Sample Size for Pearson's Correlation


Menu location: Analysis_Sample Size_Correlation.


This function gives you the minimum number of pairs of subjects needed to detect a true difference in Pearson's correlation coefficient between the null (usually 0) and alternative hypothesis levels with power POWER and two sided type I error probability ALPHA (Stuart and Ord, 1994; Draper and Smith, 1998).


Information required


Practical issues


Technical validation

The sample size estimation uses Fisher's classic z-transformation to normalize the distribution of Pearson's correlation coefficient:


This gives rise to the usual test for an observed correlation coefficient (r1) to be tested for its difference from a pre-defined reference value (r0, often 0), and from this the power and sample size (n) can be determined:


StatsDirect makes an initial estimate of n as:


StatsDirect then finds the value of n that satisfies the following power (1-β) equation:

-where norm is the area under the standard normal distribution curve.


The precise value of n is rounded up to the closest integer in the results given by StatsDirect.