Describe the Fisher transform? For what do we use it and why?
What will be an ideal response?
Ans: The sampling distribution of r itself is not generally normal, however, Sir Ronald Fisher showed that a simple transformation of r produces a new statistic, called zr, that is approximately normally distributed. The transformation from r to zr is accomplished using the formula
,
where ln is the natural logarithm of the quantity in parentheses. In addition to being approximately normal, the distributions of zr all have the same standard error. Therefore, a confidence interval around zr can be computed as zr ± z?/2(?zr). The confidence limits of this interval can be transformed back to values of r using the inverse Fisher transform.
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