Sampling Distribution of r

Sampling Distribution of Pearson's r

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.
\(-.775\) Use a calculator or table to transform \(r\) to \(z\)'. You get \(-.775\).
\(r = -.8\) 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 \(z\)'.
\(.718\) 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 \(.718\).