Naive Analysis of Variance

The Analysis of Variance is often taught in introductory statistics courses, but it is not clear that students really understand the method. This is because the derivation of the test statistic and p-value requires a relatively sophisticated mathematical background which may not be well-remembered or understood. Thus, the essential concept behind the Analysis of Variance can be obscured. On the other hand, it is possible to provide students with a graphical technique that makes the essential concept transparent. The technique discussed in this article can be understood by students with little or no background in probability or statistics. In fact, only the ability to add, subtract, compute averages, and interpret histograms is required. (Contains 7 tables and 3 figures.)