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Methodology
Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .
Daily apple consumption leads to fewer doctor’s visits.
What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Hypotheses propose a relationship between two or more types of variables .
If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.
In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .
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Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.
Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.
At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.
Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.
You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:
To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.
In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.
If you are comparing two groups, the hypothesis can state what difference you expect to find between them.
If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .
Research question | Hypothesis | Null hypothesis |
---|---|---|
What are the health benefits of eating an apple a day? | Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. | Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits. |
Which airlines have the most delays? | Low-cost airlines are more likely to have delays than premium airlines. | Low-cost and premium airlines are equally likely to have delays. |
Can flexible work arrangements improve job satisfaction? | Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. | There is no relationship between working hour flexibility and job satisfaction. |
How effective is high school sex education at reducing teen pregnancies? | Teenagers who received sex education lessons throughout high school will have lower rates of unplanned pregnancy teenagers who did not receive any sex education. | High school sex education has no effect on teen pregnancy rates. |
What effect does daily use of social media have on the attention span of under-16s? | There is a negative between time spent on social media and attention span in under-16s. | There is no relationship between social media use and attention span in under-16s. |
If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.
Statistics
Research bias
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
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McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved June 18, 2024, from https://www.scribbr.com/methodology/hypothesis/
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Example \(\PageIndex{7}\)
Joon believes that 50% of first-time brides in the United States are younger than their grooms. She performs a hypothesis test to determine if the percentage is the same or different from 50% . Joon samples 100 first-time brides and 53 reply that they are younger than their grooms. For the hypothesis test, she uses a 1% level of significance.
Set up the hypothesis test:
The 1% level of significance means that α = 0.01. This is a test of a single population proportion .
\(H_{0}: p = 0.50\) \(H_{a}: p \neq 0.50\)
The words "is the same or different from" tell you this is a two-tailed test.
Calculate the distribution needed:
Random variable: \(P′ =\) the percent of of first-time brides who are younger than their grooms.
Distribution for the test: The problem contains no mention of a mean. The information is given in terms of percentages. Use the distribution for P′ , the estimated proportion.
\[P' - N\left(p, \sqrt{\frac{p-q}{n}}\right)\nonumber \]
\[P' - N\left(0.5, \sqrt{\frac{0.5-0.5}{100}}\right)\nonumber \]
where \(p = 0.50, q = 1−p = 0.50\), and \(n = 100\)
Calculate the p -value using the normal distribution for proportions:
\[p\text{-value} = P(p′ < 0.47 or p′ > 0.53) = 0.5485\nonumber \]
where \[x = 53, p' = \frac{x}{n} = \frac{53}{100} = 0.53\nonumber \].
Interpretation of the \(p\text{-value})\: If the null hypothesis is true, there is 0.5485 probability (54.85%) that the sample (estimated) proportion \(p'\) is 0.53 or more OR 0.47 or less (see the graph in Figure).
\(\mu = p = 0.50\) comes from \(H_{0}\), the null hypothesis.
\(p′ = 0.53\). Since the curve is symmetrical and the test is two-tailed, the \(p′\) for the left tail is equal to \(0.50 – 0.03 = 0.47\) where \(\mu = p = 0.50\). (0.03 is the difference between 0.53 and 0.50.)
Compare \(\alpha\) and the \(p\text{-value}\):
Since \(\alpha = 0.01\) and \(p\text{-value} = 0.5485\). \(\alpha < p\text{-value}\).
Make a decision: Since \(\alpha < p\text{-value}\), you cannot reject \(H_{0}\).
Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of first-time brides who are younger than their grooms is different from 50%.
The \(p\text{-value}\) can easily be calculated.
Press STAT and arrow over to TESTS . Press 5:1-PropZTest . Enter .5 for \(p_{0}\), 53 for \(x\) and 100 for \(n\). Arrow down to Prop and arrow to not equals \(p_{0}\). Press ENTER . Arrow down to Calculate and press ENTER . The calculator calculates the \(p\text{-value}\) (\(p = 0.5485\)) and the test statistic (\(z\)-score). Prop not equals .5 is the alternate hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with \(\(z\) = 0.6\) (test statistic) and \(p = 0.5485\) (\(p\text{-value}\)). Make sure when you use Draw that no other equations are highlighted in \(Y =\) and the plots are turned off.
