Variance Explained in 2 x 2 Contingency Tables (1 of 3)

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The phi (φ) coefficient is used as an index of the strength of the relationship between variables in a 2 x 2 contingency table. Phi can be computed as the correlation between the two dichotomous variables.

Consider a hypothetical study investigating whether a desensitization program for people with snake phobias works better than a control treatment consisting of reading about how snakes help keep the ecological balance intact. Following the treatment, each subject is asked to pick up a harmless snake and place it in a bag. The results were as follows: Of the 10 subjects in the experimental condition, 8 were able to perform the task. Of the 10 subjects in the control condition, only 1 would perform the task. The section on the chi square test of independence shows how to test to see if the difference is significant. To compute the correlation (φ) between group (experimental versus control) and outcome (success of failure), give each subject two scores. The first score is a "1" if the subject was in the experimental group or a "0" if they were in the control group. The second score is a "1" if they succeeded at the task or a "0" if they did not.