Sampling Distribution of r

Now, we'll talk about how the shape of the sampling distribution of Pearson correlation deviates from normality and then discusses how to transform r to a normally distributed quantity. Then, we will discuss how to calculate the probability of obtaining an r above a specified value.

Sampling Distribution of Pearson's r


  1. Skewed- Unless r = 0, the sampling distribution is skewed. The reason for the skew is that r cannot take on values greater than 1.0 or less than -1.0, and therefore the distribution cannot extend as far in one direction as it can in the other.

  2. -.775 Use a calculator or table to transform r to z'. You get -.775.

  3. r = -.8 Although you could plug all of these values into the r to z' calculator, you don't need to do that. You know the r with the biggest absolute value has the most skewed sampling distribution, so it is the most different from its corresponding z'.

  4. .718 Population correlation = .6 to z' = .693, SE = 1/sqrt(N-3) = 1/sqrt(19-3) = .25, r = .50 to z' = .549, Use the "Calculate area for a given X" applet. Plug in .693 for the mean and .25 for the SD, and then calculate area above .549. You get .718.