specifying whether it is positive or negative.

The main difference between these two types of hypotheses lies in the level of specificity. A directional hypothesis provides a specific prediction about the relationship between variables, while a non-directional hypothesis leaves the prediction open-ended.

So why would a researcher choose to use a non-directional hypothesis? One reason is that it allows for more flexibility and open-mindedness in the research process. By not specifying a particular direction, the researcher is not constrained by preconceived notions or biases. This can lead to more objective and unbiased findings.

Another reason to use a non-directional hypothesis is when there is a lack of previous research or evidence to support a specific direction. If there is limited knowledge or conflicting results on the topic, it may be more appropriate to use a non-directional hypothesis to explore the relationship between variables without making any specific predictions.

In summary, the difference between directional and non-directional hypotheses lies in the level of specificity and prediction. While directional hypotheses specify the direction of the relationship, non-directional hypotheses leave the prediction open-ended. Non-directional hypotheses provide researchers with more flexibility and open-mindedness in the research process and can be especially useful in situations with limited previous research or conflicting evidence.

Why use a non-directional hypothesis

There are several reasons why researchers might choose to use a non-directional hypothesis in their studies. Firstly, it allows for more flexibility and open-mindedness in the research process. By not specifying a particular direction, researchers are not constrained by preconceived notions or biases. This can lead to more objective and unbiased findings, as the researcher is not influenced by their own expectations.

Another reason to use a non-directional hypothesis is when there is a lack of previous research or evidence to support a specific direction. Sometimes, researchers are exploring a new topic or are working in an area where there is limited knowledge or conflicting results. In these cases, it may be more appropriate to use a non-directional hypothesis to explore the relationship between variables without making any specific predictions. This allows for a more exploratory approach, where researchers can gather data and draw conclusions based on the evidence they find.

Additionally, using a non-directional hypothesis can help researchers avoid the problem of hindsight bias. Hindsight bias occurs when researchers interpret their results in a way that aligns with their initial expectations. By using a non-directional hypothesis, researchers are less likely to fall into this trap and can make more accurate interpretations of their data.

Overall, using a non-directional hypothesis can be beneficial in certain research scenarios. It allows for flexibility, open-mindedness, and exploration. It also helps researchers avoid bias and hindsight bias, leading to more objective and reliable findings. By using a non-directional hypothesis, researchers can approach their studies with a fresh perspective and make new discoveries in their field.

How to form a non-directional hypothesis

Forming a non-directional hypothesis is an essential step in conducting research. Unlike a directional hypothesis, which predicts the specific direction of the relationship between variables, a non-directional hypothesis leaves the prediction open-ended. This allows for more flexibility and exploration in the research process. Here are some key steps to consider when forming a non-directional hypothesis:

Identify the variables

Start by identifying the variables that you want to study. These variables should be measurable and have a logical connection to each other. For example, if you are interested in studying the relationship between exercise and cardiovascular health, your variables would be exercise and cardiovascular health.

Determine the type of relationship

Consider what type of relationship you want to explore between the variables. Are you looking for a relationship that is positive, negative, or simply any relationship? This will help guide the formation of your hypothesis. For example, if you want to explore any relationship between exercise and cardiovascular health, your hypothesis might be that there is a relationship between the two variables.

Keep it general

When writing your hypothesis, avoid specifying a particular direction of the relationship. Instead, keep it general and open-ended. This allows for more flexibility in the research process. For example, a non-directional hypothesis could state that "there is a relationship between exercise and cardiovascular health," without specifying whether it is positive or negative.

Be specific and testable

Although a non-directional hypothesis does not specify the direction of the relationship, it should still be specific and testable. This means that it should be clear enough to guide your research and allow you to gather data to support or reject the hypothesis. Make sure that your variables are clearly defined and that you have a clear plan for how you will measure them.

Consider alternative explanations

When forming a non-directional hypothesis, it is important to consider alternative explanations for the relationship between variables. This will help ensure that your hypothesis is comprehensive and takes into account different possibilities. For example, if you are studying the relationship between exercise and cardiovascular health, consider other factors that may influence cardiovascular health, such as diet or genetics.

By following these steps, you can effectively form a non-directional hypothesis for your research. This will allow you to explore the relationship between variables without being constrained by preconceived notions or biases. Remember to keep your hypothesis general, specific, and testable, and consider alternative explanations for the relationship.

Examples of non-directional hypotheses in research

When it comes to research, formulating a non-directional hypothesis can be particularly useful in certain scenarios. Let's explore some examples of non-directional hypotheses to understand how they can be applied in research studies.

"There is a relationship between sleep duration and academic performance."

This hypothesis suggests that there is some form of relationship between the amount of sleep an individual gets and their academic performance. However, it does not specify whether this relationship is positive or negative. By using a non-directional hypothesis, researchers can explore the potential impact of sleep duration on academic performance without making a specific prediction.

"There is a relationship between stress levels and job satisfaction." In this case, the hypothesis proposes that there is some form of relationship between stress levels and job satisfaction. However, it does not specify whether increased stress levels lead to decreased job satisfaction or vice versa. By using a non-directional hypothesis, researchers can examine the relationship between these variables without assuming a particular direction.

"There is a relationship between age and technology usage." This hypothesis suggests that there is some form of relationship between age and technology usage. However, it does not specify whether younger individuals are more likely to use technology or whether older individuals are more likely to use technology. By using a non-directional hypothesis, researchers can explore the potential relationship between age and technology usage without assuming a specific pattern.

These examples illustrate how non-directional hypotheses allow researchers to investigate relationships between variables without being tied to a specific prediction. This flexibility enables researchers to approach their studies with an open mind and gather objective data to draw conclusions.

By using non-directional hypotheses, researchers can explore uncharted territory, address conflicting evidence, and provide valuable insights into various fields of study. This approach promotes a more exploratory and unbiased research process, leading to more accurate and reliable findings. So, if you find yourself in a research scenario where a specific direction is unclear or the evidence is limited, consider using a non-directional hypothesis to guide your exploration.

Advantages and disadvantages of non-directional hypotheses

Non-directional hypotheses have several advantages and disadvantages that researchers should consider when conducting their studies. 

One of the main advantages of using a non-directional hypothesis is the flexibility it provides in the research process. By not specifying a particular direction, researchers are not limited by preconceived notions or biases.

This allows for more open-mindedness and exploration, which can lead to new insights and discoveries. It also allows researchers to consider alternative explanations and factors that may influence the relationship between variables.

Another advantage of non-directional hypotheses is that they help researchers avoid the problem of hindsight bias. Hindsight bias occurs when researchers interpret their results in a way that aligns with their initial expectations. By using a non-directional hypothesis, researchers are less likely to fall into this trap and can make more accurate interpretations of their data. This enhances the reliability and objectivity of their findings.

Non-directional hypotheses are also useful in situations where there is limited previous research or conflicting evidence. They allow researchers to explore the relationship between variables without making any specific predictions, which can be especially valuable in new or unexplored areas of study. This approach promotes a more exploratory and unbiased research process, enabling researchers to gather data and draw conclusions based on the evidence they find.

Disadvantages

However, there are also some disadvantages to using non-directional hypotheses. One disadvantage is that they may lack specificity. Without specifying the direction of the relationship, researchers may struggle to draw clear conclusions or make specific recommendations based on their findings. This can make it challenging to apply the research to practical situations or inform decision-making processes.

Another potential disadvantage is that non-directional hypotheses can be more difficult to test statistically. Without specifying the direction of the relationship, it may be harder to determine the significance of the findings or establish causal relationships between variables. This can make it more challenging to draw meaningful and robust conclusions from the research.

In summary, non-directional hypotheses offer flexibility, open-mindedness, and exploration in the research process. They help researchers avoid biases, and hindsight bias, and provide valuable insights in situations with limited previous research or conflicting evidence. However, they may lack specificity and can be more challenging to test statistically. Researchers should carefully consider these advantages and disadvantages when deciding whether to use a non-directional hypothesis in their studies.

Aims And Hypotheses, Directional And Non-Directional

March 7, 2021 - paper 2 psychology in context | research methods.

In Psychology, hypotheses are predictions made by the researcher about the outcome of a study. The research can chose to make a specific prediction about what they feel will happen in their research (a directional hypothesis) or they can make a ‘general,’ ‘less specific’ prediction about the outcome of their research (a non-directional hypothesis). The type of prediction that a researcher makes is usually dependent on whether or not any previous research has also investigated their research aim.

Variables Recap:

The  independent variable  (IV)  is the variable that psychologists  manipulate/change  to see if changing this variable has an effect on the  depen dent variable  (DV).

The  dependent variable (DV)  is the variable that the psychologists  measures  (to see if the IV has had an effect).

Research/Experimental Aim(S):

An aim is a clear and precise statement of the purpose of the study. It is a statement of why a research study is taking place. This should include what is being studied and what the study is trying to achieve. (e.g. “This study aims to investigate the effects of alcohol on reaction times”.

