Total sample size required to determine whether a correlation coefficient differs from zero.
Instructions: Enter parameters in the green cells. Answers will appear in the blue box 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.