In the Death Penalty Study, researchers used a non-probability dimensional sample of 1,600 U.S. residents to conduct an experiment. Through a mock trial, researchers also asked people to state their intended actions regarding the execution of a serial killer. As a matter of convention, statistical significance is reported here. However, in a strict sense, 'statistical significance' is not an appropriate tool for understanding how various characteristics of people influence each other. Tests of statistical significance are appropriate for probability samples only. In reporting findings of this study, researchers indicate how "influential" one characteristic is over another characteristic. This is reported as effect size, using a statistic called Eta Squared.

For example, about 26% of the people in the study oppose all methods of execution (Abolitionists). One characteristic that influences a person to identify as an Abolitionist is gender. Women are more likely to be Abolitionists (30%) than men (22%). The relationship is 'statistically significant.' However, with a large sample of 1,600, even small differences between men and women will be 'statistically significant.' According to Eta Squared, the 8-percentage point difference between men and women indicates that gender exerts only a 'small' influence on opposition to all methods of execution. 

Unlike statistical significance, the Effect Size Yardstick (see diagram) is a more useful tool. Eta Squared is a statistic that measures the 'strength' or 'power' of one characteristic (gender, for example) over another (rejecting all methods of execution, for example). Although the influence of gender on Abolitionist status is 'statistically significant,' gender only exerts a very small (weak) influence. Eta Squared is only .01. Researchers would say that gender accounts for only 1% of the variance in Abolitionist status of people in the study.  The other 99% is not accounted for. The following diagrams will illustrate how you can interpret effect size and Eta Squared.

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