FISHERINV in Google Sheets: Inverse-Scale Arithmetic and Exact Controls

• Introduced: first introduction date is not established by the reviewed official history; no desktop release number is inferred.
• Availability: documented in the rolling Google Sheets service; these examples use the web worksheet workflow.
• Checked: October 14, 2026; official FISHERINV reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=FISHERINV(value)

The value is required. Google’s complete dedicated body identifies the inverse transformation and syntax but does not print its equation or list native error codes.

The independent inverse-Fisher model used here is (EXP(2*z)-1)/(EXP(2*z)+1). All examples use moderate real z values and clearly labeled mathematical expectations. This equation is not attributed to an unshown Google formula image, and the calculations are not native Sheets tests.

For finite real z the mathematical result lies strictly between -1 and 1. Native floating-point saturation at extreme inputs remains unverified.

=FISHERINV(LN(4))

Expected result under the independent model: 15/17, approximately 0.882352941. Because EXP(2*LN(4))=16, the equation gives (16-1)/(16+1).

For a second control:

=FISHERINV(LN(1.5))

The exponential term is 2.25, giving (2.25-1)/(2.25+1)=5/13, approximately 0.384615385.

These inputs retain their logarithmic precision rather than replacing a displayed approximation with a shortened typed number.

=FISHERINV(0)
=FISHERINV(0.5)
=FISHERINV(-0.5)

Expected values are 0, approximately 0.462117157, and approximately -0.462117157. Negating a finite input negates the mathematical output.

The input 0.5 is a transformed coordinate. It is not an instruction to return 50% or a percentile rank. Formatting a result as Percentage changes its display, not the meaning of the transformation.

Enter -1,-0.5,0,0.5,1 in A2:A6. In B2 enter =FISHERINV(A2) and fill down.

Expected outputs, shown to nine decimals, are -0.761594156,-0.462117157,0,0.462117157,0.761594156.

Equal increments on the transformed scale do not produce equal increments on the original scale. The curve approaches its outer limits rather than extending linearly without bound.

This is an arithmetic illustration, not a statistical instruction to average or increment transformed coefficients without considering how they were obtained.

For a moderate coefficient r=0.8, the forward mathematical expression is 0.5*LN((1+r)/(1-r)). Here the ratio is 9, so the transformed value is LN(3).

=FISHERINV(0.5*LN((1+0.8)/(1-0.8)))

Expected result: 0.8. The negative control with r=-0.8 returns -0.8 in the same model. This formula uses an explicit expression rather than relying on undocumented native FISHER behavior in this guide.

For paired X 0,1,2,3 and Y 0,2,1,3, PEARSON has independent coefficient 0.8. Keep those original pairs and the signed coefficient when interpreting the transformed number.

Starting from z=LN(3), doubling z gives an exponential term of 81. Therefore:

=FISHERINV(2*LN(3))

Expected result: 40/41, approximately 0.975609756. Doubling raw coefficient 0.8 would give 1.6 instead, demonstrating that the two scales do not support interchangeable arithmetic.

The direct exponential audit may overflow at very large inputs even if a native implementation uses a more stable method. It is only a moderate-number cross-check here, not a recommended universal replacement for FISHERINV.

Google’s sparse reference does not establish nonnumeric, Boolean, numeric-text or source-error conversions. Those native cases remain held rather than assigned another application’s error messages.

The function supplies neither a p-value nor a confidence interval and does not inspect sample size or assumptions. A mathematically correct inverse transform cannot establish that the statistical process producing its input was appropriate.

• Google FISHERINV reference.
• Editorial testing standards.

Examples use fictional data, English function names and comma separators. Expected outputs are independent mathematical calculations or explicitly documented rules, not native Sheets captures. Check the spreadsheet locale when reproducing punctuation-sensitive formulas.