How two-way ANOVA works

Two-way ANOVA determines how a response is affected by two factors. For example, you might measure a response to three different drugs in both men and women. The ANOVA table breaks down the overall variability between measurements (expressed as the sum of squares) into four components: 

􀀹 Interactions between row and column. These are differences between rows that are not the same at each 

    column, equivalent to variation between columns that is not the same at each row. 

􀀹 Variability among columns. 

􀀹 Variability among rows. 

􀀹 Residual or error. Variation among replicates not related to systematic differences between rows and        

    columns. 

With repeated-measures ANOVA, there is a fifth component: variation between subjects. The ANOVA table shows how the sum of squares is partitioned into the four (or five) components. Most scientists will skip these results, which are not especially informative unless you have studied statistics in depth. For each component, the table shows sum-of-squares, degrees of freedom, mean square, and the F ratio. Each F ratio is the ratio of the mean-square value for that source of variation to the residual mean square (with repeated-measures ANOVA, the denominator of one F ratio is the mean square for matching rather than residual mean square). If the null hypothesis is true, the F ratio is likely to be close to 1.0. If the null hypothesis is not true, the F ratio is likely to be greater than 1.0. The F ratios are not very informative by themselves, but are used to determine P values.