t-test Assumptions | Statistical Testing
Learning Statistics with Python

# t-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.

#### 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

Course Content

Learning Statistics with Python

# t-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.

#### 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