FISHER in Calligra Sheets: Fisher z-Transformation Explained

FISHER converts a number strictly between -1 and 1 to its Fisher z-transformation. The independently calculated expected result of =FISHER(0.5) is 0.549306144334. It is useful for statistical work with correlation coefficients because ordinary Pearson r values are bounded, whereas Fisher z is unbounded. This does not mean the original data are necessarily normally distributed, nor does it automatically provide a confidence interval. Official handbook, FISHER, checked 2026-10-13; release-pinned implementation, lines 1215–1224.

=FISHER(number)

• number (required, first and only argument): one floating-point numerical value r with -1 < r < 1 when a finite real-valued Fisher z is intended. The handbook describes a float. The mathematical restriction comes from the documented transform and its 26.08.2 C++ implementation; KDE’s FISHER handbook entry does not separately spell out the limits.
• Order/types/defaults: exactly one required numeric argument; there are no optional arguments or defaults in KDE’s XML definition. FISHER(r) is not a two-argument test and does not take a sample size.
• Expected return: real floating-point z = 0.5 × ln((1+r)/(1-r)), mathematically equal to atanh(r) for -1<r<1. Positive input gives positive output, negative input gives negative output, and zero gives zero. It is not a probability or percentage.

This formula is confirmed by the version-pinned C++ body; the exact registered name is confirmed in the version-pinned function registry. The implementation itself calls the calculation library’s division, logarithm and multiplication operations. That does not certify the exact GUI error shown for an invalid input. Official KDE XML description.

Scope: Calligra Sheets 26.08.2, which KDE lists as released 2026-10-08. Both FISHER and the companion FISHERINV appear in the pinned source, and FISHER appears in KDE’s stable-KF6 English handbook. KDE’s application page lists Linux installation; build and package contents can vary. The handbook is not evidence of actual execution in every distributed package. No native Calligra application was run for this manuscript. KDE release listing, checked 2026-10-13; KDE XML and C++ references.

Start formulas with =. KDE’s formula-entry guidance specifies semicolons between multiple arguments, though FISHER itself only takes one. The examples use a period as the decimal mark to match the checked English documentation; localized installations may display or accept other decimal conventions. Enter input values as numbers, not strings, and verify your installed locale. Displayed precision depends on cell formatting. All values below are independently calculated mathematical expectations, not observed Calligra outputs.

1. Create a blank sheet. Type Correlation r in A1 and Fisher z in B1.
2. Type the numbers below in A2:A8 as numeric values (minus signs are important). Leave B2:B8 empty initially.
3. In B2 enter =FISHER(A2). Fill down through B8. Format column B to six or more decimal places.
4. Compare with the expected results; if a value is rounded differently in the cell display, inspect the number format before changing the formula.

KDE’s handbook separately illustrates FISHER(0.2859) ≈ 0.294096 and FISHER(0.8105) ≈ 1.128485 when rounded to six decimals. Our independently calculated values are 0.294095566361 and 1.128484652342 before that rounding, respectively. KDE handbook, FISHER examples.

In another empty cell try the mathematically equivalent construction:

=0.5*LN((1+A6)/(1-A6))

For A6 = 0.5 this is expected to equal 0.549306144334. The expression intentionally uses LN (natural logarithm), not LOG (base-10 logarithm). Both LN and FISHER are independently registered/documented in Calligra. The comparison is a reasoning check, not proof of identical edge-case error handling in the native program. FISHER source body; LN guide.

For any valid r, the mathematical inverse check is FISHERINV(FISHER(r)) ≈ r. With A6 = 0.5, the expected result of =FISHERINV(FISHER(A6)) is approximately 0.5. This mathematical cross-check does not certify native execution of either function. FISHERINV source body.

Suppose analysts report correlations r=0.40 and r=0.90 from otherwise comparable analyses. Type 0.40 in D2 and 0.90 in D3. Then use =FISHER(D2) in E2 and =FISHER(D3) in E3. The mathematically expected z values are approximately 0.423648930194 and 1.472219489583, a difference of 1.048570559390 z units. This is not a statement that one relationship causes another or that the two sample correlations differ significantly; significance requires sampling assumptions and sample-size information.

A conventional illustrative Fisher-z confidence-interval calculation for a Pearson correlation r uses SE_z ≈ 1/SQRT(n-3), with n>3 and the usual independent, roughly bivariate-normal paired-observation assumptions. For r = 0.60 and n = 30, the independently calculated values are:

Do not use that interval automatically for small, dependent, nonrandom or substantively non-normal data. The 1.96 approximation assumes a normal critical value, does not account for every inferential design and may be inappropriate when r is near ±1. These are explanatory statistics calculations, not KDE-guaranteed inferential features. Compare the resulting endpoints with a statistics reference suited to your analysis.

• Input is -1 or +1: the real-valued transform diverges. At +1 the inspected C++ expression attempts division by zero; at -1 the logarithm receives zero. Because the source has no explicit FISHER-specific guard, do not promise a particular #DIV/0!, #NUM! or other GUI message without native testing. Do not interpret an infinity or unexpected display as a valid finite z.
• Outside (-1,1): the logarithm’s real-domain condition fails. Fix the data, not the result with ABS or rounding. For example, 1.2 is not a permissible Pearson correlation.
• Text, blanks and Boolean values: the XML declares a numeric argument, but the exact UI conversion and error propagation are not verified. Enter a numeric test value directly before using imported strings.
• Near ±1: z grows large in absolute value. Rounding an input of 0.99999 to 1.00000 in the cell display can conceal the underlying numerical value. Check stored precision and the formula bar.
• Function not recognized: confirm the Calligra build/version and the installed function dialogue. Do not substitute a same-named function from Excel or another application as proof of Calligra behavior.
• Wrong sign: check whether your input correlation has a leading minus sign. Mathematically FISHER(-r)=-FISHER(r).

Calligra’s FISHER transform is the documented one-argument statistical transform, not the FISHER exact test or a way to calculate Pearson correlation by itself. Mathematical agreement with the common Fisher-z definition does not establish equivalence of text coercion, errors, localization or file-import behavior in Excel, LibreOffice, Google Sheets or other software. Confirm every target application separately before migrating formulas.

Related guides: LN, EXP and IF.

1. KDE Calligra Sheets handbook — FISHER: function purpose, scalar syntax, return type and official rounded examples.
2. KDE Calligra 26.08.2 statistical XML: required one-float parameter and exact help entry.
3. KDE 26.08.2 function registration, pinned source: FISHER registered distinctly from FISHERINV.
4. KDE 26.08.2 implementation, pinned source: the log-ratio calculation and lack of a local boundary guard.
5. KDE formulas guide: equals-sign and semicolon entry conventions.
6. KDE application release listing and 26.08.2 release notice: released version/date, not a claim that this function was run.

Validation status: Official handbook/XML/C++ inspected; numerical outputs independently calculated using standard mathematical functions. Native execution: NOT PERFORMED. Errors, imports, platforms other than the sourced release, localized formula entry, display messages and interface screenshots: NOT TESTED.