Table PTT3. Two-group Chi-square test comparing proportions in C categories (equal n’s)

Power, sample size, or effect size are computed based on central and non-central chi-square, see Lachin, J.M. “Sample size determinations for r x c comparative trials” Biometrics 33(1977) pp. 315-324. The non-centrality parameter is 2nΔ² where the effect size Δ² is defined in the side-table and row title. Figure PTT3 shows computations for one example, with Figure PTT3S showing the side-table computations for this example. Values for this example checked against calculations done using the 2000 version of UnifyPow. A SAS module for sample-size analysis, (see www.bio.ri.ccf.org/power.html) as well as PASS 6.0 and Power and Precision. Additional values checked against UnifyPow: significance level .001, .20, power of 80% and 95% and effect sizes of .0001669 and .0417 for 2 categories, .001 and .3510 for 8 categories, values of n per group equal to 5 and 5000.

Figure PTT3S. The actual value of Δ ² is .054501, the value seen when the side-table results are transferred to the main table.

Figure PTT3. In column 1, nQuery Advisor® 7.0 has solved for n, in column 2 for power, and in column 3 for effect size. Note that since the actual power computed in column 2 is 90.24%, the effect size corresponding to 90% power is smaller than .0545.