The task of the t-test is to determine whether the difference between the two samples' means is significant. What should we take into consideration to perform it?

• Obviously, we should consider the difference between the means itself.

• As shown in the image below, the variance matters too!

• Also, the size of each sample should be considered.

To account for the difference between the means we just take that difference.

The story is not that simple with variance.
T-test assumes the variance to be the same for both samples. We will talk more about it in the t-test assumptions chapter. To estimate the variance from two samples, the pooled variance formula is used.

And to account for the size, we need sample sizes:

Let's put it all together into t statistic.

You may have noticed that sample sizes are not used most intuitively. But this way t follows the t-distribution, as will be discussed in the next chapter.

What properties of samples does t-test consider?

Select a few correct answers