The Type I and Type II errors are as follows:
The Type I error is to conclude that the proportion of first-time brides who are younger than their grooms is different from 50% when, in fact, the proportion is actually 50%. (Reject the null hypothesis when the null hypothesis is true).
The Type II error is there is not enough evidence to conclude that the proportion of first time brides who are younger than their grooms differs from 50% when, in fact, the proportion does differ from 50%. (Do not reject the null hypothesis when the null hypothesis is false.)
Exercise \(\PageIndex{7}\)
A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.
First, determine what type of test this is, set up the hypothesis test, find the \(p\text{-value}\), sketch the graph, and state your conclusion.
Since the problem is about percentages, this is a test of single population proportions.
Because \(p > \alpha\), we fail to reject the null hypothesis. There is not sufficient evidence to suggest that the proportion of students that want to go to the zoo is not 85%.
Example \(\PageIndex{8}\)
Suppose a consumer group suspects that the proportion of households that have three cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Set up the Hypothesis Test:
\(H_{0}: p = 0.30, H_{a}: p \neq 0.30\)
Determine the distribution needed:
The random variable is \(P′ =\) proportion of households that have three cell phones.
The distribution for the hypothesis test is \(P' - N\left(0.30, \sqrt{\frac{(0.30 \cdot 0.70)}{150}}\right)\)
Exercise 9.6.8.2
a. The value that helps determine the \(p\text{-value}\) is \(p′\). Calculate \(p′\).
a. \(p' = \frac{x}{n}\) where \(x\) is the number of successes and \(n\) is the total number in the sample.
\(x = 43, n = 150\)
\(p′ = 43150\)
Exercise 9.6.8.3
b. What is a success for this problem?
b. A success is having three cell phones in a household.
Exercise 9.6.8.4
c. What is the level of significance?
c. The level of significance is the preset \(\alpha\). Since \(\alpha\) is not given, assume that \(\alpha = 0.05\).
Exercise 9.6.8.5
d. Draw the graph for this problem. Draw the horizontal axis. Label and shade appropriately.
Calculate the \(p\text{-value}\).
d. \(p\text{-value} = 0.7216\)
Exercise 9.6.8.6
e. Make a decision. _____________(Reject/Do not reject) \(H_{0}\) because____________.
e. Assuming that \(\alpha = 0.05, \alpha < p\text{-value}\). The decision is do not reject \(H_{0}\) because there is not sufficient evidence to conclude that the proportion of households that have three cell phones is not 30%.
Exercise \(\PageIndex{8}\)
Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 5% level of significance. State the null and alternative hypothesis, find the p -value, state your conclusion, and identify the Type I and Type II errors.
Because \(p < 0.05\), we reject the null hypothesis. There is sufficient evidence to conclude that fewer than 92% of American adults own cell phones.
The next example is a poem written by a statistics student named Nicole Hart. The solution to the problem follows the poem. Notice that the hypothesis test is for a single population proportion. This means that the null and alternate hypotheses use the parameter \(p\). The distribution for the test is normal. The estimated proportion \(p′\) is the proportion of fleas killed to the total fleas found on Fido. This is sample information. The problem gives a preconceived \(\alpha = 0.01\), for comparison, and a 95% confidence interval computation. The poem is clever and humorous, so please enjoy it!
Example \(\PageIndex{9}\)
My dog has so many fleas,
They do not come off with ease. As for shampoo, I have tried many types Even one called Bubble Hype, Which only killed 25% of the fleas, Unfortunately I was not pleased.
I've used all kinds of soap, Until I had given up hope Until one day I saw An ad that put me in awe.
A shampoo used for dogs Called GOOD ENOUGH to Clean a Hog Guaranteed to kill more fleas.
I gave Fido a bath And after doing the math His number of fleas Started dropping by 3's! Before his shampoo I counted 42.
At the end of his bath, I redid the math And the new shampoo had killed 17 fleas. So now I was pleased.
