Binomial Exact Test

This appendix documents binomial exact test calculation methods and presents staff's comparison of Z-test and binomial test results. Calculation methods and examples for rate measures are presented in Attachment 1.

Convergence of Z-test and binomial exact test results

Staff compared Type I error values (alpha probabilities) produced by the Z-test with those produced by the binomial test for submeasure. As with the Fisher's Exact Test, staff found that the results from the two tests converge for large sample sizes. Specifically, the size of the difference between the alphas calculated for each test was highly negatively correlated with the natural log of the CLEC sample size as listed in Table 1. "Highly negatively correlated" means that as sample size increases, the difference between the Z-test alpha and the binomial test alpha decreases in a close and predictable relationship.

Table 1

N

Correlation coefficient

p

117

-0.93

0.00

Table 2 lists the extent of the differences between the alphas for the two tests and illustrates the convergence of the results for the two tests.

Table 2

Sample sizes

N

Mean difference

Median difference

1 to 100

61

0.32

0.38

101 to 300

37

0.05

0.05

300 +

19

0.008

0.00

Sample sizes	N	Mean difference	Median difference
1 to 100	61	0.32	0.38
101 to 300	37	0.05	0.05
300 +	19	0.008	0.00