Confidence Interval on Pearson's Correlation (1 of 3)

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Since the sampling distribution of Pearson's r is not normally distributed, Pearson's r is converted to Fisher's z' and the confidence interval is computed using Fisher's z'. The values of Fisher's z' in the confidence interval are then converted back to Pearson's r's. For example, assume a researcher wished to construct a 99% confidence interval on the correlation between SAT scores and grades in the first year in college at a large state university. The researcher obtained data from 100 students chosen at random and found that the sample value of Pearson's r was 0.60. The first step in computing the confidence interval is to convert 0.60 to a value of z' using the r to z' table. The value is: z' = 0.69.

The sampling distribution of z' is known to be approximately normal with a standard error of



where N is the number of pairs of scores.