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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 $H_0$.


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josh 2010-10-20