Hypotheses:

This is a testable statement that predicts what the researcher expects to happen in their research. The research study itself is therefore a means of testing whether or not the hypothesis is supported by the findings. If the findings do support the hypothesis then the hypothesis can be retained (i.e., accepted), but if not, then it must be rejected.

(1)  Directional Hypothesis:  states that the IV will have an effect on the DV and what that effect will be (the direction of results). For example, eating smarties will significantly  improve  an individual’s dancing ability. When writing a directional hypothesis, it is important that you state exactly  how  the IV will influence the DV.

(3)  A Null Hypothesis:  states that the IV will have no significant effect on the DV, for example, ‘eating smarties will have no effect in an individuals dancing ability.’

Directional vs Non-Directional Hypothesis: Key Difference

In statistics, a directional hypothesis, also known as a one-tailed hypothesis, is a type of hypothesis that predicts the direction of the relationship between variables or the direction of the difference between groups.

The introduction of a directional hypothesis in a research study provides an overview of the specific prediction being made about the relationship between variables or the difference between groups. It sets the stage for the research question and outlines the expected direction of the findings. The introduction typically includes the following elements:

Research Context: Begin by introducing the general topic or research area that the study is focused on. Provide background information and highlight the significance of the research question.

Research Question: Clearly state the specific research question that the study aims to answer. This question should be directly related to the variables being investigated.

Previous Research: Summarize relevant literature or previous studies that have explored similar or related topics. This helps establish the existing knowledge base and provides a rationale for the hypothesis.

Hypothesis Statement: Present the directional hypothesis clearly and concisely. State the predicted relationship between variables or the expected difference between groups. For example, if studying the impact of a new teaching method on student performance, a directional hypothesis could be, “Students who receive the new teaching method will demonstrate higher test scores compared to students who receive the traditional teaching method.”

Justification: Provide a logical explanation for the directional hypothesis based on the existing literature or theoretical framework . Discuss any previous findings, theories, or empirical evidence that support the predicted direction of the relationship or difference.

Objectives: Outline the specific objectives or aims of the study, which should align with the research question and hypothesis. These objectives help guide the research process and provide a clear focus for the study.

By including these elements in the introduction of a research study, the directional hypothesis is introduced effectively, providing a clear and justified prediction about the expected outcome of the research.

When formulating a directional hypothesis, researchers make a specific prediction about the expected relationship or difference between variables. They specify whether they expect an increase or decrease in the dependent variable, or whether one group will score higher or lower than another group

What is Directional Hypothesis?

With a correlational study, a directional hypothesis states that there is a positive (or negative) correlation between two variables. When a hypothesis states the direction of the results, it is referred to as a directional (one-tailed) hypothesis; this is because it states that the results go in one direction.

Definition:

A directional hypothesis is a one-tailed hypothesis that states the direction of the difference or relationship (e.g. boys are more helpful than girls).

Research Question: Does exercise have a positive impact on mood?

Directional Hypothesis: Engaging in regular exercise will result in an increase in positive mood compared to a sedentary lifestyle.

In this example, the directional hypothesis predicts that regular exercise will have a specific effect on mood, specifically leading to an increase in positive mood. The researcher expects that individuals who engage in regular exercise will experience improvements in their overall mood compared to individuals who lead a sedentary lifestyle.

It’s important to note that this is just one example, and directional hypotheses can be formulated in various research areas and contexts. The key is to make a specific prediction about the direction of the relationship or difference between variables based on prior knowledge or theoretical considerations.

Advantages of Directional Hypothesis

There are several advantages to using a directional hypothesis in research studies. Here are a few key benefits:

Specific Prediction:

A directional hypothesis allows researchers to make a specific prediction about the expected relationship or difference between variables. This provides a clear focus for the study and helps guide the research process. It also allows for more precise interpretation of the results.

Testable and Refutable:

Directional hypotheses can be tested and either supported or refuted by empirical evidence. Researchers can design their study and select appropriate statistical tests to specifically examine the predicted direction of the relationship or difference. This enhances the rigor and validity of the research.

Efficiency and Resource Allocation:

By making a specific prediction, researchers can allocate their resources more efficiently. They can focus on collecting data and conducting analyses that directly test the directional hypothesis, rather than exploring all possible directions or relationships. This can save time, effort, and resources.

Theory Development:

Directional hypotheses contribute to the development of theories and scientific knowledge. When a directional hypothesis is supported by empirical evidence, it provides support for existing theories or helps generate new theories. This advancement in knowledge can guide future research and understanding in the field.

Practical Applications:

Directional hypotheses can have practical implications and applications. If a hypothesis predicts a specific direction of change, such as the effectiveness of a treatment or intervention, it can inform decision-making and guide practical applications in fields such as medicine, psychology, or education.

Enhanced Communication:

Directional hypotheses facilitate clearer communication of research findings. When researchers have made specific predictions about the direction of the relationship or difference, they can effectively communicate their results to both academic and non-academic audiences. This promotes better understanding and application of the research outcomes.

It’s important to note that while directional hypotheses offer advantages, they also require stronger evidence to support them compared to non-directional hypotheses. Researchers should carefully consider the research context, existing literature, and theoretical considerations before formulating a directional hypothesis.

Disadvantages of Directional Hypothesis

While directional hypotheses have their advantages, there are also some potential disadvantages to consider:

Risk of Type I Error:

Directional hypotheses increase the risk of committing a Type I error , also known as a false positive. By focusing on a specific predicted direction, researchers may overlook the possibility of an opposite or null effect. If the actual relationship or difference does not align with the predicted direction, researchers may incorrectly conclude that there is no effect when, in fact, there may be.

Narrow Focus:

Directional hypotheses restrict the scope of investigation to a specific predicted direction. This narrow focus may overlook other potential relationships, nuances, or alternative explanations. Researchers may miss valuable insights or unexpected findings by excluding other possibilities from consideration.

Limited Generalizability:

Directional hypotheses may limit the generalizability of findings. If the study supports the predicted direction, the results may only apply to the specific context and conditions outlined in the hypothesis. Generalizing the findings to different populations, settings, or variables may require further research.

Biased Interpretation:

Directional hypotheses can introduce bias in the interpretation of results. Researchers may be inclined to selectively focus on evidence that supports the predicted direction while downplaying or ignoring contradictory evidence. This can hinder objectivity and lead to biased conclusions.

Increased Sample Size Requirements:

Directional hypotheses often require larger sample sizes compared to non-directional hypotheses. This is because statistical power needs to be sufficient to detect the predicted direction with a reasonable level of confidence. Larger samples can be more time-consuming and resource-intensive to obtain.

Reduced Flexibility:

Directional hypotheses limit flexibility in data analysis and statistical testing. Researchers may feel compelled to use specific statistical tests or analytical approaches that align with the predicted direction, potentially overlooking alternative methods that may be more appropriate or informative.

It’s important to weigh these disadvantages against the specific research context and objectives when deciding whether to use a directional hypothesis. In some cases, a non-directional hypothesis may be more suitable, allowing for a more exploratory and comprehensive investigation of the research question.

Non-Directional Hypothesis:

A non-directional hypothesis, also known as a two-tailed hypothesis, is a type of hypothesis that does not specify the direction of the relationship between variables or the difference between groups. Instead of predicting a specific direction, a non-directional hypothesis suggests that there will be a significant relationship or difference, without indicating whether it will be positive or negative, higher or lower, etc.

The introduction of a non-directional hypothesis in a research study provides an overview of the general prediction being made about the relationship between variables or the difference between groups, without specifying the direction. It sets the stage for the research question and outlines the expectation of a significant relationship or difference. The introduction typically includes the following elements:

Research Context:

Begin by introducing the general topic or research area that the study is focused on. Provide background information and highlight the significance of the research question.

Research Question:

Clearly state the specific research question that the study aims to answer. This question should be directly related to the variables being investigated.

Previous Research:

Summarize relevant literature or previous studies that have explored similar or related topics. This helps establish the existing knowledge base and provides a rationale for the hypothesis.

Hypothesis Statement:

Present the non-directional hypothesis clearly and concisely. State that there is an expected relationship or difference between variables or groups without specifying the direction. For example, if studying the relationship between socioeconomic status and academic achievement, a non-directional hypothesis could be, “There is a significant relationship between socioeconomic status and academic achievement.”

Justification:

Provide a logical explanation for the non-directional hypothesis based on the existing literature or theoretical framework. Discuss any previous findings, theories, or empirical evidence that support the notion of a relationship or difference between the variables or groups.

Objectives:

Outline the specific objectives or aims of the study, which should align with the research question and hypothesis. These objectives help guide the research process and provide a clear focus for the study.

By including these elements in the introduction of a research study, the non-directional hypothesis is introduced effectively, indicating the expectation of a significant relationship or difference without specifying the direction

What is Non-directional hypothesis?

In a non-directional hypothesis, researchers acknowledge that there may be an effect or relationship between variables but do not make a specific prediction about the direction of that effect. This allows for a more exploratory approach to data analysis and interpretation

If a hypothesis does not state a direction but simply says that one factor affects another, or that there is an association or correlation between two variables then it is called a non-directional (two-tailed) hypothesis.

