Two-way analysis of variance is where the rubber hits the road, so to speak. This extends the concepts of ANOVA with only one factor to two factors. When there are two factors this means that there can be an interaction between the two factors that should be tested. As one might expect this concept can be extended beyond just two factors to an N number of factors.
This example will provide a fairly complete example of a factorial design where there are three factors and a (continuous) response value. It also provides the tests for ANOVA diagnostics including homogeneity of variance and tests for normality.
Normally, these examples are only one or two pages and are brief. However, analysis of variance can be complex and this example is quite a bit little longer but provides the necessary tools for a sufficient analysis.