  Course Content

# Learning Statistics with Python

Learning Statistics with Python

##   t-test Mathematically

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 taken into consideration. To account for the difference between the means, we simply calculate that difference: The situation becomes more complex when it comes to variance. The t-test assumes that the variance is equal for both samples. We will delve deeper into this in the t-test assumptions chapter. To estimate the variance from two samples, the pooled variance formula is applied: 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 in the most intuitive manner. However, this approach ensures that t follows the t-distribution, as we'll explore in the next chapter.

#   What sample properties does the t-test take into account?

## Select a few correct answers

Everything was clear?

Section 6. Chapter 3