The Two Factor Analysis

Such an example was discussed in Qiapter VII (t). Table 11.1 below gives the degrees of freedom and components of variance. 

Source of Variance Degrees of Freedom Components of Variance 

The tests of significance are obvious. If factor G is to exist, i.e. if a is to be greater than zero, then we must have — tag -t- oo must be greater than oo  

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There are various other ways of examining the variate in question in this case. Let us first examine simple one-way ANOVA of the variate by sex as in Table 16.16. In neither of the two cases was there any indication of significant treatment differences at any reasonable level. Because the two sexes did not show any pretreatment differences based on the two-factor analysis of the covariate, let us combine the two sexes and analyze the data by one-way ANOVA as in Table 16.17. In this case, because of the increased sample sizes for combining the two sexes, there was indication of some treatment differences (p = 0.0454). Unfortunately, this analysis assumes that because there were no pretreatment differences between the two sexes, that pattern will hold during the posttreatment period. That often may not be the case because of biological reasons. 

The two-factor analysis has thus become one factor (Grades) with t replications. This amounts to pooling the degrees of freedom and the sums of squares of the T main effect in Table 11.1 with the Residual. This gives us Table 11.19 ... 

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