Sampling Distribution of r
Completion requirements
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
Answers
- 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 \(.718\).