Total sample size required to determine whether a correlation coefficient differs from zero.

Instructions: Enter parameters in the red cells. The answer 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.
r = The expected correlation coefficient.

The standard normal deviate for α = Zα =

The standard normal deviate for β = Zβ =

C = 0.5 * ln[(1+r)/(1-r)] =

Total sample size = N = [(Zα+Zβ)/C]2 + 3 =

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 6C, page 79.