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In-Depth Information
3.6.4 MEAN SQUARES ARE NOT ADDITIVE
Note that, unlike the sum of squares and the degrees of freedom, the mean
squares are not additive. A mean square can be roughly thought of as
an average sum of squares. The averages of between-groups and within-
groups sources of variance are not directly additive because the degrees of
freedom (the denominators of the calculation) are based on very different
kinds of counts - the between-groups sum of squares is divided by the
one less than the number of groups, whereas the within-groups sum of
squares is divided by the sum of the degrees of freedom of each group.
3.7 WHERE ALL THIS LEADS
With the mean square values together with their associated degrees of
freedom in hand for each source of variance, we are ready to compute
the
F
ratio, determine its probability of occurrence based on its sampling
distribution, determine whether the mean difference was statistically sig-
nificant, and compute an eta squared value representing the strength of the
effect of the independent variable. These portions of the summary table,
and some of the issues surrounding them, are discussed in Chapter 4.