Now it is time for you to have some fun With the level of significance being .01, You must help me figure out
Use the new shampoo or go without?
\(H_{0}: p \leq 0.25\) \(H_{a}: p > 0.25\)
In words, CLEARLY state what your random variable \(\bar{X}\) or \(P′\) represents.
\(P′ =\) The proportion of fleas that are killed by the new shampoo
State the distribution to use for the test.
\[N\left(0.25, \sqrt{\frac{(0.25){1-0.25}}{42}}\right)\nonumber \]
Test Statistic: \(z = 2.3163\)
Calculate the \(p\text{-value}\) using the normal distribution for proportions:
\[p\text{-value} = 0.0103\nonumber \]
In one to two complete sentences, explain what the p -value means for this problem.
If the null hypothesis is true (the proportion is 0.25), then there is a 0.0103 probability that the sample (estimated) proportion is 0.4048 \(\left(\frac{17}{42}\right)\) or more.
Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the \(p\text{-value}\).
Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.
0.01 | Do not reject \(H_{0}\) | \(\alpha < p\text{-value}\) |
Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of fleas that are killed by the new shampoo is more than 25%.
Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.
Confidence Interval: (0.26,0.55) We are 95% confident that the true population proportion p of fleas that are killed by the new shampoo is between 26% and 55%.
This test result is not very definitive since the \(p\text{-value}\) is very close to alpha. In reality, one would probably do more tests by giving the dog another bath after the fleas have had a chance to return.
Example \(\PageIndex{11}\)
In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue, use a 0.005 significance level. Explain why the significance level should be so low in terms of a Type I error.
We will follow the four-step process.
If we commit a Type I error, we are essentially accepting a false claim. Since the claim describes cancer-causing environments, we want to minimize the chances of incorrectly identifying causes of cancer.
Figure 9.6.11.
Figure 9.6.12.
Example \(\PageIndex{12}\)
According to the US Census there are approximately 268,608,618 residents aged 12 and older. Statistics from the Rape, Abuse, and Incest National Network indicate that, on average, 207,754 rapes occur each year (male and female) for persons aged 12 and older. This translates into a percentage of sexual assaults of 0.078%. In Daviess County, KY, there were reported 11 rapes for a population of 37,937. Conduct an appropriate hypothesis test to determine if there is a statistically significant difference between the local sexual assault percentage and the national sexual assault percentage. Use a significance level of 0.01.
We will follow the four-step plan.
Figure 9.6.13.
Figure 9.6.14.
The hypothesis test itself has an established process. This can be summarized as follows:
Notice that in performing the hypothesis test, you use \(\alpha\) and not \(\beta\). \(\beta\) is needed to help determine the sample size of the data that is used in calculating the \(p\text{-value}\). Remember that the quantity \(1 – \beta\) is called the Power of the Test . A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same.If the power is low, the null hypothesis might not be rejected when it should be.
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .
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Hypothesis testing in statistics involves testing an assumption about a population parameter using sample data. Learners can download Hypothesis Testing PDF to get instant access to all information!
What exactly is hypothesis testing, and how does it work in statistics? Can I find practical examples and understand the different types from this blog?
Hypothesis Testing : Ever wonder how researchers determine if a new medicine actually works or if a new marketing campaign effectively drives sales? They use hypothesis testing! It is at the core of how scientific studies, business experiments and surveys determine if their results are statistically significant or just due to chance.
Hypothesis testing allows us to make evidence-based decisions by quantifying uncertainty and providing a structured process to make data-driven conclusions rather than guessing. In this post, we will discuss hypothesis testing types, examples, and processes!
Table of Contents
Hypothesis testing is a statistical method used to evaluate the validity of a hypothesis using sample data. It involves assessing whether observed data provide enough evidence to reject a specific hypothesis about a population parameter.
Hypothesis testing in data science is a statistical method used to evaluate two mutually exclusive population statements based on sample data. The primary goal is to determine which statement is more supported by the observed data.
