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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 Ronald Fisher's classic z-transformation to normalize the distribution of Karl Pearson's correlation coefficient:

image\STAT0087_wmf.gif

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:

image\STAT0088_wmf.gif

StatsDirect makes an initial estimate of n as:

image\STAT0089_wmf.gif

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

image\STAT0090_wmf.gif

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