# The Wary Student, Part 7: Main-Effect Results

For every hypothesis, a homogeneity of variance test (HOV) was first run, using both Leven’s criterion and a calculated Fmax value. Next, an analysis of variance (ANOVA) was used to attempt to reject the appropriate null hypothesis. Two measures of practical effect size are reported. Î·2, which explains the fraction of the variation within the sample explained by the IV, can be calculated at SSb / (SSb + SSw). Ï‰2, which shows the fraction of the variation in the sample that is explained by the IV, is derived with the formula Ï‰2 = (SSb – (k â€“ 1)(MSw)) / (SSb + SSw + MSw). Then, in the next section, an interaction effect is discussed.

Hpositive: Does Cognitive Load impact Positive Cooperation?

The HOV and ANOVA give the following results:

 Purpose Test Value Interpretations HOV Levene’s F(1,177) = 4.340 p = .039 Reject homogeneity of variance HOV Fmax 1.61 / 1.27 = 1.43 Safe to assume homogeneity of variance Between Participants ANOVA F = 2.257 p = .135 Î·2 = .013 Ï‰2 = .007 No statistically significant effect

The results do not allow the null hypothesis. While the practical significance of cognitive load on positive cooperation is 7%, the statistical effect, the p value of .135 indicates that results could be achieved by chance 13.5% of the time. For comparison, because three hypotheses are being made a p value of .0033 would be needed to even say that the results would only be found by change 5% of the time. While evolutionary responses have been found even after cognitive load has been shown to be ineffective (Hewstone, Hantzi, & Johnston, 1991; Kurzban, Tooby, & Cosmides, 2001), the results are clearly not encouraging. Finally, while the homogeneity results were ambiguous, with Fmax and Levene’s test giving different results, this is not a concern as failing to reject HOV increases the chance of a false positive, which is not an issue in this case.

Hneutral: Does Cognitive Load impact Neutral Cooperation?

The HOV and ANOVA give the following results:

 Purpose Test Value Interpretations HOV Levene’s F(1,179) = .013 p = .013 Reject homogeneity of variance HOV Fmax 1.61 / 1.27 = 1.41 Safe to assume homogeneity of variance Between Participants ANOVA F = .003 p = .955 Î·2 = 0 Ï‰2 = 0 No statistically significant effect

The results were neutral cooperation were even less promising that the results for positive cooperation. Not only was there no practical significance to the results, such results would be found by change nearly 96% of the time. As for the previous hypothesis, problematic results on the HOV tests are a non issue as the null hypothesis Hneutral is not rejected.

Hnegative: Does Cognitive Load impact Negative Cooperation?

The HOV and ANOVA give the following results:

 Purpose Test Value Interpretations HOV Levene’s F(1,179) = 29.568 p < .001 Cannot reject homogeneity of variance HOV Fmax .697 / .315 = 1.99 Safe to assume homogeneity of variance Between Participants ANOVA F = 7.109 p = .008 Î·2 = .038 Ï‰2 = .033 Statistically significant effect at corrected .05 and uncorrected .01 level, which explains % of variance in the population

While results were poor with positive and neutral cooperation, the negative null hypothesis can be firmly rejected. The p value of .008 is enough to say that the results would be achieved by change less than 2.5% of the time, even after adjusting for running three hypotheses. The ANOVA indicates that the cognitive load condition explained more than 3% of the variation within the population. Because the null hypothesis is rejected, the disagreement between Levene’s test (which fails to reject heterogeneity of variance) and Fmax becomes a concern. Adding a factor to the analysis, as is done in the next section, clarifies the results for this hypothesis and removes the fear that unequal variance is unduly biasing the results.

The Wary Student, a tdaxp research project
1. Abstract