Sampling Distribution of Pearson's r (1 of 3)

Just like any other statistic, Pearson's r has a sampling distribution. If N pairs of scores were sampled over and over again the resulting Pearson r's would form a distribution. When the absolute value of the correlation in the population is low (say less than about 0.4) then the sampling distribution of Pearson's r is approximately normal. However, with high values of correlation, the distribution has a negative skew. The graph below shows the sampling distribution of Pearson's r when the population correlation is 0.60 and when N = 12. The negative skew is apparent.

sampling distribution of r showing negative skew

A transformation called Fisher's z' transformation converts Pearson's r to a value that is normally distributed and with a standard error of:

standard error is 1 over the square root of N-3.