Explaining the Two-Sample t-Test

One of the most important tools in research

TLDR:

The two-sample t-test looks the way it does because of the Central Limit Theorem and standardization. This is exactly why the one-sample t-test looks like how it does, and for that matter, the proportion tests as well. Knowing why the tests look like they do is much simpler than memorizing a long list of hypothesis tests in Statistics 101. In short, the Central Limit Theorem ensures that the distribution of the sample means is approximately Normal; the standardization property is why the test statistic looks the way it does.

Using the Null Hypothesis Significance Testing framework, we just need to identify the parameter we want to study, a null hypothesis, a test statistic and the null distribution.

There are other small details about the two-sample t-test that I glossed over: what can we assume about the variances? What about different sample sizes for the two groups? Due to the t-test being implemented in R, we don’t really have to worry about these details. If viewers/readers really want to know more about those gritty details, I’m happy to talk about those in another video.