SIMPLE COMPARISONS

The objective of this theme is to give an overview of the most common methods for simple comparisons of groups. The comparisons are described as simple because we are only comparing a solitary outcome across two or more groups, for example, the effect of a fertility treatment on conception rates. There is no control for other variables. As such these “simple” comparisons are more commonly used for experimental type studies or as a preliminary analysis for an observational study.  When we need to control for other variables, such as in an observational study, then more sophisticated methods such as multiple regression are required. We will look at regression in the theme on statistical modelling  (Topic 14).

The first topic of this theme (topic 7) covers approaches that involve estimating parameters from a distribution, and hence involve making assumptions about the sampling distribution of the point estimate; these are called parametric approaches. We cover comparisons involving means and proportions. The second topic (topic 8) gives an overview of non-parametric tests; these are used when assumptions for parametric tests are violated.

There are many different statistical tests for simple comparisons and a whole unit could be put together solely to describe them all. However, you will hopefully be able to spot the common elements that run through all the tests we cover, particularly with respect to the underlying concepts and interpretation. In fact, if you’ve understood all of the ideas in the earlier topics on confidence intervals and p-values, then you’ll find that most of this topic is just applying those ideas to a series of slightly different settings defined by the type of outcome variable and the number of groups to be compared.