2.9 How to do the t-test

We have two groups and we want to figure out the likelihood of $H_0$ being correct. Are these two groups identical?

1. Calculate the difference in the means

We use eqn 2.1 to calculate ${\mu }_m$ and ${\mu }_w$ and subtract, getting $\mathrm{\Delta }\mu ={\mu }_m-{\mu }_2$.

2. Calculate the estimated variance of this difference

We use eqn. 2.11 to do get $Var(\mathrm{\Delta }\mu )$.

3. Form t

$t=\mathrm{\Delta }\mu /\sqrt{Var(\mathrm{\Delta }\mu )}$.

3. Calculate likelihood

The number of degrees of freedom $\nu$, is one less than the total number of data points, that is it equals $n_m+n_w-1$. With that and t, we feed it into a program, or use a table to calculate the area under the curve as pictured in fig. 2.7.

4. Verdict

If this area is less than our cutoff for significance, say $p_0=.05$ we reject $H_0$ and say the difference is statistically significant. Otherwise, we can’t reject $H_0$.