Research Methods Chapter 9: Factorial Designs

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Suppose we hypothesize that as room temperature increases from 20 to 35 degrees celsius, this will have a nonlinear effect on peoples task performance. We want to determine whether this nonlinear effect will be under the same conditions of low and high humidity. If we only included these two temperature levels, then we would only be able to asses linear relations. It immediately apparent that the yellow and orange lines are not parallel, and this lack of parallelism suggests the presence of an interaction. As room temperature increases, errors increase both when humidity is low and high, but the temperature change has a larger effect when humidity is high. We would use statistical analyses to determine whether this finding is statistically significant and, if it is, conclude that an interaction is present. Still, even with an interaction, with only two levels of temperature for which to plot data, the graph implies that increases in temperature have a linear effect on performance at each level of humidity. Suppose we included 4 levels of temperature, we can again see the interaction: The increase in temperature has a stronger effect on task performance when humidity is high, but now the nonlinear effects of temperature are revealed at both levels of humidity. Regardless of humidity, the increase in room temperature has little effect on performance. Beyond that point, errors increase at higher temperature levels more rapidly when humidity is high than when it is low. If we also wish to examine whether humidity has a nonlinear influence on performance, we will need to create at least three humidity levels.
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