Compare the mean of a continuous measurement in two samples, using a z-statistic to approximate the t-statistic.

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

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 = Proportion of subjects that are in Group 0 (unexposed); 1-q1
E = Effect size
S = Standard deviation of the outcome in the population

The standard normal deviate for α = Zα =

The standard normal deviate for β = Zβ =

A = (1/q1 + 1/q0) =

B = (Zα+Zβ)2 =

Standardized Effect Size = (E/S) =

Total group size = N = AB/(E/S)2 =



Total: 0

Because the formula used here is based on approximating the t statistic with a z statistic, it will slightly underestimate the sample size when N is less than about 30.

Reference: 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 6A, page 73.