Hypothesis testing assists in supporting the certainty of findings in research and data science projects. This statistical inference aids in making decisions about population parameters using sample data. For those who are looking to deepen their knowledge in data science and expand their skillset, we highly recommend checking out Master Generative AI: Data Science Course by Physics Wallah .
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The hypothesis testing procedure in data science involves a structured approach to evaluating hypotheses using statistical methods. Here’s a step-by-step breakdown of the typical procedure:
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Hypothesis testing is a fundamental concept in statistics that aids analysts in making informed decisions based on sample data about a larger population. The process involves setting up two contrasting hypotheses, the null hypothesis and the alternative hypothesis, and then using statistical methods to determine which hypothesis provides a more plausible explanation for the observed data.
Once these hypotheses are established, analysts gather data from a sample and conduct statistical tests. The objective is to determine whether the observed results are statistically significant enough to reject the null hypothesis in favor of the alternative.
Hypothesis testing is a cornerstone in statistical analysis, providing a framework to evaluate the validity of assumptions or claims made about a population based on sample data. Within this framework, several specific tests are utilized based on the nature of the data and the question at hand. Here’s a closer look at the three fundamental types of hypothesis tests:
The z-test is a statistical method primarily employed when comparing means from two datasets, particularly when the population standard deviation is known. Its main objective is to ascertain if the means are statistically equivalent.
A crucial prerequisite for the z-test is that the sample size should be relatively large, typically 30 data points or more. This test aids researchers and analysts in determining the significance of a relationship or discovery, especially in scenarios where the data’s characteristics align with the assumptions of the z-test.
The t-test is a versatile statistical tool used extensively in research and various fields to compare means between two groups. It’s particularly valuable when the population standard deviation is unknown or when dealing with smaller sample sizes.
By evaluating the means of two groups, the t-test helps ascertain if a particular treatment, intervention, or variable significantly impacts the population under study. Its flexibility and robustness make it a go-to method in scenarios ranging from medical research to business analytics.
The Chi-Square test stands distinct from the previous tests, primarily focusing on categorical data rather than means. This statistical test is instrumental when analyzing categorical variables to determine if observed data aligns with expected outcomes as posited by the null hypothesis.
By assessing the differences between observed and expected frequencies within categorical data, the Chi-Square test offers insights into whether discrepancies are statistically significant. Whether used in social sciences to evaluate survey responses or in quality control to assess product defects, the Chi-Square test remains pivotal for hypothesis testing in diverse scenarios.
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Hypothesis testing is a fundamental concept in statistics used to make decisions or inferences about a population based on a sample of data. The process involves setting up two competing hypotheses, the null hypothesis H 0 and the alternative hypothesis H 1.
Through various statistical tests, such as the t-test, z-test, or Chi-square test, analysts evaluate sample data to determine whether there’s enough evidence to reject the null hypothesis in favor of the alternative. The aim is to draw conclusions about population parameters or to test theories, claims, or hypotheses.
In research, hypothesis testing serves as a structured approach to validate or refute theories or claims. Researchers formulate a clear hypothesis based on existing literature or preliminary observations. They then collect data through experiments, surveys, or observational studies.
Using statistical methods, researchers analyze this data to determine if there’s sufficient evidence to reject the null hypothesis. By doing so, they can draw meaningful conclusions, make predictions, or recommend actions based on empirical evidence rather than mere speculation.
R, a powerful programming language and environment for statistical computing and graphics, offers a wide array of functions and packages specifically designed for hypothesis testing. Here’s how hypothesis testing is conducted in R:
Hypothesis testing is an integral part of statistics and research, offering a systematic approach to validate hypotheses. Leveraging R’s capabilities, researchers and analysts can efficiently conduct and interpret various hypothesis tests, ensuring robust and reliable conclusions from their data.
Yes, data scientists frequently engage in hypothesis testing as part of their analytical toolkit. Hypothesis testing is a foundational statistical technique used to make data-driven decisions, validate assumptions, and draw conclusions from data. Here’s how data scientists utilize hypothesis testing:
Let’s delve into some common examples of hypothesis testing and provide solutions or interpretations for each scenario.
