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Hypothesis Testing – A Complete Guide with Examples
Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023
In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.
What is a Hypothesis and a Hypothesis Testing?
A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.
What is Hypothesis Testing?
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.
Example: The academic performance of student A is better than student B
Characteristics of the Hypothesis to be Tested
A hypothesis should be:
- Clear and precise
- Capable of being tested
- Able to relate to a variable
- Stated in simple terms
- Consistent with known facts
- Limited in scope and specific
- Tested in a limited timeframe
- Explain the facts in detail
What is a Null Hypothesis and Alternative Hypothesis?
A null hypothesis is a hypothesis when there is no significant relationship between the dependent and the participants’ independent variables .
In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.
If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.
Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.
If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.
If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.
Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.
If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.
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How to Conduct Hypothesis Testing?
Here is a step-by-step guide on how to conduct hypothesis testing.
Step 1: State the Null and Alternative Hypothesis
Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.
A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.
Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.
Step 2: Data Collection
Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to gather the data obtained through a large number of samples from a specific population.
Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.
Step 3: Select Appropriate Statistical Test
There are many types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.
Note: Your choice of the type of test depends on the purpose of your study
One-sided Test
In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.
Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.
Two-sided Test
In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance.
Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.
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Step 4: Select the Level of Significance
When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided.
If the significance level is minimum, then it prevents the researchers from false claims.
The significance level is denoted by P, and it has given the value of 0.05 (P=0.05)
If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.
Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.
Step 5: Find out Whether the Null Hypothesis is Rejected or Supported
After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.
Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.
Step 6: Present the Outcomes of your Study
The final step is to present the outcomes of your study . You need to ensure whether you have met the objectives of your research or not.
In the discussion section and conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.
In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.
If we talk about the findings, our study your results will be as follows:
Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.
Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis?
Always remember that you either conclude to reject Ho in favor of Haor do not reject Ho . It would help if you never rejected Ha or even accept Ha .
Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude reject Ho in favor of Haor do not reject Ho, then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.
Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)
Frequently Asked Questions
What are the 3 types of hypothesis test.
The 3 types of hypothesis tests are:
- One-Sample Test : Compare sample data to a known population value.
- Two-Sample Test : Compare means between two sample groups.
- ANOVA : Analyze variance among multiple groups to determine significant differences.
What is a hypothesis?
A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.
What are null hypothesis?
A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.
What is the probability value?
The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.
What is p value?
The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.
What is a t test?
A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.
When to reject null hypothesis?
Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.
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Hypothesis Testing: A Complete Guide for Beginners
In this blog, we’ll explain statistical hypothesis testing from the basics to more advanced ideas, making it easy to understand even for 10th-grade students.
By the end of this blog, you’ll be able to understand hypothesis testing and how it’s used in research.
What is a Hypothesis?
Table of Contents
A hypothesis is a statement that can be tested. It’s like a guess you make after observing something, and you want to see if that guess holds when you collect more data.
For example:
- “Eating more vegetables improves health.”
- “Students who study regularly perform better in exams.”
These statements are testable because we can gather data to check if they are true or false.
What is Hypothesis Testing?
Hypothesis testing is a statistical process that helps us make decisions based on data. Suppose you collect data from an experiment or survey. Hypothesis testing helps you decide whether the results are significant or could have happened by chance.
For example, if you believe a new teaching method helps students score better, hypothesis testing can help you decide if the improvement is real or just a random fluctuation.
Null and Alternative Hypothesis
Hypothesis testing usually involves two competing hypotheses:
- Example: “There is no difference in exam scores between students using the new method and those who don’t.”
- Example: “Students using the new method perform better in exams than those who don’t.”
Key Terms in Hypothesis Testing
Before diving into the details, let’s understand some important terms used in hypothesis testing:
1. Test Statistic
The test statistic is a number calculated from your data that is compared against a known distribution (like the normal distribution) to test the null hypothesis. It tells you how much your sample data differs from what’s expected under the null hypothesis.
The p-value is the probability of observing the sample data or something more extreme, assuming the null hypothesis is true. A smaller p-value suggests that the null hypothesis is less likely to be true. In many studies, a p-value of 0.05 or less is considered statistically significant.
3. Significance Level (α)
The significance level is the threshold at which you decide to reject the null hypothesis. Commonly, this level is set at 5% (α = 0.05), meaning there’s a 5% chance of rejecting the null hypothesis even when it is true.
4. Critical Value
The critical value is the boundary that defines the region where we reject the null hypothesis. It is calculated based on the significance level and tells us how extreme the test statistic needs to be to reject the null hypothesis.
