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.