Scenario : A coffee shop owner believes that the average waiting time for customers during peak hours is 5 minutes. To test this, the owner takes a random sample of 30 customer waiting times and wants to determine if the average waiting time is indeed 5 minutes.
Hypotheses :
Solution : Using a t-test (assuming population variance is unknown), calculate the t-statistic based on the sample mean, sample standard deviation, and sample size. Then, determine the p-value and compare it with a significance level (e.g., 0.05) to decide whether to reject the null hypothesis.
Scenario : An e-commerce company wants to determine if changing the color of a “Buy Now” button from blue to green increases the conversion rate.
Solution : Split website visitors into two groups: one sees the blue button (control group), and the other sees the green button (test group). Track the conversion rates for both groups over a specified period. Then, use a chi-square test or z-test (for large sample sizes) to determine if there’s a statistically significant difference in conversion rates between the two groups.
The formula for hypothesis testing typically depends on the type of test (e.g., z-test, t-test, chi-square test) and the nature of the data (e.g., mean, proportion, variance). Below are the basic formulas for some common hypothesis tests:
Z-Test for Population Mean :
Z=(σ/n)(xˉ−μ0)
T-Test for Population Mean :
t= (s/ n ) ( x ˉ −μ 0 )
s = Sample standard deviation
Chi-Square Test for Goodness of Fit :
χ2=∑Ei(Oi−Ei)2
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While you can perform hypothesis testing manually using the above formulas and statistical tables, many online tools and software packages simplify this process. Here’s how you might use a calculator or software:
When using any calculator or software, always ensure you understand the underlying assumptions of the test, interpret the results correctly, and consider the broader context of your research or analysis.
What are the key components of a hypothesis test.
The key components include: Null Hypothesis (H0): A statement of no effect or no difference. Alternative Hypothesis (H1 or Ha): A statement that contradicts the null hypothesis. Test Statistic: A value computed from the sample data to test the null hypothesis. Significance Level (α): The threshold for rejecting the null hypothesis. P-value: The probability of observing the given data, assuming the null hypothesis is true.
The significance level (often denoted as α) is the probability threshold used to determine whether to reject the null hypothesis. Commonly used values for α include 0.05, 0.01, and 0.10, representing a 5%, 1%, or 10% chance of rejecting the null hypothesis when it's actually true.
The choice between one-tailed and two-tailed tests depends on your research question and hypothesis. Use a one-tailed test when you're specifically interested in one direction of an effect (e.g., greater than or less than). Use a two-tailed test when you want to determine if there's a significant difference in either direction.
The p-value is a probability value that helps determine the strength of evidence against the null hypothesis. A low p-value (typically ≤ 0.05) suggests that the observed data is inconsistent with the null hypothesis, leading to its rejection. Conversely, a high p-value suggests that the data is consistent with the null hypothesis, leading to no rejection.
No, hypothesis testing cannot prove a hypothesis true. Instead, it helps assess the likelihood of observing a given set of data under the assumption that the null hypothesis is true. Based on this assessment, you either reject or fail to reject the null hypothesis.
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Statistics Made Easy
In statistics, hypothesis tests are used to test whether or not some hypothesis about a population parameter is true.
To perform a hypothesis test in the real world, researchers will obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:
If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.
The following examples provide several situations where hypothesis tests are used in the real world.
Hypothesis tests are often used in biology to determine whether some new treatment, fertilizer, pesticide, chemical, etc. causes increased growth, stamina, immunity, etc. in plants or animals.
For example, suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.
She then performs a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then she can reject the null hypothesis and conclude that the fertilizer leads to increased plant growth.
Hypothesis tests are often used in clinical trials to determine whether some new treatment, drug, procedure, etc. causes improved outcomes in patients.
For example, suppose a doctor believes that a new drug is able to reduce blood pressure in obese patients. To test this, he may measure the blood pressure of 40 patients before and after using the new drug for one month.
He then performs a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then he can reject the null hypothesis and conclude that the new drug leads to reduced blood pressure.
Hypothesis tests are often used in business to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales.
For example, suppose a company believes that spending more money on digital advertising leads to increased sales. To test this, the company may increase money spent on digital advertising during a two-month period and collect data to see if overall sales have increased.
