ANOVA: The Mean Within Sums of Squares as an Average Variance The Mean Within Sums of Squares

(MSW) is used to test for treatment differences in completely randomized analysis of variance designs. The Mean Within Sums of Squares is the Sums of Squares Within (SSW) divided by its degrees of freedom. The MSW is also known as the Mean Error Sums of Squares (MSE) or the Mean Residual Sums of Squares (MSR). This Mean Sums of Squares is the weighted mean of the variances for each treatment in the ANOVA, and it's use as the error term depends on the assumption of homogeneity of variance. The assumption of homogeneity of variance for completely randomized ANOVA designs1 means that the data for each treatment2 has a constant variance or standard error. The specific value of this constant variance is usually unknown and must be estimated from the data. The MSW provides the "best " estimate for this variance since it uses all the data available in the ANOVA. Calculation of the MSW should follow these steps: 1. First check the homogeneity of variance assumption. There are several tests available (Milliken and Johnson, pgs 18-24), but most are complicated to calculate. The simplest test available is Hartley's Fmax-test, and it is useful for a quick check. The observed Fmax-value i