Exact Unconditional Tests

Exact Unconditional Homogeneity/Independence Tests for 2X2 Tables

This performs exact, unconditional tests of homogeneity (binomial model) or independence (multinomial model) for 2X2 tables. These tests are usually uniformly more powerful than Fisher's exact test. See references below.

Cell Counts:

Model: For binomial model, the row totals are the fixed binomial sample sizes.
binomial multinomial

Hypothesis: The one-sided hypotheses are
Ho: odds ratio >= 1 vs Ha: odds ratio < 1 more explanation
one-sided two-sided

Test Statistic:
Fisher's Exact-Boschloo z-pooled z-unpooled

Confidence Interval Method:
yes no

Confidence Coefficient:

REFERENCES

Berger, Roger L. (1996). "More powerful tests from confidence interval p values." American Statistician, 50, 314-318.
[ Download paper]
Berger, Roger L. (1994). "Power comparison of exact unconditional tests for comparing two binomial proportions." Institute of Statistics Mimeo Series No. 2266.
[ Download paper]
Berger, Roger. L., and Boos, Dennis D. (1994). "P values maximized over a confidence set for the nuisance parameter." Journal of the American Statistical Association 89, 1012-1016.
[ Download paper]

Computer program
xun2x2v2.f, a Fortran program to perform these analyses for larger sample sizes.

Created 12/12/96. Last modified 04/29/05.
Questions or comments to Roger L. Berger.