FISHER Function (Gnumeric)

• Introduced: Documented by 1.12.62; original introduction not established.
• Availability: Supported in Gnumeric 1.12.62, based on the function-specific registration.
• Scope: Desktop; the fn-stat function module must be included and enabled.
• Checked: October 14, 2026. Documentation/source check; no new native test in Gnumeric 1.12.62.

FISHER applies the Fisher z-transformation to a number strictly between −1 and 1. It is useful when comparing correlations and, with suitable statistical assumptions, building approximate confidence intervals. The mathematical expression is

[z=\operatorname{atanh}(r)=\tfrac{1}{2}\ln\left(\frac{1+r}{1-r}\right).]

Here r is commonly a Pearson correlation coefficient. FISHER is not a function that computes the correlation from raw data: use CORREL or PEARSON for that step. Gnumeric’s Statistics manual explicitly identifies FISHER as the Fisher transformation and points to FISHERINV and ATANH. [S1]

=FISHER(x)

There is one argument only; there are no optional flags or defaults. The order is not interchangeable with anything else. An input at exactly −1 or 1 is outside the permitted domain, even though it is a valid correlation coefficient. [S1, S3]

Type the following numbers into separate worksheet cells and place each formula in another cell. The expected numeric outputs below are calculated independently from the mathematical definition, not observed in Gnumeric.

For a manual cross-check of A4 = 0.75, calculate LN((1+A4)/(1-A4))/2: LN(7)/2 ≈ 0.9729550745. This is an independent equivalent calculation, not evidence that Gnumeric returned either cell value during this research. [S1]

Suppose A2:A6 contains five campaign-spend amounts and B2:B6 contains associated responses. In D2, enter:

=CORREL(A2:A6,B2:B6)

In D3, transform that result:

=FISHER(D2)

Or combine the operations:

=FISHER(CORREL(A2:A6,B2:B6))

Check that the underlying CORREL result is strictly between −1 and 1 and that rows represent valid matched observations. An exact or nearly perfect relationship may require special attention because Fisher z tends toward positive or negative infinity as r approaches ±1. The link to Gnumeric’s CORREL guide is CORREL. [S1]

For a sufficiently large independent sample from an approximately bivariate-normal population, the Fisher transformation is often used as an approximation for a correlation confidence interval. Suppose:

In B6, calculate the lower transformed-bound then back-transform it:

=FISHERINV(FISHER(B2)-B4/SQRT(B3-3))

In B7, calculate the upper bound:

=FISHERINV(FISHER(B2)+B4/SQRT(B3-3))

Independently calculated expected values: lower ≈ 0.5340205334; upper ≈ 0.8740903987. These are approximate statistical limits, not guaranteed coverage for arbitrary data or very small, dependent or non-normal samples. Ensure n > 3; do not interpret the interval as proof of causation. In an instructional example using the Gnumeric FISHERINV function, see FISHERINV. [S1, S3]

Avoid silently forcing out-of-range data to 0.9999 or −0.9999: that changes the meaning of a perfect observed correlation. Validate the data, not just the formula. Gnumeric’s own manual states both the numeric-domain and type-error cases. [S1]

• FISHERINV — returns to the original correlation scale; separate canonical function.
• ATANH — the inverse hyperbolic tangent, mathematically the same transformation for the valid real domain.
• CORREL / PEARSON — compute a correlation from paired data before transforming it.

• Documentation target: Gnumeric 1.12, cross-checked with the 1.12.62 release (released September 20, 2026; GNOME download directory posted September 21). This is documentation/source checking, not an on-device runtime certification. [S1–S4]
• The function has a dedicated entry in Gnumeric’s Statistics reference and an implementation registered Complete with Basic upstream tests in the public catalogue. Registered means the upstream distribution advertises the function; it does not prove that the individual examples here were run successfully on your OS, distribution, locale or plugin configuration. [S1–S3]
• Gnumeric’s manual writes English-function examples with an equals sign, uses commas between arguments, and states function names are case-insensitive. Its locale and number formats can vary; these examples use an English-language, dot-decimal configuration. Verify localized input syntax and displayed separators inside your installed application rather than assuming another spreadsheet’s settings. [S5–S6]
• Gnumeric marks this function Microsoft Excel compatible in its own function help. That is a vendor statement about the documented function, not proof of identical results for all imported files, spreadsheet programs, edge cases or historical editions. ODF/other-spreadsheet behavior has not been used to infer undocumented Gnumeric behavior. [S1]

The approximate Fisher confidence-interval method is described by Penn State STAT 505, Lesson 5; its statistical assumptions are separate from Gnumeric’s function contract.

1. S1 — Official Gnumeric 1.12 Statistics function manual. Relevant lines in current published HTML: 772–794; defines function name, exact argument order, documented errors and vendor Excel-compatibility statement. Publication/update date of the HTML page is not specified; access checked 2026-10-13.
2. S2 — Official public function catalogue. Statistics listing registers fisher as Implementation: Complete; Testing: Basic. This is upstream catalogue status, not a test performed for this guide; access checked 2026-10-13.
3. S3 — Official Gnumeric 1.12.62 source archive. Its plugins/fn-stat/functions.c help and callback were inspected after verification against GNOME’s published SHA-256 checksum. This is source-level evidence, not a native test.
4. S4 — Gnumeric release 1.12.62 announcement and GNOME official source-release index. The Gnumeric source ChangeLog records 2026-09-20, and GNOME’s source index timestamps the tarball 2026-09-21. Release availability does not prove that this guide’s examples were run on any installed OS.
5. S5 — Gnumeric formula entry/type/reference manual, including =, commas, relative/absolute references and typical error names; checked 2026-10-13.
6. S6 — Gnumeric language/locale manual, locale-controlled numeric representation; checked 2026-10-13.

Validation limits: Official documentation and checksum-verified Gnumeric 1.12.62 source were inspected, and examples were independently calculated. No native Gnumeric execution, screenshots, locale regression or workbook round-trip was performed.