The point estimate of a difference is found by taking the difference in the sample means: \(\(\large \bar{x}_{esc} - \bar{x}_{control}\)\)

Using the \(t\)-distribution for a difference in means

The \(t\)-distribution can be used for inference when working with the standardized difference of two means if - Independence, extended: The data ase independent within and between the two groups, e.g. the data come from independent random samples or from a randomized experiment - Normality: We check the outliers rules of thumb for each group separately. The standard error may be computed as \(\(\large SE=\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}\)\) If statistical software isn't available, use the smaller of \(n_1-1\) and \(n_2-1\) for the degrees of freedom.

As with one-sample cases, compute the standard error using the sample standard deviations rather than the population standard deviations.