They may perform a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then the company can reject the null hypothesis and conclude that increased digital advertising leads to increased sales.
Hypothesis tests are also used often in manufacturing plants to determine if some new process, technique, method, etc. causes a change in the number of defective products produced.
For example, suppose a certain manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, they may measure the mean number of defective widgets produced before and after using the new method for one month.
They can then perform a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then the plant can reject the null hypothesis and conclude that the new method leads to a change in the number of defective widgets produced per month.
Introduction to Hypothesis Testing Introduction to the One Sample t-test Introduction to the Two Sample t-test Introduction to the Paired Samples t-test
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Hypothesis Definition, Format, Examples, and Tips
Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk, "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.
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Falsifiability of a hypothesis.
Hypotheses examples.
A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.
Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."
A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.
In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:
The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.
Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen.
In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.
Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.
In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.
In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."
In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."
So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:
Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the journal articles you read . Many authors will suggest questions that still need to be explored.
To form a hypothesis, you should take these steps:
In the scientific method , falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.
Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that if something was false, then it is possible to demonstrate that it is false.
One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.
A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.
Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.
For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.
These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.
One of the basic principles of any type of scientific research is that the results must be replicable.
Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.
Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.
To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.
The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:
A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable .
The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."
Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.
Descriptive research such as case studies , naturalistic observations , and surveys are often used when conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.
Once a researcher has collected data using descriptive methods, a correlational study can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.
Experimental methods are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).
Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually cause another to change.
The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.
Thompson WH, Skau S. On the scope of scientific hypotheses . R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607
Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:]. Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z
Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004
Nosek BA, Errington TM. What is replication ? PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691
Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies . Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18
Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.
By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
It's the initial building block in the scientific method.
What makes a hypothesis testable.
Bibliography.
A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method . Many describe it as an "educated guess" based on prior knowledge and observation. While this is true, a hypothesis is more informed than a guess. While an "educated guess" suggests a random prediction based on a person's expertise, developing a hypothesis requires active observation and background research.
The basic idea of a hypothesis is that there is no predetermined outcome. For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation. This concept, called falsifiability and testability, was advanced in the mid-20th century by Austrian-British philosopher Karl Popper in his famous book "The Logic of Scientific Discovery" (Routledge, 1959).
A key function of a hypothesis is to derive predictions about the results of future experiments and then perform those experiments to see whether they support the predictions.
A hypothesis is usually written in the form of an if-then statement, which gives a possibility (if) and explains what may happen because of the possibility (then). The statement could also include "may," according to California State University, Bakersfield .
Here are some examples of hypothesis statements:
A useful hypothesis should be testable and falsifiable. That means that it should be possible to prove it wrong. A theory that can't be proved wrong is nonscientific, according to Karl Popper's 1963 book " Conjectures and Refutations ."
An example of an untestable statement is, "Dogs are better than cats." That's because the definition of "better" is vague and subjective. However, an untestable statement can be reworded to make it testable. For example, the previous statement could be changed to this: "Owning a dog is associated with higher levels of physical fitness than owning a cat." With this statement, the researcher can take measures of physical fitness from dog and cat owners and compare the two.
In an experiment, researchers generally state their hypotheses in two ways. The null hypothesis predicts that there will be no relationship between the variables tested, or no difference between the experimental groups. The alternative hypothesis predicts the opposite: that there will be a difference between the experimental groups. This is usually the hypothesis scientists are most interested in, according to the University of Miami .
For example, a null hypothesis might state, "There will be no difference in the rate of muscle growth between people who take a protein supplement and people who don't." The alternative hypothesis would state, "There will be a difference in the rate of muscle growth between people who take a protein supplement and people who don't."
If the results of the experiment show a relationship between the variables, then the null hypothesis has been rejected in favor of the alternative hypothesis, according to the book " Research Methods in Psychology " (BCcampus, 2015).
There are other ways to describe an alternative hypothesis. The alternative hypothesis above does not specify a direction of the effect, only that there will be a difference between the two groups. That type of prediction is called a two-tailed hypothesis. If a hypothesis specifies a certain direction — for example, that people who take a protein supplement will gain more muscle than people who don't — it is called a one-tailed hypothesis, according to William M. K. Trochim , a professor of Policy Analysis and Management at Cornell University.
