Syntax
FISHER(x)
| Parameter | Description |
|---|---|
| x | Parameter of the FISHER function. |
Examples
Transform a correlation
Formula
=FISHER(0.75)
Returns 0.973 — the Fisher z-transformation of a correlation coefficient of 0.75.
Confidence interval for correlation
Formula
=FISHER(CORREL(A2:A50, B2:B50))
Transforms the sample correlation to Fisher z-space, where you can add/subtract 1/SQRT(n-3) to build a confidence interval.
Comparing two correlations
Formula
=(FISHER(0.85) - FISHER(0.70)) / SQRT(1/47 + 1/47)
Tests whether two correlations (0.85 and 0.70 from samples of 50) are significantly different using the Fisher z-test.
Common Errors
#NUM!
Returned when x is less than or equal to -1, or greater than or equal to 1. The input must be strictly between -1 and 1.
#VALUE!
Non-numeric input.
Tips
Input must be between -1 and 1 exclusive
FISHER is undefined at exactly -1 and 1. Valid inputs are strictly -1 < x < 1, which matches the range of correlation coefficients (excluding perfect correlation).
Inverse is FISHERINV
After performing calculations in Fisher z-space, use FISHERINV to convert back to the correlation scale.
Why transform?
Correlation coefficients are not normally distributed (especially near -1 or 1). The Fisher transformation makes them approximately normal so standard statistical tests apply.
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