Research Question: Is there a relationship between social media usage and self-esteem ?

Non-Directional Hypothesis: There is a significant relationship between social media usage and self-esteem.

In this example, the non-directional hypothesis suggests that there is a relationship between social media usage and self-esteem without specifying whether higher social media usage is associated with higher or lower self-esteem. The hypothesis acknowledges the possibility of an effect but does not make a specific prediction about the direction of that effect.

It’s important to note that this is just one example, and non-directional hypotheses can be formulated in various research areas and contexts. The key is to indicate the expectation of a significant relationship or difference without specifying the direction, allowing for a more exploratory approach to data analysis and interpretation.

Advantages of Non-directional hypothesis

Non-directional hypotheses, also known as two-tailed hypotheses, offer several advantages in research studies. Here are some of the key advantages:

Flexibility in Data Analysis:

Non-directional hypotheses allow for flexibility in data analysis. Researchers are not constrained by a specific predicted direction and can explore the relationship or difference in various ways. This flexibility enables a more comprehensive examination of the data, considering both positive and negative associations or differences.

Objective and Open-Minded Approach:

Non-directional hypotheses promote an objective and open-minded approach to research. Researchers do not have preconceived notions about the direction of the relationship or difference, which helps mitigate biases in data interpretation. They can objectively analyze the data without being influenced by their initial expectations.

Comprehensive Understanding:

By not specifying the direction, non-directional hypotheses facilitate a comprehensive understanding of the relationship or difference being investigated. Researchers can explore and consider all possible outcomes, leading to a more nuanced interpretation of the findings. This broader perspective can provide deeper insights into the research question.

Greater Sensitivity:

Non-directional hypotheses can be more sensitive to detecting unexpected or surprising relationships or differences. Researchers are not solely focused on confirming a specific predicted direction, but rather on uncovering any significant association or difference. This increased sensitivity allows for the identification of novel patterns and relationships that may have been overlooked with a directional hypothesis.

Replication and Generalizability:

Non-directional hypotheses support replication studies and enhance the generalizability of findings. By not restricting the investigation to a specific predicted direction, the results can be more applicable to different populations, contexts, or conditions. This broader applicability strengthens the validity and reliability of the research.

Hypothesis Generation:

Non-directional hypotheses can serve as a foundation for generating new hypotheses and research questions. Significant findings without a specific predicted direction can lead to further investigations and the formulation of more focused directional hypotheses in subsequent studies.

It’s important to consider the specific research context and objectives when deciding between a directional or non-directional hypothesis. Non-directional hypotheses are particularly useful when researchers are exploring new areas or when there is limited existing knowledge about the relationship or difference being studied.

Disadvantages of Non-directional hypothesis

Non-directional hypotheses have their advantages, there are also some potential disadvantages to consider:

Lack of Specificity: Non-directional hypotheses do not provide a specific prediction about the direction of the relationship or difference between variables. This lack of specificity may limit the interpretability and practical implications of the findings. Stakeholders may desire clear guidance on the expected direction of the effect.

Non-directional hypotheses often require larger sample sizes compared to directional hypotheses. This is because statistical power needs to be sufficient to detect any significant relationship or difference, regardless of the direction. Obtaining larger samples can be more time-consuming, resource-intensive, and costly.

Reduced Precision:

By not specifying the direction, non-directional hypotheses may result in less precise findings. Researchers may obtain statistically significant results indicating a relationship or difference, but the lack of direction may hinder their ability to understand the practical implications or mechanism behind the effect.

Potential for Post-hoc Interpretation:

Non-directional hypotheses can increase the risk of post-hoc interpretation of results. Researchers may be tempted to selectively interpret and highlight only the significant findings that support their preconceived notions or expectations, leading to biased interpretations.

Limited Theoretical Guidance:

Non-directional hypotheses may lack theoretical guidance in terms of understanding the underlying mechanisms or causal pathways. Without a specific predicted direction, it can be challenging to develop a comprehensive theoretical framework to explain the relationship or difference being studied.

Potential Missed Opportunities:

Non-directional hypotheses may limit the exploration of specific directions or subgroups within the data. By not focusing on a specific direction, researchers may miss important nuances or interactions that could contribute to a deeper understanding of the phenomenon under investigation.

It’s important to carefully consider the research question, available literature, and research objectives when deciding whether to use a non-directional hypothesis. Depending on the context and goals of the study, a non-directional hypothesis may be appropriate, but researchers should also be aware of the potential limitations and address them accordingly in their research design and interpretation of results.

Difference between directional and non-directional hypothesis

the main difference between a directional hypothesis and a non-directional hypothesis lies in the specificity of the prediction made about the relationship between variables or the difference between groups.

Directional Hypothesis:

A directional hypothesis, also known as a one-tailed hypothesis, makes a specific prediction about the direction of the relationship or difference. It states the expected outcome, whether it is a positive or negative relationship, a higher or lower value, an increase or decrease, etc. The directional hypothesis guides the research in a focused manner, specifying the direction to be tested.

Example: “Students who receive tutoring will demonstrate higher test scores compared to students who do not receive tutoring.”

A non-directional hypothesis, also known as a two-tailed hypothesis, does not specify the direction of the relationship or difference. It acknowledges the possibility of a relationship or difference between variables without predicting a specific direction. The non-directional hypothesis allows for exploration and analysis of both positive and negative associations or differences.

Example: “There is a significant relationship between sleep quality and academic performance.”

In summary, a directional hypothesis makes a specific prediction about the direction of the relationship or difference, while a non-directional hypothesis suggests a relationship or difference without specifying the direction. The choice between the two depends on the research question, existing literature, and the researcher’s objectives. Directional hypotheses provide a focused prediction, while non-directional hypotheses allow for more exploratory analysis .

When to use Directional Hypothesis?

A directional hypothesis is appropriate to use in specific situations where researchers have a clear theoretical or empirical basis for predicting the direction of the relationship or difference between variables. Here are some scenarios where a directional hypothesis is commonly employed:

Prior Research and Theoretical Framework: When previous studies, existing theories, or established empirical evidence strongly suggest a specific direction of the relationship or difference, a directional hypothesis can be formulated. Researchers can build upon the existing knowledge base and make a focused prediction based on this prior information.

Cause-and-Effect Relationships: In studies aiming to establish cause-and-effect relationships, directional hypotheses are often used. When there is a clear theoretical understanding of the causal relationship between variables, researchers can predict the expected direction of the effect based on the proposed mechanism.

Specific Research Objectives: If the research study has specific objectives that require a clear prediction about the direction, a directional hypothesis can be appropriate. For instance, if the aim is to test the effectiveness of a particular intervention or treatment, a directional hypothesis can guide the evaluation by predicting the expected positive or negative outcome.

Practical Applications: Directional hypotheses are useful when the research findings have direct practical implications. For example, in fields such as medicine, psychology, or education, researchers may formulate directional hypotheses to predict the effects of certain interventions or treatments on patient outcomes or educational achievement.

Hypothesis-Testing Approach: Researchers who adopt a hypothesis-testing approach, where they aim to confirm or disconfirm specific predictions, often use directional hypotheses. This approach involves formulating a specific hypothesis and conducting statistical tests to determine whether the data support or refute the predicted direction of the relationship or difference.

When to use non directional hypothesis?

A non-directional hypothesis, also known as a two-tailed hypothesis, is appropriate to use in several situations where researchers do not have a specific prediction about the direction of the relationship or difference between variables. Here are some scenarios where a non-directional hypothesis is commonly employed:

Exploratory Research:

When the research aims to explore a new area or investigate a relationship that has limited prior research or theoretical guidance, a non-directional hypothesis is often used. It allows researchers to gather initial data and insights without being constrained by a specific predicted direction.

Preliminary Studies:

Non-directional hypotheses are useful in preliminary or pilot studies that seek to gather preliminary evidence and generate hypotheses for further investigation. By using a non-directional hypothesis, researchers can gather initial data to inform the development of more specific hypotheses in subsequent studies.

Neutral Expectations:

If researchers have no theoretical or empirical basis to predict the direction of the relationship or difference, a non-directional hypothesis is appropriate. This may occur in situations where there is a lack of prior research, conflicting findings, or inconclusive evidence to support a specific direction.

Comparative Studies:

In studies where the objective is to compare two or more groups or conditions, a non-directional hypothesis is commonly used. The focus is on determining whether a significant difference exists, without making specific predictions about which group or condition will have higher or lower values.

Data-Driven Approach:

When researchers adopt a data-driven or exploratory approach to analysis, non-directional hypotheses are preferred. Instead of testing specific predictions, the aim is to explore the data, identify patterns, and generate hypotheses based on the observed relationships or differences.

Hypothesis-Generating Studies:

Non-directional hypotheses are often used in studies aimed at generating new hypotheses and research questions. By exploring associations or differences without specifying the direction, researchers can identify potential relationships or factors that can serve as a basis for future research.

