Compare proportion with a dichotomous outcome between two samples, using the Chi-squared statistic (or z test).

Instructions: Enter parameters in the red cells. Answer will appear in the blue cells.

α (two-tailed) = Threshold probability for rejecting the null hypothesis. Type I error rate.
β = Probability of failing to reject the null hypothesis under the alternative hypothesis. Type II error rate.
q1 = Proportion of subjects that are in Group 1 (exposed)
q0 = 0.500 Proportion of subjects that are in Group 0 (unexposed); 1-q1
P0 = Risk in Group 0 (baseline risk)

Enter any ONE of the following three parameters (the other two will be calculated automatically):

P1 = Risk in Group 1 (exposed)
OR = Odds ratio
(P1/(1 - P1))/(P0/(1-P0))
RR = Risk ratio (P1 to P0)

The standard normal deviate for α = Zα = 0.000

The standard normal deviate for β = Zβ = 0.000

Pooled proportion = P = (q1*P1) + (q0*P0) = 0.000

A = ZαP(1-P)(1/q1 + 1/q0) = 0.000

B = ZβP1(1-P1)(1/q1) + P0(1-P0)(1/q0) = 0.000

C = (P1-P0)2 = 0.000

Total group size = N = (A+B)2/C = 0

Continuity correction (added to N for Group 0) = CC = 1/(q1 * |P1-P0|) = 0

Sample size (with continuity correction)
N Outcome+ Outcome-
Group 1:
Group 0:
Total:
Sample size (without continuity correction)
N Outcome+ Outcome-
Group 1:
Group 0:
Total:

Note:

This calculator uses the normal distribution (with and without the continuity correction) as an approximation to the binomial distribution.

References:

Hulley SB, Cummings SR, Browner WS, Grady D, Newman TB. Designing clinical research : an epidemiologic approach. 4th ed. Philadelphia, PA: Lippincott Williams & Wilkins; 2013. Appendix 6B, page 75.

(Continuity Correction) Fleiss JL, Tytun A, Ury HK. A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics 1980;36:343-46.