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What is Hypothesis Testing? Types and Methods

Soumyaa Rawat
Jul 23, 2021

Hypothesis Testing

Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not.

In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number.

In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true.

Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started!

Types of Hypotheses

In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.

Alternative Hypothesis

Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing.

It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence.

When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.

Null Hypothesis

The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it.

The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis.

(Must read: What is ANOVA test? )

Non-Directional Hypothesis

The Non-directional hypothesis states that the relation between two variables has no direction.

Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa.

Directional Hypothesis

The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables.

Herein, the hypothesis clearly states that variable A affects variable B, or vice versa.

Statistical Hypothesis

A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics.

By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not.

(Related blog: z-test vs t-test )

Performing Hypothesis Testing

Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner.

In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure.

To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test.

A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful.

At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%.

(Read also: Types of data sampling techniques )

Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.

Establish the hypotheses

First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing.

These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis.

Generate a testing plan

Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size.

All these factors are very important while one is working on hypothesis testing.

Analyze data samples

As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples.

While analyzing the data samples, a researcher needs to determine a set of things -

Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.

Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples.

Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.

P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis.

Infer the results

The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible.

Methods of Hypothesis Testing

As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -

Frequentist Hypothesis Testing

The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data.

The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST).

The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s.

Bayesian Hypothesis Testing

A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis.

The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand.

On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis.

The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.

(Also read - Introduction to Bayesian Statistics )

To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach.

Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing.

(Also read: Introduction to probability distributions )

A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis.

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Hypothesis Testing: A Complete Guide for Beginners

Statistical hypothesis testing is a key concept in statistics. It helps researchers, data analysts, and scientists make decisions based on data. Hypothesis testing allows you to determine whether your results are meaningful when analyzing experiments, surveys, or other data.

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.