Sometimes, errors take place during an experiment. These errors can happen in one of two ways. A type I error is when the null hypothesis is rejected when it is true. This is also known as a false positive. A type II error occurs when the null hypothesis is not rejected when it is false. This is also known as a false negative, according to the University of California, Berkeley .
A hypothesis can be rejected or modified, but it can never be proved correct 100% of the time. For example, a scientist can form a hypothesis stating that if a certain type of tomato has a gene for red pigment, that type of tomato will be red. During research, the scientist then finds that each tomato of this type is red. Though the findings confirm the hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, the hypothesis is true, but it may not be true 100% of the time.
The best hypotheses are simple. They deal with a relatively narrow set of phenomena. But theories are broader; they generally combine multiple hypotheses into a general explanation for a wide range of phenomena, according to the University of California, Berkeley . For example, a hypothesis might state, "If animals adapt to suit their environments, then birds that live on islands with lots of seeds to eat will have differently shaped beaks than birds that live on islands with lots of insects to eat." After testing many hypotheses like these, Charles Darwin formulated an overarching theory: the theory of evolution by natural selection.
"Theories are the ways that we make sense of what we observe in the natural world," Tanner said. "Theories are structures of ideas that explain and interpret facts."
Encyclopedia Britannica. Scientific Hypothesis. Jan. 13, 2022. https://www.britannica.com/science/scientific-hypothesis
Karl Popper, "The Logic of Scientific Discovery," Routledge, 1959.
California State University, Bakersfield, "Formatting a testable hypothesis." https://www.csub.edu/~ddodenhoff/Bio100/Bio100sp04/formattingahypothesis.htm
Karl Popper, "Conjectures and Refutations," Routledge, 1963.
Price, P., Jhangiani, R., & Chiang, I., "Research Methods of Psychology — 2nd Canadian Edition," BCcampus, 2015.
University of Miami, "The Scientific Method" http://www.bio.miami.edu/dana/161/evolution/161app1_scimethod.pdf
William M.K. Trochim, "Research Methods Knowledge Base," https://conjointly.com/kb/hypotheses-explained/
University of California, Berkeley, "Multiple Hypothesis Testing and False Discovery Rate" https://www.stat.berkeley.edu/~hhuang/STAT141/Lecture-FDR.pdf
University of California, Berkeley, "Science at multiple levels" https://undsci.berkeley.edu/article/0_0_0/howscienceworks_19
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The Difference Between Hypothesis and Theory
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.
A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.
A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.
In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.
Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.
The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)
This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.
The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”
While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."
hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.
hypothesis implies insufficient evidence to provide more than a tentative explanation.
theory implies a greater range of evidence and greater likelihood of truth.
law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.
These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.
Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do
1641, in the meaning defined at sense 1a
This is the Difference Between a...
In scientific reasoning, they're two completely different things
hypothermia
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“Hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/hypothesis. Accessed 18 Jun. 2024.
Kids definition of hypothesis, medical definition, medical definition of hypothesis, more from merriam-webster on hypothesis.
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Statistical tests are used in hypothesis testing. They can be used to: determine whether a predictor variable has a statistically significant relationship with an outcome variable. ... Consult the tables below to see which test best matches your variables. Choosing a parametric test: regression, comparison, or correlation ...
Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test. Step 4: Decide whether to reject or fail to reject your null hypothesis. Step 5: Present your findings. Other interesting articles. Frequently asked questions about hypothesis testing.
Test Statistic: z = x¯¯¯ −μo σ/ n−−√ z = x ¯ − μ o σ / n since it is calculated as part of the testing of the hypothesis. Definition 7.1.4 7.1. 4. p - value: probability that the test statistic will take on more extreme values than the observed test statistic, given that the null hypothesis is true.
S.3 Hypothesis Testing. In reviewing hypothesis tests, we start first with the general idea. Then, we keep returning to the basic procedures of hypothesis testing, each time adding a little more detail. The general idea of hypothesis testing involves: Making an initial assumption. Collecting evidence (data).
