FISHER Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas. Locale and file-format mappings may differ.
• Checked: October 14, 2026. Eight reference formulas and the listed boundary cases were recalculated in 4.1.16 on Linux x86-64, Build 9816, using XLSX import. Source and independent mathematics were also checked.

FISHER applies the Fisher z transformation, atanh(r)=0.5×LN((1+r)/(1−r)). It maps correlations strictly between −1 and 1 onto the real line. A transformed correlation is not a probability, a p-value or an ordinary standardized observation. Release implementation.

=FISHER(Correlation)

Exactly one numeric value is used. It must satisfy −1<Correlation<1. The evaluator explicitly rejects either endpoint and values beyond them. Zero maps to zero, and changing the sign of the input changes the sign of the output. Do not round a valid correlation to 1 before applying the transformation.

These eight formulas were recalculated in the stated 4.1.16 build using XLSX import. Saved numeric results agree with independent high-precision calculations; values below are rounded to twelve decimal places. The comparison concerns stored values, not a claim that every display format prints the same digits.

If a calculated correlation is 0.5, =FISHER(0.5) gives approximately 0.549306144334. For 0.8, the result is 1.098612288668. Put the unrounded correlation in J2 and use =FISHER(J2); keep the original correlation beside the transformed value.

The difference between these transformed values is about 0.549306144334. This is a difference on the z scale. It should not be reported as a percentage-point change in correlation or as evidence that two samples differ significantly without an appropriate sampling model.

An approximate interval for a population correlation can be formed on the transformed scale under an independent-pairs, approximately bivariate-normal model. With observed r=0.6 and n=30 pairs, use z=FISHER(0.6), standard error 1/SQRT(30−3), and transformed endpoints z±1.96/SQRT(27). Apply FISHERINV to each endpoint. The numerical interval is approximately [0.3058,0.7896]; retain the full calculated endpoints for reporting.

This is an approximate construction, not an exact interval for every dataset. It is unsuitable when the independence or model assumptions fail, and n must exceed 3. Applying the inverse after subtracting endpoints gives a different quantity; transform each endpoint separately.

The mathematical round trip =FISHERINV(FISHER(0.5)) returns 0.5 up to numerical rounding. Close to either endpoint, small input errors can create large changes because the derivative is 1/(1−r²).

A perfect sample correlation of ±1 cannot be transformed to a finite value. Preserve the error and assess the data; replacing the correlation with 0.999 without justification changes the statistical problem.

An empty cell and a genuine zero correlation have different meanings even if numeric coercion gives the same calculation result. The specific empty-cell observation below documents the tested formula only. Other text, locale and import coercion rules are not inferred from it.

The following boundary formulas were recalculated in the same named method. H5 and H6 are deliberately empty cells where referenced. An error display remains an error even if the underlying ODS numeric attribute stores zero.

• CORREL
• PEARSON

• Function-specific release entry
• Numeric helper or argument collection

The retained input and saved ODS preserve the tested formula identities. A stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence is limited to the eight reference formulas and listed boundary cases in this exact release and method. Composite explanatory examples are independent calculations unless listed among those cases; other releases, locales and extreme-parameter accuracy were not established.