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

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The number of standard deviations from the mean can be calculated with the formula:



where: z is the number of standard deviations above the z' associated with the population correlation, z' is the value of Fisher's z' for the sample correlation (z' =.97 in this case), μ is the value of z' for the population correlation (.55 in this case) and is the mean of the sampling distribution of z'. is the standard error of Fisher's z'; it was previously calculated to be .25 for N = 19.

Plugging the numbers into the formula: z = (.97 - .55)/.25 = 1.68. Therefore, a correlation of .75 is associated with a value 1.68 standard deviations above the mean. As shown previously, a z table can be used to determine the probability of a value more than 1.68 standard deviations above the mean. The probability is .95. Therefore there is a .05 probability of obtaining a Pearson's r of .75 or greater when the "true" correlation is only .50.



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