In some experiments with several observations per cell the analyst is prepared to assume that there is no interaction between groups and blocks. Any apparent interaction found is then attributed to random error. When such an assumption is made, the analysis is carried out in the usual way, except that what were previously the interaction and error sums of squares are now added together to form a new error sum of squares. Similarly, the corresponding degrees of freedom are added. If the assumption of no interaction is correct, this approach has the advantage of providing more error degrees of freedom and, hence, more powerful tests of the equality of group and block means.
For the study of Exercise 15.47, suppose that we now make the assumption of no interaction between dormitory ratings and student years.
a. State, in your own words, what is implied by this assumption.
b. Given this assumption, set up the new analysis of variance table.
c. Test the null hypothesis that the population mean ratings are the same for all dormitories.
d. Test the null hypothesis that the population mean ratings are the same for all four student years.