Comparing the populations

For two-group data sets, we usually want to compare the underlying populations. In particular, the main questions of interest are:

Randomness of sample difference

Unfortunately, cannot give a definitive answer to questions about µ2 - µ1 since it is a random summary statistic — it varies from sample to sample. The distribution of must be understood before we can make any inference about µ2 - µ1.

Effect of zinc on colds

A simulation is used to demonstrate the fact that the difference between the two sample means has a distribution.

Birth weights in summer and winter

In practice, the underlying population means (and their difference) are unknown, and only a single sample from each group is available. The data set below is a typical example.