Two-Group versus Multiple-Group Analysis

In a simple statistical analysis we may be characterizing one group of data or comparing that group with a standard value. It is slightly more intricate to compare two groups when we want to characterize each group and determine whether the groups are statistically different. Much more concern must be applied to the situation when we have three or more groups. In this case of multiple groups, two distinct types of questions can be asked. First, we might wish to know whether the groups are significantly different or whether they are all the same (with any numerical differences attributed solely to random fluctuations). Second, if we do conclude that the groups are statistically not all the same, we might want to know which groups are different from one another—that is, are they all distinct or are just one or a few different whereas the rest are similar to each other.

In summary, three questions should be asked when choosing between tests (see Table 23-3 ):

1. One group, two groups, or many groups?
2. Paired or unpaired groups?
3. Parametric (interval data following a normal distribution) or nonparametric methods?