FISHERINV Function (Gnumeric)

Gnumeric’s FISHERINV reverses the Fisher z-transformation and is mathematically equivalent to the hyperbolic tangent for a real numeric input:

[r=\tanh(z)=\frac{\exp(2z)-1}{\exp(2z)+1}.]

The result falls between −1 and 1 for finite real z, making FISHERINV suitable for translating transformed correlation values or approximate confidence limits back onto the familiar correlation scale. FISHERINV does not perform statistical analysis of a data range by itself. The official Gnumeric Statistics reference identifies this purpose and lists FISHER and TANH as related functions. [S1]

=FISHERINV(x)

This function requires one argument, without optional parameters. Unlike FISHER, it has no documented requirement that its argument be between −1 and 1. For example, Gnumeric’s own upstream help gives =FISHERINV(2) as a sample expression. [S1, S3]

Put the numbers in column A; enter each formula in another column.

The values were independently calculated with the mathematical tanh function. They are predicted worksheet outputs rather than screenshots or native observations. Display decimal-place settings should not be confused with source accuracy or measurement precision. [S1, S3]

Set B2 = 0.75 and enter:

=FISHERINV(FISHER(B2))

Expected result: approximately 0.75. The intermediary value is FISHER(0.75) ≈ 0.9729550745276566. If you instead enter the rounded intermediary value 0.972955, the reverse result will only be approximately 0.75, because rounding has discarded information. [S1]

The direction of the operations matters: a correlation coefficient r goes into FISHER, while a transformed z goes into FISHERINV. Placing an already transformed value into FISHER a second time changes the statistic and may fail if its magnitude is at least 1.

Suppose a survey of 30 paired observations reports a sample Pearson correlation of 0.75. With the same statistical assumptions required for the usual large-sample Fisher-z approximation, construct an illustrative, approximate 95% interval:

Independently calculated values: B5 ≈ 0.9729550745, B6 ≈ 0.5340205334, B7 ≈ 0.8740903987. The interval transformation and assumptions are statistical methodology, not an assertion that Gnumeric’s help automatically computes confidence intervals. n must exceed 3. Correlation and its interval do not establish causation. [S1]

A useful reusable layout puts the z value in column C and calls =FISHERINV(C2) in D2, then copies down; this helps avoid mixing transformed z scores with raw correlations in reports.

For calculations where extreme z inputs are possible, retain full numeric precision in the source and review the transformation’s suitability for your statistical model rather than blindly reporting 1.00 or −1.00.

• FISHER — transforms a valid correlation to z before the inverse.
• TANH — mathematical hyperbolic tangent; separately registered function.
• CORREL and PEARSON — compute correlations from paired measurements.

• 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: 795–818; 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 fisherinv 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.