Strategies to improve directional and non-directional hypothesis

To improve the quality of both directional and non-directional hypotheses, researchers can employ various strategies. Here are some strategies to enhance the formulation of hypotheses:

Strategies to Improve Directional Hypotheses:

Review existing literature:.

Conduct a thorough review of relevant literature to identify previous research findings, theories, and empirical evidence related to the variables of interest. This will help inform and support the formulation of a specific directional hypothesis based on existing knowledge.

Develop a Theoretical Framework:

Build a theoretical framework that outlines the expected causal relationship between variables. The theoretical framework should provide a clear rationale for predicting the direction of the relationship based on established theories or concepts.

Conduct Pilot Studies:

Conducting pilot studies or preliminary research can provide valuable insights and data to inform the formulation of a directional hypothesis. Initial findings can help researchers identify patterns or relationships that support a specific predicted direction.

Seek Expert Input:

Seek input from experts or colleagues in the field who have expertise in the area of study. Discuss the research question and hypothesis with them to obtain valuable insights, perspectives, and feedback that can help refine and improve the directional hypothesis.

Clearly Define Variables:

Clearly define and operationalize the variables in the hypothesis to ensure precision and clarity. This will help avoid ambiguity and ensure that the hypothesis is testable and measurable.

Strategies to Improve Non-Directional Hypotheses:

Preliminary exploration:.

Conduct initial exploratory research to gather preliminary data and insights on the relationship or difference between variables. This can provide a foundation for formulating a non-directional hypothesis based on observed patterns or trends.

Analyze Existing Data:

Analyze existing datasets to identify potential relationships or differences. Exploratory data analysis techniques such as data visualization, descriptive statistics, and correlation analysis can help uncover initial insights that can guide the formulation of a non-directional hypothesis.

Use Exploratory Research Designs:

Employ exploratory research designs such as qualitative studies, case studies, or grounded theory approaches. These designs allow researchers to gather rich data and explore relationships or differences without preconceived notions about the direction.

Consider Alternative Explanations:

When formulating a non-directional hypothesis, consider alternative explanations or potential factors that may influence the relationship or difference between variables. This can help ensure a comprehensive and nuanced understanding of the phenomenon under investigation.

Refine Based on Initial Findings:

Refine the non-directional hypothesis based on initial findings and observations from exploratory analyses. These findings can guide the formulation of more specific hypotheses in subsequent studies or inform the direction of further research.

In conclusion, both directional and non-directional hypotheses have their merits and are valuable in different research contexts.

 Here’s a summary of the key points regarding directional and non-directional hypotheses:

• A directional hypothesis makes a specific prediction about the direction of the relationship or difference between variables.
• It is appropriate when there is a clear theoretical or empirical basis for predicting the direction.
• Directional hypotheses provide a focused approach, guiding the research towards confirming or refuting a specific predicted direction.
• They are useful in studies where cause-and-effect relationships are being examined or when specific practical implications are desired.
• Directional hypotheses require careful consideration of prior research, theoretical frameworks, and available evidence.
• A non-directional hypothesis does not specify the direction of the relationship or difference between variables.
• It is employed when there is limited prior knowledge, conflicting findings, or a desire for exploratory analysis.
• Non-directional hypotheses allow for flexibility and open-mindedness in exploring the data, considering both positive and negative associations or differences.
• They are suitable for preliminary studies, exploratory research, or when the research question does not have a clear predicted direction.
• Non-directional hypotheses are beneficial for generating new hypotheses, replication studies, and enhancing generalizability.

In both cases, it is essential to ensure that hypotheses are clear, testable, and aligned with the research objectives. Researchers should also be open to revising and refining hypotheses based on the findings and feedback obtained during the research process. The choice between a directional and non-directional hypothesis depends on factors such as the research question, available literature, theoretical frameworks, and the specific objectives of the study. Researchers should carefully consider these factors to determine the most appropriate type of hypothesis to use in their research

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• v.37(16); 2022 Apr 25

A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

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Non-Directional Hypothesis

A non-directional hypothesis is a two-tailed hypothesis that does not predict the direction of the difference or relationship (e.g. girls and boys are different in terms of helpfulness).

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Directional vs. Non-Directional Hypothesis in Research

In the world of research and statistical analysis, formulating hypotheses is a crucial step in the scientific process. Hypotheses guide researchers in making predictions and testing relationships between variables. When it comes to hypotheses, there are two main types: directional and non-directional.

Directional Hypothesis

A directional hypothesis, also known as a one-tailed hypothesis, is formulated with a specific predicted direction of the relationship between variables. It indicates an expectation of the relationship being either positive or negative.

Example of Directional Hypothesis

Advantages of directional hypothesis, non-directional hypothesis.

Non-directional hypotheses are often used when there is insufficient prior knowledge or theoretical basis to predict the direction of the relationship. It allows for a more exploratory approach, where the researcher is open to discovering the nature of the relationship through data analysis .

Example of Non-Directional Hypothesis

Read More: Population vs Sample | Examples

Advantages of Non-Directional Hypothesis:

Difference between directional and non-directional hypotheses.

Choosing Between Directional and Non-Directional Hypotheses: The choice between a directional and non-directional hypothesis depends on the research question, existing knowledge, and theoretical background. Here are a few considerations for selecting the appropriate type of hypothesis:

Directional vs. Non-Directional Hypothesis

Directional hypotheses offer specific predictions about the expected direction of the relationship, whereas non-directional hypotheses allow for more exploratory investigations without preconceived notions of the direction.

Remember, hypotheses serve as a roadmap for research, and regardless of their type, they play a crucial role in scientific inquiry and the pursuit of knowledge.

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A research hypothesis is a statement that predicts or expects a relationship between variables, and it is tested through research. To create a hypothesis, researchers often review existing literature on the topic. This hypothesis is based on theories, observations, or empirical evidence. It guides the research process, including experiment design, data collection, and analysis. Ultimately, the hypothesis aims to predict the outcome of the study.

What is a Hypothesis in a Dissertation?

This article compares directional and non-directional hypotheses and provides guidelines for writing an effective hypothesis in research. The study explores the differences in predictions and research design implications between the two hypotheses.

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Types of hypothesis.

There are two main types of hypotheses in research:

Null Hypothesis (H0) 

The null hypothesis is the default assumption in statistical analysis that there is no significant relationship or effect between the variables being studied. It suggests that any observed differences or relationships are due to chance.

Alternative Hypothesis (Ha or H1)

The alternative hypothesis proposes a significant relationship or effect between variables, contradicting the null hypothesis. It reflects the researcher's expectations based on existing theories or observations.

What is Directional Hypotheses?

A directional hypothesis is a type of hypothesis that is used to predict a specific change or outcome in a research study. It is typically used when researchers have a clear idea of the direction in which they expect their results to go, either an increase or decrease, and want to test this prediction. By making a directional hypothesis, researchers can focus their research efforts and design studies that are more likely to uncover meaningful results. In essence, a directional hypothesis is a statement that predicts the direction of the change that is expected to occur between two groups or variables that are being investigated.

Examples of Directional Hypothesis

Example 1: Online versus Traditional Classroom Learning

For instance, consider a study comparing the average study time of college students in online courses versus those in traditional classroom settings. Drawing on prior research indicating that online learning might lead to reduced engagement, a potential directional hypothesis could be: "Students enrolled in online classes will spend fewer weekly study hours than those in traditional classrooms."

In this scenario, our hypothesis presents a clear expectation—that the average number of weekly study hours among online learners will be lower than that of traditional learners. If the actual findings reveal no significant difference or even higher study times among online learners, then our hypothesis would be refuted.

Example 2: Carbon Dioxide Levels and Global Warming

A directional hypothesis in this scenario would propose a specific change in direction between these two variables. For instance, a directional hypothesis might state that as carbon dioxide levels increase, global temperatures will also rise. This hypothesis suggests a causal relationship between the increase in CO2 levels and the phenomenon of global warming, indicating a direction of change in global temperatures corresponding to changes in CO2 levels.

What is a Non-Directional Hypotheses?

In scientific research, a non-directional hypothesis, or null hypothesis, is a statement that suggests the absence of a relationship or difference between the variables being studied. This type of hypothesis is used to test the validity of a research question by assuming that there is no significant effect or relationship between the variables under investigation. The null hypothesis is typically tested against an alternative hypothesis, which proposes that there is a significant effect or relationship between the variables. If the null hypothesis is rejected, it means that there is enough evidence to suggest that the alternative hypothesis is true, and the variables are indeed related or different from each other.

Non-Directional Hypothesis Example

Example: Is there a difference in anxiety levels between students who receive traditional classroom instruction and those who participate in online learning?

In this non-directional hypothesis, researchers are interested in understanding if there's a disparity in anxiety levels between students who are taught in traditional classrooms versus those who learn online. The non-directional hypothesis posits that there won't be any notable variance in anxiety levels between the two groups. This means that the researchers are not predicting whether one group will have higher or lower anxiety levels; rather, they are exploring if there's any difference at all.

