Degree of freedom. Two sampled test

Question

According to this blog/article:

To calculate degrees of freedom for a 2-sample t-test, use N – 2 because there are now two parameters to estimate.

What parameters are they talking about? 2 means: for group 1 and mean for group 2? Or something other?

Answer 1

The "classical" $t$-test is used to test the hypothesis, whether the two samples come from the gaussian distributions with the same mean, assuming that the variances are identical (!). Under this hypothesis, the $t$-value follows a $t$-distribution with N-2 degrees of freedom. And the 2 parameters to estimate are:

• mean (if it is the same) and
• variance (which is assumed to be the same).

If the two variances are not assumed to be the same, everything is more complicated. The $t$-value no longer follows a $t$-distribution. The alternative calculation procedure for this case is called the Welch procedure.