## Counterbalancing

Show students how to interpret the results of a counterbalanced design (Going over Tables 13.7 - 13.10 will help). Then, if you have time, show students how to counterbalance complex designs (use handout 13.2). Usually, explaining how to interpret the results of a counterbalanced design takes a class period because

1. Most students have not seen an ANOVA summary table for a mixed design before.

2. Students may confuse the within-subjects factor of order and the between-subjects factor of counterbalanced sequence. To help them, go through several examples and keep asking/prompting/telling them " What three effects are we looking for (Treatment, Counterbalanced sequence, and First vs. Last Trial)? What does a treatment main effect tell us? How do the two (counterbalanced) groups differ? What will the main effect of the between groups factor of counterbalancing tell you? Now, how do find out about your performance on the first trial versus your performance on the last trial?"

3. If the investigator makes "order"the within-subjects factor in the analysis, then the interaction reflects the effect of the treatment, but if the investigator makes the treatment the within-subjects variable in the analysis, the effect of order is reflected in the interaction term. Fortunately, the investigator usually makes the treatment the within-subjects factor.

If you want students to realize that "order" could be a main effect or an interaction, give them a data set and have them do the analysis on the computer twice. The first time, the treatment is coded as the within-subjects variable. The second time, order is coded as the within-subjects variable. Then, have students compare the two printouts. Much to their surprise, they will find that the interaction in analysis one is the same as the main effect in analysis two, and vice-versa.

From this demonstration, some students gain

1. An increased appreciation of how important it is to properly code data in within subject designs; and

2. an increased understanding of what interactions represent.

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