Chi-square test
Find sample size:

If you know the two proportions, use this form to find how many subjects you need.
Find effect size:

If you know the proportion for group 1 and the number of subjects, use this form to find largest and smallest detectable proportions for group 2.
Group 1 proportion:
Group 2 proportion:
Click here for sample size:
You will need subjects in Group 1
You will need subjects in Group 2
N for Group 1:
Group 1 proportion:
Click here for effect size:

You can detect p2 <
You can detect p2 >
For different power or significance level, change the fields below:
Alpha: Prob(reject H0 when H0 is true)
Power: Prob(reject H0 when H1 is true)
For unequal sample sizes, change the ratio below:
Group2/Group1:
The calculations here use equations 4.18 & 4.19 in J.L. Fleiss, et al., Statistical Methods for Rates and Proportions, 4th ed., and are consistent with their Table A.4. The results here may differ from other webpages or software because most of them ignore the continuity correction. The Fleiss book discusses the importance of the continuity correction; see also Levin and Chen, American Statistician 53:62-66.
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v. 03/03
Contact: sfh2@columbia.edu