What’s Under the Hood of a Paired Student’s t-Test?

Once you do statistics by hand, you understand the concepts a little bit better.

There’s a neat YouTube channel I discovered a couple of years ago where Eugene O’Loughlin, Ph.D., does some statistical analyses by hand. I thought it was neat because it allows us to see that statistical analysis is not something that only computers can do. Sure, computers can do these analyses much faster than we ever could, but you really can do a lot with just a pen and paper and a good calculator.

Of course, you need some knowledge of numbers and how they work, and the basic statistical concepts that will help you get the work done, but there’s not much else after that. For example, here is Dr. O’Loughlin doing a paired t-test by hand:

Paired t tests are used to test the theory that the average score of a test taken by one group is different (or the same) as the average score of another test taken by the same group. (One group, two tests… Paired.) Now that you’ve seen the video on how to do it by hand, how can you do it in R in a way that teaches you how the base t.test function works internally?