Essentials

REPEATED-MEASURES ANOVA 187the F ratio for the between-subjects (instruction) main effect: F instructionMS instruction/MS w 16/3 5.33. We have actually averaged across the three typesof sound and then ignored that factor completely, performing an ordinary onewayANOVA (as in Chapter 5) on those averages (subject means). The critical Ffor this part is based on df groupand df w; in this case, F .05(1, 10) 4.96, so the maineffect of instruction is significant.The Within-Subjects PartIf you subtract SS wfrom SS within-cells(49.333 – 30 19.333) you get the SS for theRM error term. We will call this SS subRM, because it is the same as the subject bytreatment interaction in the one-way RM ANOVA, except that it is equivalent tocalculating that SS term separately for each group of participants and then adding,rather than calculating it across all participants from all groups. For some experiments,calculating SS subRMseparately for each group can bestow a considerableadvantage, as we will see shortly. Finding df subRMis easy because it always equalsdf wtimes df RM; for this example it is 10 2 20, so MS subRMequals 19.333/20 .967. Now that we have found the error term for the main effect of the RM factor,we can calculate the main effect of sound type: F sound MS sound/MS subRM12.25/.967 12.67. The rationale for this error term is the same as for the onewayRM ANOVA. The more consistently that participants respond to the severalRM conditions, the smaller is SS subRM, regardless of overall differences in thelevel of participants (the latter contributes to SS w). The critical F for this effect isbased on df RMand df subRM; in this case, F .05(2, 20) 3.49, so the main effect ofsound type is significant.What may be surprising is that MS subRMis also used as the error term for theF ratio testing the interaction of the two factors. However, this arrangementmakes sense when you look at a graph of data from a hypothetical mixed design(see Figure 8.2). The individual participants are shown, as well as the cell means(heavy lines). The more that the participants in a particular group are parallel toeach other, the more they will be parallel to the heavy line for that group. The reliabilityof the interaction is a function of the extent to which participants withina group follow the same pattern, and this is measured by MS subRM. Note particularlythat if MS subRMwere calculated across all participants it would be affectedby the fact that participants in one group exhibit a generally different patternfrom participants in the other group. When MS subRMis in effect calculated separatelyfor each group, MS interdoes not affect the error term.Now we can calculate the third F ratio; F inter MS inter/MS subRM 5.083/.967