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Directional vs. Non-Directional Hypotheses in Research

Both directional and non directional hypothesis have their place in research, and choosing the appropriate type depends on the research question being investigated. Researchers can use directional or non-directional hypotheses in their studies, depending on their specific expectations about the relationship between variables. A directional hypothesis predicts a specific direction of change, while a non-directional hypothesis predicts that there will be a difference between groups or conditions without specifying the direction of that difference. It's important to understand the difference between these types of hypotheses to conduct rigorous and insightful research. Directional hypotheses are useful when researchers want to test a specific expectation about the relationship between variables, while non-directional hypotheses are more appropriate when researchers simply want to test if there is any difference between groups or conditions.

How to Write an Effective Hypothesis in Research?

Writing an effective hypothesis involves several key steps to ensure clarity, testability, and relevance to the research question. Here's a guide on how to write an effective hypothesis:

• Identify the Research Question: Start by clearly defining the research question or problem you want to investigate. Your hypothesis should directly address this question.
• State the Null Hypothesis: The null hypothesis (H0) is a statement that there is no relationship or effect between the variables being studied. It serves as the default assumption and is typically stated as the absence of an effect or difference.
• Formulate the Alternative Hypothesis: The alternative hypothesis (H1 or Ha) is the statement that contradicts the null hypothesis and suggests that there is a relationship or effect between the variables. It reflects what you expect to find in your research.
• Make it Testable: Your hypothesis should be testable through empirical observation or experimentation. This means that there must be a way to collect data or evidence to support or refute the hypothesis.
• Be Specific and Clear: Clearly state the variables involved and the expected relationship between them. Avoid vague or ambiguous language to ensure that your hypothesis is easy to understand and interpret.
• Use Quantifiable Terms: Whenever possible, use quantifiable terms or measurable variables in your hypothesis. This makes it easier to collect data and analyze results objectively.
• Consider the Scope: Ensure that your hypothesis is focused and specific to the research hypothesis at hand. Avoid making broad generalizations that are difficult to test or validate.
• Revise and Refine: Once you've drafted your hypothesis, review it carefully to ensure accuracy and coherence. Revise as needed to clarify any ambiguities or inconsistencies.

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In conclusion, directional hypotheses predict whether variables will increase or decrease, providing a definite expectation about the direction of the relationship under investigation. Non-directional hypotheses, on the other hand, only claim that there is a difference between variables without specifying the direction of the change, leaving it open to any possibility. Both types of hypotheses play an important role in guiding research investigations and developing testable predictions.

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What is The Null Hypothesis & When Do You Reject The Null Hypothesis

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Editor at Simply Psychology

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A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.

The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

The null hypothesis is the statement that a researcher or an investigator wants to disprove.

Testing the null hypothesis can tell you whether your results are due to the effects of manipulating ​ the dependent variable or due to random chance. 

How to Write a Null Hypothesis

Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.

It is a default position that your research aims to challenge or confirm.

For example, if studying the impact of exercise on weight loss, your null hypothesis might be:

There is no significant difference in weight loss between individuals who exercise daily and those who do not.

Examples of Null Hypotheses

When Do We Reject The Null Hypothesis? 

We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected. 

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).

If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables. 

You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.

Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.

The level of statistical significance is often expressed as a  p  -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.

When your p-value is less than or equal to your significance level, you reject the null hypothesis.

In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.

In this case, the sample data provides insufficient data to conclude that the effect exists in the population.

Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.

When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.

Why Do We Never Accept The Null Hypothesis?

The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.

A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist. 

It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null. 

One can either reject the null hypothesis, or fail to reject it, but can never accept it.

Why Do We Use The Null Hypothesis?

We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.

The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).

A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.

Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists. 

Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.

It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter. 

Purpose of a Null Hypothesis 

• The primary purpose of the null hypothesis is to disprove an assumption. 
• Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
• A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.

Do you always need both a Null Hypothesis and an Alternative Hypothesis?

The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true. 

While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables. 

The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study. 

What is the difference between a null hypothesis and an alternative hypothesis?

The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.

It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.

What are some problems with the null hypothesis?

One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.

Why can a null hypothesis not be accepted?

We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.

We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.

Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis.

Is a null hypothesis directional or non-directional?

A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.

A nondirectional hypothesis contains the not equal sign (“≠”).  However, a null hypothesis is neither directional nor non-directional.

A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.

The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.

Gill, J. (1999). The insignificance of null hypothesis significance testing.  Political research quarterly ,  52 (3), 647-674.

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method.  American Psychologist ,  56 (1), 16.

Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing.  Behavior research methods ,  43 , 679-690.

Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy.  Psychological methods ,  5 (2), 241.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test.  Psychological bulletin ,  57 (5), 416.

Directional vs Non-Directional Hypothesis – Collect Feedback More Effectively 

To conduct a perfect survey, you should know the basics of good research . That’s why in Startquestion we would like to share with you our knowledge about basic terms connected to online surveys and feedback gathering . Knowing the basis you can create surveys and conduct research in more effective ways and thanks to this get meaningful feedback from your customers, employees, and users. That’s enough for the introduction – let’s get to work. This time we will tell you about the hypothesis .

What is a Hypothesis?

A Hypothesis can be described as a theoretical statement built upon some evidence so that it can be tested as if it is true or false. In other words, a hypothesis is a speculation or an idea, based on insufficient evidence that allows it further analysis and experimentation.  

The purpose of a hypothetical statement is to work like a prediction based on studied research and to provide some estimated results before it ha happens in a real position. There can be more than one hypothesis statement involved in a research study, where you need to question and explore different aspects of a proposed research topic. Before putting your research into directional vs non-directional hypotheses, let’s have some basic knowledge.

Most often, a hypothesis describes a relation between two or more variables. It includes:

An Independent variable – One that is controlled by the researcher

Dependent Variable – The variable that the researcher observes in association with the Independent variable.

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How to write an effective Hypothesis?

To write an effective hypothesis follow these essential steps.

• Inquire a Question

The very first step in writing an effective hypothesis is raising a question. Outline the research question very carefully keeping your research purpose in mind. Build it in a precise and targeted way. Here you must be clear about the research question vs hypothesis. A research question is the very beginning point of writing an effective hypothesis.

Do Literature Review

Once you are done with constructing your research question, you can start the literature review. A literature review is a collection of preliminary research studies done on the same or relevant topics. There is a diversified range of literature reviews. The most common ones are academic journals but it is not confined to that. It can be anything including your research, data collection, and observation.

At this point, you can build a conceptual framework. It can be defined as a visual representation of the estimated relationship between two variables subjected to research.

Frame an Answer

After a collection of literature reviews, you can find ways how to answer the question. Expect this stage as a point where you will be able to make a stand upon what you believe might have the exact outcome of your research. You must formulate this answer statement clearly and concisely.

Build a Hypothesis

At this point, you can firmly build your hypothesis. By now, you knew the answer to your question so make a hypothesis that includes:

• Applicable Variables                     
• Particular Group being Studied (Who/What)
• Probable Outcome of the Experiment

Remember, your hypothesis is a calculated assumption, it has to be constructed as a sentence, not a question. This is where research question vs hypothesis starts making sense.

Refine a Hypothesis

Make necessary amendments to the constructed hypothesis keeping in mind that it has to be targeted and provable. Moreover, you might encounter certain circumstances where you will be studying the difference between one or more groups. It can be correlational research. In such instances, you must have to testify the relationships that you believe you will find in the subject variables and through this research.

Build Null Hypothesis

Certain research studies require some statistical investigation to perform a data collection. Whenever applying any scientific method to construct a hypothesis, you must have adequate knowledge of the Null Hypothesis and an Alternative hypothesis.

Null Hypothesis: 

A null Hypothesis denotes that there is no statistical relationship between the subject variables. It is applicable for a single group of variables or two groups of variables. A Null Hypothesis is denoted as an H0. This is the type of hypothesis that the researcher tries to invalidate. Some of the examples of null hypotheses are:

–        Hyperactivity is not associated with eating sugar.

–        All roses have an equal amount of petals.

–        A person’s preference for a dress is not linked to its color.

Alternative Hypothesis: 

An alternative hypothesis is a statement that is simply inverse or opposite of the null hypothesis and denoted as H1. Simply saying, it is an alternative statement for the null hypothesis. The same examples will go this way as an alternative hypothesis:

–        Hyperactivity is associated with eating sugar.

–        All roses do not have an equal amount of petals.

–        A person’s preference for a dress is linked to its color.

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Types of Hypothesis

Apart from null and alternative hypotheses, research hypotheses can be categorized into different types. Let’s have a look at them:

Simple Hypothesis:

This type of hypothesis is used to state a relationship between a particular independent variable and only a dependent variable.

Complex Hypothesis:

A statement that states the relationship between two or more independent variables and two or more dependent variables, is termed a complex hypothesis.

