ABSTRACT
Data summarizing ANOVA computations are usually presented in an ANOVA table which identifies the sources of variance, sums of squares and degrees of freedom, means squares and F-statistics. (See for example, Figure 8.13.)
Source of variation Degrees of Freedom (df)
SS MS (SS/df)
F (MSmod/MSerror)
Consider for example the data presented in Table 8.9. The df(between groups) is (3-1)=2. A degree of freedom is lost because deviations from the overall mean sum to zero. The constraint here is that the deviations of the subgroup means from the overall mean must sum to zero hence 1 df is lost. The degrees of freedom between individuals within groups, what is usually termed df(error), is again given by the constraint that deviations from each subgroup mean sum to zero. Here there are three subgroup means so the df are: (n1-1)+(n2-1)+(n3-1)=(8-1) +(8−l)+(8−1)=21. The error degrees of freedom can be evaluated simply by subtraction, df(error)=df(corrected total)−df(between groups)=(24-1)−2=21. The
principle of evaluating the degrees of freedom is important to grasp. The corrected total degrees of freedom is simply, number of subjects −1=(24-1)=23.
