# Improved confidence limits for comparing two independent binomial proportions

The two-sample chi-square test (e.g. CROSSTABS in SPSS) can be used to test statistical significance of the difference in two independent proportions but this test does not provide a confidence interval on the magnitude of this difference.

Newcombe (1998) further goes on to compare various methods for giving confidence intervals for the difference in a pair of proportions from two different groups. he concludes that the Wald confidence interval is biased when the difference in proportions is close to zero or (+/-) one. As for a single proportion he recommends the two-sample analogue of the Wilson one-sample confidence interval.

This EXCEL spreadsheet computes the two sample analogues of the methods in the one-sample spreadsheet.

References

Moore DS & McCabe GP (2006) Introduction to the practice of statistics (5th ed.). WH Freeman:New York. (This mentions the two sample analogue of the Agresti-Coull method which was not mentioned in the original paper which dealt with the one-sample case).

Newcombe RG (1998) Interval estimation for the difference between independent proportions: comparison of eleven methods. *Statistics in Medicine* **17** 873-890.