Doing a t-test


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Table of Contents

What is a t-test?

T-test is inferential statistical method used to determine the significance and strength of the relationship between the means of two groups. It states the difference between the two sample groups and tell whether the difference that is measured through calculating the mean, is due to a random chance or due to the causal relationship. 

The T-test is used for the prime purpose of testing a hypothesis formulated based on how the variables react to each other.

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T-test assumptions

  • The scale of measurement applied to the data collected should follow a continuous or ordinal scale (age, height, weight).
  • The data is collected from a representative, randomly selected sample of the total population.
  • When the results are plotted on a graph, there should be a bell shape denoting normal distribution.
  • Homogeneous, variance and standard deviation.

There are three types of t-test:

In this article, let us look at how to do a t-test and what constitutes the conclusion.


Step 1: Define the hypothesis

By looking at the data you have, the first thing you do is to define the null hypothesis and alternative hypothesis. As you are going to perform a t-test, and a t-test is meant to test the formulated hypothesis.

Generally, the hypothesis looks like below:

  • H0 Null hypothesis – means of two sample groups are equal
  • H1 Alternative hypothesis – means of two sample groups are not equal. 

When the means are equal, it means there is no such difference between the two groups. When the means are not equal, it means there is a difference between the two groups and the variables have a certain relationship between them. 

Step 2: Degrees of freedom

Degrees of freedom is nothing but the allowance to the variables to vary or get selected at random. It is calculated with the formula:

dF = N – 1

where N is the sample size. So if we have 10 variables or observations in our study, we can choose first (10-1 = 9) 9 observations at random to study, but the last 10th variable needs to be chosen in a way that it makes up to the defined mean.

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Step 3: T-distribution

T-distribution takes the null hypothesis as accepted and true. To know whether that is correct and to see if sample data matches the null hypothesis, you can compare the t-value of your data against the t-distribution and look for compatibilities. 

Doing a t-test t-test

The t-values

As the name suggests, “t-tests” use t-values to evaluate the hypothesis. T-values are nothing but the test statistics that your get from your data. When you get a specified t-value for your data, you can use this value to compare to the t-distribution and decide whether your null hypothesis is rejected or accepted.

Step 4: Conclusion

After you have compared your t statistics to the t distribution limits, if the value is less than or greater than the t distribution – your null hypothesis is rejected, hence accepting the alternative hypothesis.

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