Assume You Have Conducted a Study in Which You Were

Assume you have conducted a study in which you were interested in the relationship between the number of police officers/population ratio and the level of overall job satisfaction within the individual police department. You arbitrarily divide the variable officer/population ratio into high, medium, and low (with high having the greatest number of officers per 1,000 inhabitants) and the variable job satisfaction into low, medium, and high. You are utilizing a random sample of 121 police departments from all over the United States. The results are to be found in the table below. Compute gamma and interpret your results. Indicate whether gamma is a symmetric or asymmetric measure of association.
Officer/population
ratio
$\begin{array} { l l l l c } \text { Job } & \text { Low } & \text { Medium } & \text { High } & \text { Totals } \\ \text { satisfaction } & & & & \\ \text { Low } & \text { A } & \text { B } & \text { C } & 45 \\ & 31 & 12 & 2 & \\ \text { Medium } & \mathrm { D } & \mathrm { E } & \mathrm { F } & 44 \\ & 8 & 32 & 4 & \\ \text { High } & \mathrm { G } & \mathrm { H } & \mathrm { I } & 32 \\ & 3 & 12 & 17 & \\ \text { Totals } & 42 & 56 & 23 & 121 \end{array}$