Associative and Causal Hypothesis:

This type of hypothesis involves predicting that there is a point of interdependency between two variables. It says that any kind of change in one variable will cause a change in the other one.  Similarly, a casual hypothesis says that a change in the dependent variable is due to some variations in the independent variable.

Directional vs non-directional hypothesis

Directional hypothesis:.

A hypothesis that is built upon a certain directional relationship between two variables and constructed upon an already existing theory, is called a directional hypothesis. To understand more about what is directional hypothesis here is an example, Girls perform better than boys (‘better than’ shows the direction predicted)

Non-directional Hypothesis:

It involves an open-ended non-directional hypothesis that predicts that the independent variable will influence the dependent variable; however, the nature or direction of a relationship between two subject variables is not defined or clear.

For Example, there will be a difference in the performance of girls & boys (Not defining what kind of difference)

As a professional, we suggest you apply a non-directional alternative hypothesis when you are not sure of the direction of the relationship. Maybe you’re observing potential gender differences on some psychological test, but you don’t know whether men or women would have the higher ratio. Normally, this would say that you are lacking practical knowledge about the proposed variables. A directional test should be more common for tests. 

Author: Ula Kamburov-Niepewna

Updated: 18 November 2022

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11 Independent-samples t-Test

Learning outcomes.

In this chapter, you will learn how to:

• Identify when to use an independent-samples t -test
• Conduct an independent-samples t -test hypothesis test
• Evaluate effect size for an independent-samples t-test
• Identify the assumptions for conducting an independent-samples t -test

We have seen how to compare a single mean against a given value. While single sample techniques are used in real research, most research requires the comparison of at least two sets of data. Now, we will learn how to compare two separate means from two different groups to see if there is a difference between them. The process of testing hypotheses about two means is exactly the same as it is for testing hypotheses about a single mean, and the logical structure of the formula is the same as well. However, we will be adding a few extra steps this time to account for the fact that our data are coming from different sources.

The research designs used to obtain two sets of data can be classified into two general categories. If there’s no logical or meaningful way to link individuals across groups, or if there is no overlap between the groups, then we say the groups are independent and use the independent samples t -test (AKA between-subjects), the subject of this chapter. If they came from two time points with the same people, you know you are working with repeated measures data (the measurement literally was repeated) and will use a repeated measures (sometimes called a dependent samples or paired samples) t -test, which we will discuss in the next chapter. It is very important to keep these two tests separate and understand the distinctions between them because they assess very different questions and require different approaches to the data. When in doubt, think about how the data were collected and where they came from.

Research Questions about Independent Means

Remember that our research questions are always about the populations of interest, though we conduct the studies on samples. Thus, an independent samples t -test is truly designed to compare populations. If we want to know if two populations differ and we do not know the mean of either population, we take a sample from each and then conduct an independent sample t -test. Many research ideas in the behavioral sciences and other areas of research are concerned with whether or not two means are the same or different. Logically, we therefore say that these research questions are concerned with group mean differences. That is, on average, do we Group A to be higher or lower on some variable than Group B. In any time of research design looking at group mean differences, there are some key criteria we must consider: the groups must be mutually exclusive (i.e., you can only be part of one group at any given time) and the groups have to be measured on the same variable (i.e., you can’t compare personality in one group to reaction time in another group because those values would not be the same anyway).

Figure 1. Collecting data from two different samples drawn from two different populations.

Let’s look at one of the most common and logical examples: testing a new medication. When a new medication is developed, the researchers who created it need to demonstrate that it effectively treats the symptoms they are trying to alleviate. The simplest design that will answer this question involves two groups: one group that receives the new medication (the “treatment” group) and one group that receives a placebo (the “control” group). Participants are randomly assigned to one of the two groups (remember that random assignment is the hallmark of a true experiment), and the researchers test the symptoms experienced by each person in each group after they received either the medication or the placebo. They then calculate the average symptoms in each group and compare them to see if the treatment group did better (i.e., had fewer or less severe symptoms) than the control group.

In this example, we had two groups (the independent variable): treatment and control. Membership in these two groups was mutually exclusive; each individual participant received either the experimental medication or the placebo. No one in the experiment received both, so there was no overlap between the two groups. Additionally, each group could be measured on the same variable: symptoms related to the disease or ailment being treated (the dependent variable). Because each group was measured on the same variable, the average scores in each group could be meaningfully compared. If the treatment was ineffective, we would expect that the average symptoms of someone receiving the treatment would be the same as the average symptoms of someone receiving the placebo (i.e., there is no difference between the groups). However, if the treatment was effective, we would expect fewer symptoms from the treatment group, leading to a lower group average.

Now, let’s look at an example using groups that already exist. A common, and perhaps salient, question is how students feel about their job prospects after graduation. Suppose that we have narrowed our potential choice of colleges down to two universities and, in the course of trying to decide between the two, we come across a survey that has data from each university on how students at those universities feel about their future job prospects. As with our last example, we have two groups: University A and University B, and each participant is in only one of the two groups. Because students at each university completed the same survey, they are measuring the same thing, so we can use an independent samples t -test to compare the average perceptions of students at each university to see if they are the same. If they are the same, then we should continue looking for other things about each university to help us decide on where to go. But, if they are different, we can use that information in favor of the university with higher job prospects.

As we can see, the grouping variable we use for an independent samples t -test can be a set of groups we create (as in the experimental medication example) or groups that already exist naturally (as in the university example). There are countless other examples of research questions relating to two group means, making the independent samples t -test one of the most widely used analyses around.

Hypotheses and Decision Criteria

The process of testing hypotheses using an independent samples t -test is the same as it was in the last two chapters, and it starts with stating our hypotheses and laying out the criteria we will use to test them.

The Null and Alternative Hypotheses

We still state the null and alternative hypotheses mathematically in terms of the population parameters and and then in words written out as statements answering the research questions as yes and no answers.  Just like before, we need to decide if we are looking for directional or non-directional hypotheses. For a non-directional hypothesis test, our null hypothesis for an independent samples t -test is the same as all others: there is no difference. But instead of comparing a single 𝜇 to a numerical value, we are now comparing two populations, thus to 𝜇’s. The means of the two groups are the same under the non-directional null hypothesis. Mathematically, this takes on two equivalent forms:

𝐻 0 : 𝜇 1 = 𝜇 2

𝐻 0 : 𝜇 1 − 𝜇 2 = 0

Both of these formulations of the null hypothesis tell us exactly the same thing: that the numerical values of the means are the same in both groups. This is more clear in the first formulation, but the second formulation also makes sense (any number minus itself is always zero) and helps us out a little when we get to the math of the test statistic. Either one is acceptable and you only need to report one. The written out version of both of them is also the same:

H 0 : There is no difference between the means of the two groups

Our alternative hypotheses are also unchanged. We simply replace the equal sign (=) with the inequality sign (≠):

𝐻 𝐴 : 𝜇 1 ≠ 𝜇 2

𝐻 𝐴 : 𝜇 1 − 𝜇 2 ≠ 0

Whichever format you chose for the null hypothesis should be the one you use for the alternative hypothesis (be consistent), and the interpretation of them is always the same:

H A : There is a difference between the means of the two groups

Notice that we are now dealing with two means instead of just one, so it will be very important to keep track of which mean goes with which population and, by extension, which dataset and sample data. We use subscripts to differentiate between the populations, so make sure to keep track of which is which. If it is helpful, you can also use more descriptive subscripts. To use the experimental medication example:

H 0 : There is no difference between the means of the treatment and control groups

𝐻 0 : 𝜇 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 = 𝜇 𝑐𝑜𝑛𝑡𝑟𝑜𝑙

H A : There is a difference between the means of the treatment and control groups

𝐻 𝐴 : 𝜇 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 ≠ 𝜇 𝑐𝑜𝑛𝑡𝑟𝑜𝑙

Degrees of Freedom for the Critical Value

Once we have our hypotheses laid out, we can set our criteria to test them using the same three pieces of information as before: significance level (α), directionality (one-tailed: left or right, or two-tailed), and degrees of freedom, which for an independent samples t -test are calculated a bit differently than before.

Calculating degrees of freedom for Independent Samples t-test

[latex]df=(n_1-1)+(n_2-1)[/latex]

Where  n 1 represents the sample size for group 1 and n 2 represents the sample size for group 2. We have two separate groups, each with their own possible sample mean, so each has their own possible set of degrees of freedom ( df = n -1).

This looks different than before, but it is just adding the individual degrees of freedom from each group (n – 1) together. Notice that the sample sizes, n , also get subscripts so we can tell them apart.

For an independent samples t -test, it is often the case that our two groups will have slightly different sample sizes, either due to chance or some characteristic of the groups themselves. Generally, this is not as issue, so long as one group is not massively larger than the other group. What is of greater concern is keeping track of which is which using the subscripts.

Computing the Test Statistic

The test statistic for our independent samples t -test takes on the same logical structure and format as our other t -tests: our observed effect minus our null hypothesis value, all divided by the standard error.

