A POWER STRUGGLE: BETWEEN- VS. WITHIN-SUBJECTS DESIGNS IN DEDUCTIVE REASONING RESEARCH

Abstract

This experiment examined the relative merits of using within-and between-subjects designs to investigate deductive reasoning. Two issues were investigated: 1) the potential for expectancy and fatigue effects when using within-subjects designs, and 2) the relative power of within- vs between-subjects designs. Participants were presented with problems in a standard belief-bias paradigm in which the believability of putative conclusions varied orthogonally to their validity. The belief bias effect, as well as the effect of validity, and the interaction between beliefs and validity, were not affected by reasoners’ expectations regarding the number of problems they had to solve. The effect of beliefs and the belief by validity interaction were only marginally affected by the number of problems solved, despite adequate power to observe an effect. Thus, neither expectancy nor fatigue appear to have affected performance, suggesting that there are few drawbacks to using a within-subjects design. In contrast, however, a power analysis clearly established the desirability of using within- relative to between-subjects designs. Within-subjects designs require far fewer participants to detect effects of comparable size; this was especially true for higher-order (interaction) effects. Finally, we provide a power analysis of within- and between-subjects designs that should be of general utility to researchers planning studies using proportions as a dependent measure.