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Learning Statistics with Python

t-test Assumptionst-test Assumptions

The main idea behind the t-test is that it follows the t-distribution. For it to be true, a few important assumptions are made:

  1. Homogeneity of Variance. The variances of the two compared groups should be approximately the same.
  2. Normality. Both samples should roughly follow a Normal distribution.
  3. Independence. The samples need to be independent, implying that the values in one group shouldn't be influenced by those in the other group.

It's important to note that the t-test may yield inaccurate results if these assumptions are not met.

There are different types of t-tests that handle violations of some of the assumptions:

  • If the variances are different, you can run Welch's t-test. Its idea is the same. The only thing that differs is the degrees of freedom. Performing Welch's t-test instead of the ordinary t-test in Python is as easy as setting equal_var=False.
  • If samples are not independent(for example, if you want to compare the means of the same group at different time periods), you can run a paired t-test. A paired t-test will be discussed in a later chapter.
question-icon

Select the appropriate type of t-test for each case:

Normality, Homogeneity but no Independence —
Normality, Homogeneity, Independence —

Normality, Independence but no Homogeneity —

Click or drag`n`drop items and fill in the blanks

Everything was clear?

Section 6. Chapter 5