Analysis of Variance (ANOVA) compares differences in average scores directly, rather than differences in percentages for those who agree/disagree.* Relevant to the Death Penalty Study, eta squared indicates how much influence pro-death penalty beliefs exert on the intended actions of execution actors. The larger the Eta Squared value, the more influence is exerted.

When all four groups are compared and tested, the effect size of pro-death penalty beliefs is very large. Eta Squared for this test is .36, where an Eta Squared of .25 is considered a large (strong, powerful) effect size. This is because the average pro-death penalty belief scores are very low among Abolitionists (mean=2.37), when compared to the other three groups.

When the three pro-death penalty groups are compared (Abolitionists excluded), the effect size (Eta Squared) is .07. This is below a medium effect size of .09 but closer to a medium effect size than a small one (Eta Squared=.01). This effect size is because Executioners have higher pro-death penalty belief scores (mean=3.76) than do the two types of soft abstract supporters.

When Soft Abstract and Hard Abstract Supporters are analyzed separately, the effect size is very small. Hard Abstract Supporters have higher average scores (mean=3.41) than Soft Abstract Supporters (mean=3.32), but the difference in averages is small. Eta Squared is only .005. This is about half an effect size (Eta Squared=.01) that is considered the standard for small effect size.

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*Every person in the study had an average "score" for this belief system. That score ranged from 1.00 (strongly disagree) to 5.0 (strongly agree), where 3.0 is neither agree/disagree. Analysis of Variance (ANOVA) tests differences in average scores across groups. Inherently, ANOVA is a more powerful statistic than the Chi-Square statistic. As with the Chi-Square statistic, a Sig. less than .05 indicates that differences in averages are significant. Further, ANOVA provides an estimate of effect size (Eta Squared). With non-probability samples, effect size is a more meaningful measure of the influence of underlying belief systems on roles (intended actions) that people play as execution actors.