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Sample size calculation: Correlation coefficient


Calculates the required sample size for a correlation coefficient. The sample size takes into account the required significance level and power of the test (see Sample size calculation: Introduction).

Required input

  • Type I error - alpha: the probability of making a Type I error (α-level, two-sided), i.e. the probability of rejecting the null hypothesis when in fact it is true.
  • Type II error - beta: the probability of making a Type II error (β-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
  • Correlation coefficient: the hypothesized or anticipated correlation coefficient.


For example, the correlation coefficient between two variables is thought to be 0.60. How many patients are required for this correlation coefficient to be significantly different from 0.0?

For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).

Sample size calculation for correlation.

After you click Calculate the program displays the required sample size (19 in the example, meaning that you will need 19 cases in which both variables must be measured).

A table shows the required sample size for different Type I and Type II Error levels.


  • Bland M (2000) An introduction to medical statistics, 3rd ed. Oxford: Oxford University Press.

See also