8: A general formula for t-calc

Let’s summarise what we had on the last page. Here are the two important pieces: the difference between the means (call that DM) and the standard error of the difference of the means (SEDM). That’s easy enough to remember:


If you look it up in a textbook or on the web, you may see something that looks much more frightening:

Don’t despair – the subscripts 1 and 2 refer to the two groups (control and treatment), the x with the bar over the top is shorthand for mean, and the letter s is shorthand for standard deviation and the letter n is the sample size.  Also, because both terms under the square root sign have been squared (as part of the Pythagorean theorem) you don’t see a square root sign over the sample sizes.  Despite looking more complicated, this formula combines in one place all the separate steps we took to calculate t.

Either formula will give exactly the same final answer!