5. Type I and Type II Errors
- Type I Error (False Positive): Rejecting the null hypothesis when it’s true.
- Type II Error (False Negative): Failing to reject the null hypothesis when it’s false.
In simpler terms:
- Type I error is like thinking something has changed when it hasn’t.
- Type II error is like thinking nothing has changed when it actually has.
Types of Hypothesis Testing
1. one-tailed test.
A one-tailed test checks for an effect in a single direction. For example, if you are only interested in testing whether students who study 2 hours daily score higher than those who don’t, that’s a one-tailed test.
2. Two-Tailed Test
A two-tailed test checks for an effect in both directions. This means you’re testing if the scores are different , regardless of whether they are higher or lower. For example, “Do students who study 2 hours daily score differently than those who don’t?” That’s a two-tailed test.
Steps in Hypothesis Testing
Step 1: define hypotheses.
Start by defining the:
- Null Hypothesis (H₀): The status quo or no change.
- Alternative Hypothesis (H₁): The hypothesis you believe in, suggesting that something has changed.
Step 2: Set the Significance Level (α)
Next, set the significance level, typically 0.05 . This means you’re willing to accept a 5% risk of incorrectly rejecting the null hypothesis.
Step 3: Collect and Analyze Data
Conduct your experiment or survey and collect data. Then, analyze this data to calculate the test statistic. The formula you use depends on the type of test you’re conducting (e.g., Z-test, T-test).
Step 4: Calculate the P-value or Critical Value
Compare the test statistic to a standard distribution (such as the normal distribution). If you calculate a p-value , compare it to the significance level. If the p-value is less than the significance level, reject the null hypothesis.
Alternatively, you can compare your test statistic to a critical value from statistical tables to determine if you should reject the null hypothesis.
Step 5: Make a Decision
Based on your calculations:
- If the p-value is less than the significance level (e.g., p < 0.05), reject the null hypothesis.
- If the p-value is greater than the significance level, do not reject the null hypothesis.
Step 6: Interpret the Results
Finally, interpret the results in context. If you reject the null hypothesis, you have evidence to support the alternative hypothesis. If not, the data does not provide enough evidence to reject the null.
P-Value and Significance
The p-value is a key part of hypothesis testing. It tells us the likelihood of getting results as extreme as the observed data, assuming the null hypothesis is true. In simple terms:
- A low p-value (≤ 0.05) suggests strong evidence against the null hypothesis, so you reject it.
- A high p-value (> 0.05) means the data is consistent with the null hypothesis, and you don’t reject it.
Here’s a table to summarize:
Common Hypothesis Tests
There are different types of hypothesis tests depending on the data and what you are testing for.
Example of Hypothesis Testing
Let’s say a nutritionist claims that a new diet increases the average weight loss for people by 5 kg in a month.
- Null Hypothesis (H₀): The average weight loss is not 5 kg (no difference).
- Alternative Hypothesis (H₁): The average weight loss is greater than 5 kg.
Suppose we collect data from 30 people and find that the average weight loss is 5.5 kg. Now we follow these steps:
- Significance level : Set α = 0.05 (5%).
- Calculate the test statistic: Using the T-test formula.
- Find the p-value : Calculate the p-value for the test statistic.
- Make a decision : Compare the p-value to the significance level.
If the p-value is less than 0.05, we reject the null hypothesis and conclude that the new diet results in more than 5 kg of weight loss.
Statistical hypothesis testing is an essential method in statistics for making informed decisions based on data. By understanding the basics of null and alternative hypotheses, test statistics, p-values, and the steps in hypothesis testing, you can analyze experiments and surveys effectively.
Hypothesis testing is a powerful tool for everything from scientific research to everyday decisions, and mastering it can lead to better data analysis and decision-making.
Also Read: Step-by-step guide to hypothesis testing in statistics
What is the difference between the null hypothesis and the alternative hypothesis?
The null hypothesis (H₀) is the default assumption that there is no effect or no difference. It’s what we try to disprove. The alternative hypothesis (H₁) is what you want to prove. It suggests that there is a significant effect or difference.
What is the difference between a one-tailed test and a two-tailed test?
A one-tailed test looks for evidence of an effect in one direction (either greater or smaller). A two-tailed test checks for evidence of an effect in both directions (whether greater or smaller), making it a more conservative test.
Can we always reject the null hypothesis if the p-value is less than 0.05?
Yes, if the p-value is less than 0.05 , we typically reject the null hypothesis. However, this does not guarantee that the alternative hypothesis is true; it simply indicates that the data provide strong evidence against it.
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