FISHERINV in Calligra Sheets: Reverse a Fisher z-Transform

FISHERINV converts a Fisher z value back into the corresponding correlation-scale number between -1 and 1 (for finite real z). For =FISHERINV(0.5), the independently calculated expected result is 0.462117157260, not 0.5. It is the inverse of the Fisher z-transform, not an inverse-normal probability calculator and not a procedure that estimates correlation from raw observations. KDE handbook, FISHERINV; pinned C++ implementation.

=FISHERINV(number)

• number (required): one scalar floating-point Fisher z value. Positive, negative and zero inputs are mathematically legitimate; the KDE handbook has no stated finite lower or upper bound for the input. number is not a correlation, percentage, confidence level or array of raw observations.
• Argument order and defaults: one required numeric argument, no second argument, no optional parameter and no default. KDE’s 26.08.2 XML marks its sole argument as Float.
• Expected return: the inverse hyperbolic tangent’s inverse operation, mathematically tanh(z) = (exp(2z)-1)/(exp(2z)+1), which is strictly between -1 and 1 for finite real z. The source implements the displayed ratio using Calligra’s calculation library. This is mathematical behavior for ordinary finite inputs, not evidence that extreme inputs always produce a clean numeric cell. Official XML; pinned implementation.

The official Calligra handbook gives FISHERINV(0.2859) ≈ 0.278357 and FISHERINV(0.8105) ≈ 0.669866 to six decimal places. Independently calculated values before rounding are 0.278356823855 and 0.669865991724. Official handbook.

This guide is scoped to Calligra Sheets 26.08.2 (listed by KDE on 2026-10-08). The exact FISHERINV name is present in the pinned 26.08.2 C++ function registration and corresponding XML help entry. The public handbook supports syntax and described behavior, but does not prove that an individual build, package or platform has been executed. KDE’s current application page lists Linux installation. No native Calligra execution or GUI screenshot was performed for this guide. Registration; KDE release listing; KDE source XML.

Enter formulas with a leading =. For formulas with multiple arguments, KDE’s formula guide describes ; separators. FISHERINV itself requires only one. The examples use English documentation’s decimal point; regional entry/display conventions should be confirmed on the installed software. Formatting and floating-point precision can change displayed digits; the tables report mathematical expectations calculated independently of Calligra.

1. In a blank sheet, enter Fisher z in A1 and Correlation scale r in B1.
2. Enter A2:A10 as numeric values, not text. They may be negative, zero or positive.
3. In B2 enter =FISHERINV(A2) and fill through B10. Format column B to six to twelve decimal places.
4. Compare each output with the expected table. Negative z values should give negative correlations; positive z values should give positive correlations.

An output of 0.669865991724 for z=0.8105 is entirely consistent with KDE’s rounded 0.669866 example. Use six or more displayed decimals only if your statistical workflow requires them. KDE FISHERINV example.

The 26.08.2 implementation calculates:

=(EXP(2*A8)-1)/(EXP(2*A8)+1)

With A8=0.5 the independently calculated expected result is 0.462117157260. This is an explanatory comparison using another documented function, not a native test demonstrating identical error propagation. Pinned implementation, lines 1231–1237; EXP guide.

For ordinary finite z, FISHER(FISHERINV(z)) ≈ z. Therefore the expected result of =FISHER(FISHERINV(A9)) is approximately 0.8105. In the other direction, for any correlation r with -1 < r < 1, FISHERINV(FISHER(r)) ≈ r. Both functions are separately registered in KDE. KDE registrations.

A standard approximate confidence-interval construction for a Pearson correlation first transforms r to z, forms a symmetric interval on the z scale, then converts its endpoints with FISHERINV. For example, set r=0.60 in D2 and the paired sample size n=30 in D3. The usual independent, roughly bivariate-normal paired-data approximation uses SE_z = 1/SQRT(n-3) and a nominal 95% multiplier of 1.96. Independently calculated results:

The final approximate correlation interval is 0.306 to 0.790, not a z interval. FISHERINV is what returns the endpoints to the bounded correlation scale. This is a statistics illustration derived from standard formulas, not an explicit KDE help example, a native Calligra test or a substitute for study-design review. It assumes n > 3 and assumptions under which the Fisher approximation is reasonable; it is not appropriate to use uncritically for dependent, clustered, strongly non-normal, tiny-sample or selected observations.

• Very large positive z: the exact mathematical result approaches +1, but the pinned code evaluates EXP(2*z) first. For a sufficiently large z, an internal exponential may overflow, and the subsequent (exp-1)/(exp+1) can become numerically indeterminate. This is a source-based potential numerical limitation; the threshold and application-visible error are not verified natively. Do not rely on enormous z to produce a clean displayed 1.
• Very large negative z: the mathematical output approaches -1. Exponential underflow may also affect the implementation’s numerical precision near that endpoint, even if the expression ultimately returns a value near -1. This is not a reason to treat -1 as a finite inverse result.
• Input of +1: the input z=1 is valid and should give about 0.761594155956. Do not confuse the FISHER input domain (-1,1) with the FISHERINV input domain (all finite real z).
• Text, blanks, error cells, imported booleans: KDE’s XML specifies a float, but this inspection did not run the application to verify scalar coercion, blanks or exact UI errors. Use a numeric literal as your control test.
• Unexpected value: confirm that you supplied z rather than raw correlation, did not pre-multiply or divide by 100, and used a numeric cell. Confirm the formula bar precision before interpreting a displayed 1.00.
• Unrecognized function: verify the installed Calligra version and use its function dialog. The name’s presence in release source is not proof that every packaged executable supports it.

This is the documented Calligra inverse Fisher-z function. It is not the same operation as FISHER, Pearson’s CORREL, an inverse CDF such as NORMSINV, or a claim of identical behavior in Excel and Google Sheets. Other spreadsheet implementations may disagree on invalid inputs, text coercion, imported formulas, locale separators, precision and extreme-value overflow. Do not use another product’s behavior as Calligra evidence.

Related guides: EXP, LN and IF.

1. KDE Sheets handbook — FISHERINV: the one-argument syntax, numeric type, purpose and two rounded examples.
2. KDE 26.08.2 statistical XML: one required Float parameter and function help.
3. KDE pinned registration lines 181–184: FISHER and FISHERINV are distinct function names.
4. KDE pinned FISHERINV implementation lines 1231–1237: direct exponential-ratio calculation; basis for potential overflow warning.
5. KDE formula-entry guidance: equals-sign and separator convention.
6. KDE release listing and 26.08.2 announcement: release identity/date and platform context.

Validation status: Official handbook, XML, registration and implementation inspected; worksheet values and interval arithmetic independently calculated. Native Calligra execution, GUI error rendering, locale behavior, import/export and screenshots were not tested.