Calculating the test statistic for Independent Samples t-test

[latex]t_{test}=\frac{(M_1-M_2)-(𝜇_1-𝜇_2)}{s_{(M_1-M_2)}}[/latex]

M 1 is the sample mean for group 1 and M 2 is the sample mean for group 2. This looks like more work to calculate, but remember that our null hypothesis states that the quantity μ 1 – μ 2 = 0, so we can drop that out of the equation and are left with:

[latex]t_{test}=\frac{(M_1-M_2)}{s_{(M_1-M_2)}}[/latex]

Our standard error in the denominator is still estimated standard deviation (s) with a subscript denoting what it is the standard error of. Because we are dealing with the difference between two separate means, rather than a single mean, we put both means in the subscript. Calculating our standard error, as we will see next, is where the biggest differences between this t -test and other t -tests appears. However, once we do calculate it and use it in our test statistic, everything else goes back to normal. Our decision criteria is still comparing our obtained test statistic to our critical value, and our interpretation based on whether or not we reject the null hypothesis is unchanged as well.

Standard Error and Pooled Variance

Recall that the standard error is the average distance between any given sample mean and the center of its corresponding sampling distribution, and it is a function of the standard deviation of the population (either given or estimated) and the sample size. This definition and interpretation hold true for our independent samples t -test as well, but because we are working with two samples drawn from two populations, we have to first combine their estimates of standard deviation – or, more accurately, their estimates of variance – into a single value that we can then use to calculate our standard error.

The combined estimate of variance using the information from each sample is called the pooled variance and is denoted s p 2 ; the subscript p serves as a reminder indicating that it is the pooled variance. The term “pooled variance” is a literal name because we are simply pooling or combining the information on variance – the Sum of Squares and Degrees of Freedom – from both of our samples into a single number. The result is a weighted average of the observed sample variances, the weight for each being determined by the sample size, and will always fall between the two observed variances.

Calculating the Pooled Variance and Standard Error for Independent Samples t-test

[latex]s_p^2=\frac{SS_1+SS_2}{df_1+df_2}[/latex]

Notice that pooled variance requires that we calculate the sum of squares for each sample and the degrees of freedom for each sample. Make sure you add before you divide when calculating pooled variance!

Once we have our pooled variance calculated, we can drop it into the equation for our standard error:

[latex]s_{(M_1-M_1)}=\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_2}}[/latex]

Unlike when calculating the pooled variance, here you want to make sure that you divide your fractions before you add!

Once again, although this formula may seem different than it was before, in reality it is just a different way of writing the same thing. Think back to the standard error options presented before, when our standard error was the square root of the just a single variance divided by a single sample size.

[latex]s_M=\sqrt{\frac{s^2}{n}}[/latex]

Looking at that, we can now see that, once again, we are simply adding together two pieces of information: no new logic or interpretation required. Once the standard error is calculated, it goes in the denominator of our test statistic, as shown above and as was the case in all previous chapters. Thus, the only additional step to calculating an independent samples t -statistic is computing the pooled variance. Let’s see an example in action.

Example: Movies and Mood

We are interested in whether the type of movie someone sees at the theater affects their mood when they leave. We decide to ask people about their mood as they leave one of two movies: a comedy (group 1, n 1 = 35) or a horror film (group 2, n 2 = 29). Our data are coded so that higher scores indicate a more positive mood. We have good reason to believe that people leaving the comedy will be in a better mood, so we use a one-tailed test at α = 0.05 to test our hypothesis.

Research Question : Will those who watch a comedy movie have a better mood than those who watch a horror film?

Step 1: State the Hypotheses

As always, we start with hypotheses:

H 0 : Those who watch the comedy will not have a better mood than those who watch the horror film

H 0 : μ comedy < μ horror

(Note that the null hypothesis includes both no difference (the equal sign) and a decrease in mood.)

H A : Those who watch the comedy will have a better mood than those who watch the horror film

H A : μ comedy > μ horror

Notice that we used labels to make sure that our data stay clear when we do our calculations later in this hypothesis test.

Step 2: Find the Critical Values

Just like before, we will need critical values, which come from our t -table. In this example, we have a one-tailed test at α = 0.05 and expect a positive answer (because we expect the difference between the means to be greater than zero). Our degrees of freedom for our independent samples t -test is just the degrees of freedom from each group added together:

[latex]df=(n_{comedy}-1)+(n_{horror}-1)=(35-1)+(29-1)=34+28=62[/latex]

From our t -table, we find that our critical value is t crit = 1.671. Note that because 62 does not appear on the table, we use the next lowest value, which in this case is 60. Also, remember that since we are using a directional test, and looking for an increase or a positive change, that we keep the positive critical value. So, if we were to draw this out on a normal distribution, our critical region would be on the right side.

Step 3: Compute the Test Statistic

The data from our two groups are presented in the tables below. Table 1 shows the values for the Comedy group, and Table 2 shows the values for the Horror group. Values for both have already been placed in the Sum of Squares tables since we will need to use them for our further calculations. (See attached raw data set for additional practice.) Example Independent Samples t-test data (1)

Table 1. Raw scores and Sum of Squares for Group 1

Table 2. Raw scores and Sum of Squares for Group 2.

These values have all been calculated and take on the same interpretation as they have since chapter 3 – no new computations yet. Before we move on to the pooled variance that will allow us to calculate standard error, let’s compute our standard deviation for each group; even though we will not use them in our calculation of the test statistic, they are still important descriptors of our data.

[latex]s_{comedy}^2=\frac{5061.60}{34}=148.87[/latex]

[latex]s_{comedy}=\sqrt{\frac{5061.60}{34}}=12.20[/latex]

[latex]s_{horror}^2=\frac{3896.45}{28}=139.16[/latex]

[latex]s_{horror}=\sqrt{\frac{3896.45}{28}}=11.80[/latex]

Now we can move on to our new calculation, the pooled variance, which is the Sums of Squares that we calculated from our table and the degrees of freedom, which is n – 1, for each group.

[latex]s_p^2=\frac{SS_{comedy}+SS_{horror}}{df_{comedy}+df_{horror}}[/latex]

[latex]s_p^2=\frac{5061.60+3896.45}{34+28}=\frac{8958.05}{62}=144.48[/latex]

As you can see, if you follow the regular process of calculating standard deviation using the Sum of Squares table, finding the pooled variance is very easy.

  Now we can use the pooled variance calculated above to calculate our standard error, the last step before we can find our test statistic.

[latex]s_{M_1-M_2}=\sqrt{\frac{s_p^2}{n_{comedy}}+\frac{s_p^2}{n_{horror}}}[/latex]

[latex]s_{M_1-M_2}=\sqrt{\frac{144.48}{35}+\frac{144.48}{29}}=\sqrt{4.13+4.98}=\sqrt{9.11}=3.02[/latex]

Finally, we can use our standard error and the means we calculated earlier to compute our test statistic. Because the null hypothesis value of μ 1 – μ 2 is 0, we will leave that portion out of the equation for simplicity.

[latex]t_{test}=\frac{M_{comedy}-M_{horror}}{s_{M_1-M_2}}[/latex]

[latex]t_{test}=\frac{24.00-16.50}{3.02}=\frac{7.50}{3.02}=2.48[/latex]

The process of calculating our test statistic t test = 2.48 followed the same sequence of steps as before: use raw data to compute the mean and sum of squares (this time for two groups instead of one), use the sum of squares and degrees of freedom to calculate standard error (this time using pooled variance instead of standard deviation), and use that standard error and the observed means to get t test .

Now we can move on to the final step of the hypothesis testing procedure.

Step 4: Make and Interpret the Decision

Our test statistic has a value of t test = 2.48, and in step 2 we found that the critical value is t crit = 1.671. 2.48 > 1.671, so we reject the null hypothesis. We can now write our decision up in APA style. Notice that we use our combined degrees of freedom in our inferential statistics in the statement below.

Reject H 0 . The average mood after watching a comedy movie ( M = 24.00, SD = 12.20) is significantly better than the average mood after watching a horror movie ( M = 16.50, SD = 11.80), t (62) = 2.48, p < .05.

However, we shouldn’t stop there. Since we found an effect, we want to make sure to calculate effect size next.

Effect Sizes and Confidence Intervals

We have seen in previous chapters that even a statistically significant effect needs to be interpreted along with an effect size to see if it is practically meaningful. We have also seen that our sample means, as a single estimate, are not perfect and would be better represented by a range of values that we call a confidence interval. As with all other topics, this is also true of our independent samples t -tests.

Our effect size for the independent samples t -test is still Cohen’s d , and it is still just our observed effect or difference divided by the standard deviation. Remember that standard deviation is just the square root of the variance, and because we work with pooled variance in our test statistic, we will use the square root of the pooled variance as our denominator in the formula for Cohen’s d . 

