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Overview
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| City Size/Arenas | Small | Medium | Large |
| Weak Mayor | a = 10 | b = 5 | c = 2 |
| Strong Mayor | d = 10 | e = 15 | f = 20 |
P = a(e+f) + bf = 10(15+20) + 5*20 = 450
Q = c(d+e) + bd = 2(10+15) + 5*10 = 100
gamma = (P - Q)/(P + Q) = (450-100)/(450 + 100) = .636
Since gamma has a known sampling distribution approximating normal for large samples it is possible to compute its standard error and significance. SPSS and other major packages report the significance level of the computed phi value. Computation of the variance of gamma is given in Liebetrau (1983: 75-76).
| CITY SIZE BY RIOT INTENSITY | City Size 1 | City Size 2 | Row Totals |
| Riot Size 1 | 1 | 0 | 1 |
| Riot Size 2 | 3 | 4 | 7 |
| Column Totals | 4 | 4 | 8 |
tau-b = (4 - 0) / SQRT[(4 + 0 + 12)(4 + 0 + 3)] = 4/SQRT[112] = .378
Since tau-b has a known sampling distribution it is possible to compute its standard error and significance. SPSS and other major packages report the significance level of the computed tau-b value. The formula for the variance of tau-b is given in Liebetrau (1983: 70).
| CITY SIZE BY RIOT INTENSITY | City Size 1 | City Size 2 | City Size 3 | Row Totals |
| Riot Size 1 | 4 | 2 | 0 | 6 |
| Riot Size 2 | 2 | 3 | 4 | 9 |
| Column Totals | 6 | 5 | 4 | 15 |
tau-c = (36 - 4)*[4/(152(1))] = 128/225 = .57
Since tau-c has a known sampling distribution it is possible to compute its standard error and significance. SPSS and other major packages report the significance level of the computed tau-c value. The formula for the variance of tau-c is given in Liebetrau (1983: 73-74).
| CITY SIZE (X) BY RIOT INTENSITY (Y) |
City Size 1 | City Size 2 | City Size 3 | Row Totals |
| Riot Size 1 | 6 | 0 | 0 | 6 |
| Riot Size 2 | 0 | 5 | 4 | 9 |
| Column Totals | 6 | 5 | 4 | 15 |
dyx = (P - Q)/(P + Q + Y0)
dyx = (54 - 0)/(54 + 0 + 20) = .73
dxy = (P - Q)/(P + Q + X0)
dxy = (54 - 0)/(54 + 0 + 0) = 1.0