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 $\Delta\mu = \mu_m - \mu_2$. 2. Calculate the estimated variance of this difference We use eqn. 2.11 to do get $Var(\Delta\mu)$. 3. Form t $t= \Delta\mu/\sqrt{Var(\Delta\mu)}$. 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 $H_0$.