Calculating Cohen’s d for Independent Samples t-test

[latex]d=\bigg |\frac{M_1-M_2}{\sqrt{s_p^2}}\bigg |[/latex]

For our example above, we can calculate the effect size to be:

[latex]d=\bigg |\frac{24.00-16.50}{\sqrt{144.48}}\bigg |=\bigg |\frac{7.50}{12.02}\bigg |=0.62[/latex]

We interpret this using the same guidelines as before, so we would consider this a medium effect. And, now we should add this to our sentence from above.

The average mood after watching a comedy movie ( M = 24.00, SD = 12.20) is significantly better than the average mood after watching a horror movie ( M = 16.50, SD = 11.80), t (62) = 2.48, p < .05, d = 0.62.

Confidence Intervals

Our confidence intervals also take on the same form and interpretation as they have in the past. The value we are interested in is the difference between the two means, so our single estimate is the value of one mean minus the other, or M 1 – M 2 . Just like before, this is our observed effect and is the same value as the one we place in the numerator of our test statistic. We calculate this value then place the margin of error – still our two-tailed critical value times our standard error – above and below it.

Calculating Confidence Interval for Independent Samples t-test

[latex]CI_{upper}=(M_1-M_2)+t_{crit}\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_2}}[/latex]

[latex]CI_{lower}=(M_1-M_2)-t_{crit}\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_2}}[/latex]

Because our hypothesis testing example used a one-tailed test, it would be inappropriate to calculate a confidence interval on those data (remember that we can only calculate a confidence interval for a two-tailed test because the interval extends in both directions). Let’s say we find summary statistics on the average life satisfaction of people from two different towns and want to create a confidence interval to see if the difference between the two might actually be zero.

Our sample data are  M 1 =28.65, s 1 = 12.40, n 1 = 40 and M 2 = 25.40, s 2 = 15.68, n 2 = 42. At face value, it looks like the people from the first town have higher life satisfaction (28.65 vs. 25.40), but it will take a confidence interval (or complete hypothesis testing process) to see if that is true or just due to random chance.

First, we want to calculate the difference between our sample means, which is 28.65 – 25.40 = 3.25.

Next, we need a critical value from our t -table. If we want to test at the normal 95% level of confidence, then our sample sizes will yield degrees of freedom equal to (40-1) + (42-1) = 40 + 42 – 2 = 80. From our table, that gives us a critical value of t crit = 1.990.

Finally, we need our standard error. Recall that our standard error for an independent samples t -test uses pooled variance, which requires the Sum of Squares and degrees of freedom. Up to this point, we have calculated the Sum of Squares using raw data, but in this situation, we do not have access to it. So, what are we to do?

If we have summary data like standard deviation and sample size, it is very easy to calculate the pooled variance another version of the formula.

Calculating Pooled Variance from Sample Standard Deviations

[latex]s_p^2=\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}[/latex]

If s 1 = 12.40, then s 1 2 = 12.40*12.40 =  153.76, and if s 2 = 15.68, then s 2 2 = 15.68*16.68 = 245.86. With n 1 = 40 and n 2 = 42, we are all set to calculate the pooled variance.

[latex]s_p^2=\frac{(40-1)(153.76)+(42-1)(245.86)}{40+42-2}=\frac{(39)(153.76)+(41)(245.86)}{80}[/latex]

[latex]s_p^2=\frac{5996.64+10080.36}{80}=\frac{16077.00}{80}=200.96[/latex]

Now we can plug s p 2 = 200.96, n 1 = 40, and n 2 = 42nd, in to our standard error equation.

[latex]s_{M_1-M_2}=\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_2}}=\sqrt{\frac{200.96}{40}+\frac{200.96}{42}}=\sqrt{5.02+4.78}=\sqrt{9.89}=3.14[/latex]

All of these steps are just slightly different ways of using the same formula, numbers, and ideas we have worked with up to this point. Once we get out standard error, it’s time to build our confidence interval.

95% CI = 3.25 + 1.990(3.14)

95% CI upper = 3.25 + 1.990(3.14) = 3.25 + 6.25 = 9.50

95% CI lower = 3.25 – 1.990(3.14) = 3.25 – 6.25 = -3.00

CI 95 [-3.00, 9.50]

Our confidence interval, as always, represents a range of values that would be considered reasonable or plausible based on our observed data. In this instance, our interval (-3.00, 9.50) does contain zero. Thus, even though the means look a little bit different, it may very well be the case that the life satisfaction in both of these towns is the same. Proving otherwise would require more data.

Homogeneity of Variance

Before wrapping up the coverage of independent samples t -tests, there is one other important topic to cover. Using the pooled variance to calculate the test statistic relies on an assumption known as homogeneity of variance AKA equality of variances AKA homoscedasticity. In statistics, an assumption is some characteristic that we assume is true about our data, and our ability to use our inferential statistics accurately and correctly relies on these assumptions being true. If these assumptions are not true, then our analyses are at best ineffective (e.g., low power to detect effects) and at worst inappropriate (e.g., too many Type I errors). A detailed coverage of assumptions is beyond the scope of this textbook, but it is important to know that they exist for all analyses.

For the current hypothesis test, one important assumption is homogeneity of variance. This is fancy statistical talk for the idea that the true population variance for each group is the same and any difference in the observed sample variances is due to random chance. (If this sounds eerily similar to the idea of testing the null hypothesis that the true population means are equal, that’s because it is exactly the same!) This notion allows us to compute a single pooled variance that uses our easily calculated degrees of freedom. If the assumption is shown to not be true, then we have to use a very complicated formula to estimate the proper degrees of freedom. There are formal tests to assess whether or not this assumption is met, but we will not discuss them here., however most statistical programs will run these assumption checks for us.

Many statistical programs incorporate the test of homogeneity of variance automatically and can report the results of the analysis assuming it is true or assuming it has been violated. You can easily tell which is which by the degrees of freedom: the corrected degrees of freedom (which is used when the assumption of homogeneity of variance is violated) will have decimal places. Fortunately, the independent samples t -test is very robust to violations of this assumption (an analysis is “robust” if it works well even when its assumptions are not met), which is why we do not bother going through the tedious work of testing and estimating new degrees of freedom by hand.

Review: Statistical Power

There are three factors that can affect statistical power:

• Sample size: Larger samples provide greater statistical power
• Effect size: A given design will always have greater power to find a large effect than a small effect (because finding large effects is easier)
• Type I error rate: There is a relationship between Type I error and power such that (all else being equal) decreasing Type I error will also decrease power.

We can see this through simulation. First let’s simulate a single experiment, in which we compare the means of two groups using a standard t-test. We will vary the size of the effect (specified in terms of Cohen’s d), the Type I error rate, and the sample size, and for each of these we will examine how the proportion of significant results (i.e. power) is affected. Figure 1 shows an example of how power changes as a function of these factors.

Figure 1: Results from power simulation, showing power as a function of sample size, with effect sizes shown as different colors, and alpha shown as line type. The standard criterion of 80 percent power is shown by the dotted black line.

This simulation shows us that even with a sample size of 96, we will have relatively little power to find a small effect (d=0.2) with α=0.005. This means that a study designed to do this would be futile – that is, it is almost guaranteed to find nothing even if a true effect of that size exists.

There are at least two important reasons to care about statistical power. First, if you are a researcher, you probably don’t want to spend your time doing futile experiments. Running an underpowered study is essentially futile, because it means that there is a very low likelihood that one will find an effect, even if it exists. Second, it turns out that any positive findings that come from an underpowered study are more likely to be false compared to a well-powered study . Fortunately, there are tools available that allow us to determine the statistical power of an experiment. The most common use of these tools is in planning an experiment, when we would like to determine how large our sample needs to be in order to have sufficient power to find our effect of interest.

Assumptions of independent-samples t-tests

Assumptions are conditions that must be met in order for our hypothesis testing conclusion to be valid. [Important: If the assumptions are not met then our hypothesis testing conclusion is not likely to be valid. Testing errors can still occur even if the assumptions for the test are met.]

Recall that inferential statistics allow us to make inferences (decisions, estimates, predictions) about a population based on data collected from a sample. Recall also that an inference about a population is true only if the sample studied is representative of the population. A statement about a population based on a biased sample is not likely to be true.

Assumption 1: Individuals in the sample were selected randomly and independently, so the sample is highly likely to be representative of the larger population.

• Random sampling ensures that each member of the population is equally likely to be selected.
• An independent sample is one in which the selection of one member has no effect on the selection of any other.

Assumption 2: The distribution of sample mean differences is a normal, because we drew the samples from a population that was normally distributed or we drew large enough samples that the law of large numbers has worked in our favor.

• This assumption is very important because we are estimating probabilities using the t- table, which provide accurate estimates of probabilities for events distributed normally.

Assumption 3: Sampled populations have equal variances or have homogeneity of variance as discussed above.

a research design that uses a separate group of participants for each treatment condition

the statistical assumption of equal variance, meaning that the average squared distance of a score from the mean is the same across all groups sampled in a study.

Introduction to Statistics for the Social Sciences Copyright © 2021 by Jennifer Ivie; Alicia MacKay is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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