FISHERINV 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.

FISHERINV evaluates tanh(z), the inverse of the Fisher correlation transformation. It takes a value on the transformed z scale and returns a value on the correlation scale. It is not the inverse of a normal cumulative probability. Release implementation.

=FISHERINV(Z)

Exactly one numeric argument is used. The source calls the hyperbolic tangent directly. For every finite real input the exact mathematical result lies strictly between −1 and 1, although floating-point results can round to an endpoint for large magnitudes. Negative inputs are valid.

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.

A transformed value of 0.5 gives =FISHERINV(0.5) approximately 0.462117157260. A transformed value of 1 gives approximately 0.761594155956. Keep the transformed values in one column and the resulting correlations in another; labeling both simply “z” would hide the scale change.

To reverse a Fisher transformation of 0.8, the independent composition =FISHERINV(FISHER(0.8)) gives 0.8 to ordinary floating-point precision. Do not substitute NORMINV: its argument contract and meaning are different.

When an interval was calculated on the Fisher z scale, transform the lower and upper endpoints separately. For r=0.6 and n=30 independent pairs under the usual approximate bivariate-normal model, use =FISHERINV(FISHER(0.6)-1.96/SQRT(27)) and the analogous plus expression. The correlation interval is asymmetric around 0.6 even though the z interval is symmetric.

Averaging transformed correlations and applying FISHERINV does not generally equal averaging the original correlations. Independently, the z-scale average of 0.2 and 0.8 transforms back to 0.572122461732, whereas their ordinary average is 0.5. Neither averaging method is automatically an appropriate pooled estimate; sampling weights and the analysis design matter.

The stable mathematical identity tanh(z) explains odd symmetry. Writing the equivalent exponential ratio manually can overflow for large positive z, even though tanh(z) remains bounded.

Large finite inputs can saturate at ±1 in the stored numeric result. That does not mean the mathematical inverse reaches its endpoints at a finite z. Passing such a rounded endpoint into FISHER can then produce an error instead of recovering the original value.

Use full internal precision and assess round trips with a tolerance. Do not treat a single exact round-trip result as a guarantee for all inputs, especially values close to the correlation endpoints.

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.