The above image shows a table with some of the most common test statistics and their corresponding tests or models.. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently support a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic.Then a decision is made, either by comparing the ...
Photo from StepUp Analytics. Hypothesis testing is a method of statistical inference that considers the null hypothesis H₀ vs. the alternative hypothesis Ha, where we are typically looking to assess evidence against H₀. Such a test is used to compare data sets against one another, or compare a data set against some external standard. The former being a two sample test (independent or ...
Formulate the Hypotheses: Write your research hypotheses as a null hypothesis (H 0) and an alternative hypothesis (H A).; Data Collection: Gather data specifically aimed at testing the hypothesis.; Conduct A Test: Use a suitable statistical test to analyze your data.; Make a Decision: Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
7. Hypothesis Testing in the Age of Big Data - Challenges and opportunities with large datasets. - The role of software and automation in hypothesis testing. 8. Conclusion - Summarising key takeaways.
A test statistic assesses how consistent your sample data are with the null hypothesis in a hypothesis test. Test statistic calculations take your sample data and boil them down to a single number that quantifies how much your sample diverges from the null hypothesis. As a test statistic value becomes more extreme, it indicates larger ...
Testing Hypotheses using Confidence Intervals. We can start the evaluation of the hypothesis setup by comparing 2006 and 2012 run times using a point estimate from the 2012 sample: ˉx12 = 95.61 minutes. This estimate suggests the average time is actually longer than the 2006 time, 93.29 minutes.
Step 1: Testing Method. The test we need to use is a one sample t-test for means (Hypothesis test for means is a t-test because we don't know the population standard deviation, so we have to estimate it with the sample standard deviation s).. Step 2: Assumptions. List all the assumptions for your test to be valid. Even if assumptions are not met, we should comment on how that would affect ...
Unit 12: Significance tests (hypothesis testing) Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values ...
A hypothesis test consists of five steps: 1. State the hypotheses. State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false. 2. Determine a significance level to use for the hypothesis. Decide on a significance level.
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used ...
A statistical hypothesis test may return a value called p or the p-value. This is a quantity that we can use to interpret or quantify the result of the test and either reject or fail to reject the null hypothesis. This is done by comparing the p-value to a threshold value chosen beforehand called the significance level.
Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence.
6. Write a null hypothesis. If your research involves statistical hypothesis testing, you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a.
For rejecting a null hypothesis, a test statistic is calculated. This test-statistic is then compared with a critical value. The critical values are the boundaries of the critical region. If the ...
Example 8.4.7. Joon believes that 50% of first-time brides in the United States are younger than their grooms. She performs a hypothesis test to determine if the percentage is the same or different from 50%. Joon samples 100 first-time brides and 53 reply that they are younger than their grooms.
P (n,r)=nCr*p^r*q^n-r. q is the probability of failure. Long Answer: The binomial theorem formula is a formula use to calculate the probability that an event will be successful r times if n times occur. To use the example in the video, we are given that the probability the event is successful is 99% or 0.99.
Here's a closer look at the three fundamental types of hypothesis tests: 1. Z-Test: The z-test is a statistical method primarily employed when comparing means from two datasets, particularly when the population standard deviation is known. Its main objective is to ascertain if the means are statistically equivalent.
Example 1: Biology. Hypothesis tests are often used in biology to determine whether some new treatment, fertilizer, pesticide, chemical, etc. causes increased growth, stamina, immunity, etc. in plants or animals. For example, suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than ...
A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process. Consider a study designed to examine the relationship between sleep deprivation and test ...
Thus, the hypothesis is true, but it may not be true 100% of the time. Scientific theory vs. scientific hypothesis. The best hypotheses are simple. They deal with a relatively narrow set of phenomena.
When it comes to hypothesis testing, you're likely seeking the best software to analyze data and reach sound conclusions. Hypothesis testing is a statistical method that determines whether there ...
hypothesis: [noun] an assumption or concession made for the sake of argument. an interpretation of a practical situation or condition taken as the ground for action.