Zoho Sheet FISHERINV Function: Reverse Fisher Z with Examples

Fisher z is a transformation of a Pearson correlation coefficient. FISHERINV reverses that transformation, returning a number between −1 and +1 for an ordinary finite real input. Mathematically:

r = tanh(z) = (exp(2z) − 1)/(exp(2z) + 1).

The input z can be negative, zero, or positive. In contrast to the forward FISHER function, there is no mathematical requirement that z lie between −1 and +1. For instance, z = 2 becomes approximately r = 0.964027580, while z = −1 becomes approximately r = −0.761594156. This is a transformation back to correlation units; it is not the reciprocal 1/z and not a general statistical hypothesis test.

Use FISHERINV when you have transformed a correlation with FISHER, calculated limits on the Fisher-z scale, or combined approximately comparable transformed correlations and need an interpretable result. To obtain the initial correlation from raw observations, use Zoho CORREL or Zoho PEARSON first, not FISHERINV.

=FISHERINV(z)

No optional parameters or defaults are documented. Zoho does not state a first supported product version, a browser-specific restriction, or an account-tier rule in the checked function article; do not infer universal historical/device parity from its presence on a current cloud help page. The article lists generic #NAME!, #VALUE!, #REF! and #N/A! messages but does not give a special #NUM! rule for ordinary finite z. Avoid inventing a Zoho-specific overflow limit. Zoho FISHERINV syntax and error table, checked 2026-10-12.

In a clean worksheet, type Fisher z in A1 and Correlation r in B1. Enter the values below as numbers and place =FISHERINV(A2) in B2, then fill down to B7.

1. Check the input column contains actual numeric data, including each sign.
2. Enter the formula once in B2. Do not type a second range argument—this function takes one value.
3. Copy B2 through B7. Each result should refer to its own row.
4. Compare the results with the table after rounding to nine decimals. A minor difference in the final displayed digit can be a formatting issue; a larger discrepancy warrants native investigation.
5. For a round trip, put =FISHER(B2) into C2. With the example, its independently calculated output should be approximately 0.608400231 again. Rounding the intermediate r to too few digits loses some precision.

Zoho documents =FISHERINV(0.60840023073448) → 0.543, and examples using cell references. The additional input/output pairs in this table are independently calculated using hyperbolic tangent, not results observed in an open Zoho Sheet document. Zoho: FISHERINV worked examples, checked 2026-10-12.

A transparent mathematical cross-check

For moderate z values, the following proposed spreadsheet expression implements the mathematical inverse:

=(EXP(2*A2)-1)/(EXP(2*A2)+1)

For A2 = 1, this evaluates to approximately 0.761594156, which agrees with tanh(1). The expression is for conceptual verification; it has not been run in Zoho Sheet here. Because exponentials can overflow for sufficiently large positive numbers, the EXP expression is not a robust substitute for an implementation of tanh over all machine-scale inputs. The checked Zoho documentation does not establish FISHERINV’s internal algorithm or its overflow thresholds. See Zoho EXP and Zoho FISHER (checked 2026-10-12).

Suppose three independent studies measured the same kind of Pearson association, with sample correlations of 0.20, 0.50, and 0.70. Their sample sizes are 20, 40, and 30 respectively. A simple approximate approach is to transform each r to z, compute an (n−3)-weighted average z, and use FISHERINV on the result. This is a teaching example, not a full random-effects meta-analysis; it assumes independent samples and roughly comparable underlying associations.

Set up this sheet with the following headers and values:

Next use these cells:

The pooled estimate is about 0.525, not the raw unweighted average (0.20 + 0.50 + 0.70)/3 = 0.467. This difference arises because Fisher z is nonlinear and the sample sizes differ. The weight n−3 derives from the usual approximate variance of transformed correlations, not from a special Zoho setting. If a study has n ≤ 3, these weights are inappropriate; if studies overlap, measure different constructs, or have strong heterogeneity, seek a more suitable statistical model. The numerical result is independently computed, not proof of any built-in Zoho pooling function.

For a simple approximate transformed-scale interval around an estimate, the inverse also turns interval endpoints back into correlation units. With r = 0.543 from n = 30, the Fisher-z centre is 0.608400231, the z standard error is 0.192450090, and the approximate 95% endpoints are 0.231198055 and 0.985602407. Applying FISHERINV separately gives approximately 0.227164892 and 0.755480926. Do not apply FISHERINV to just the margin of error and then subtract it from r; the nonlinearity makes that incorrect. Normal-approximation assumptions and the independence of sampled pairs remain material.

For comma-decimal locales or Excel-to-Zoho imports, verify numeric input and separators in the destination workbook. The unary FISHERINV call has no inter-argument separator, but nested functions such as Zoho’s two-range CORREL(x; y) do. Zoho: CORREL, checked 2026-10-12.

Official cross-product links checked 2026-10-12: Zoho FISHERINV, Excel FISHERINV, and Google Sheets function list. A Microsoft/Google feature’s presence is not evidence that a particular historical Zoho release, mobile app, subscription tier, or CSV import mode behaves identically. Native availability must be tested in the target Zoho account and platform.

Is FISHERINV the same as FISHER? No. FISHER goes from the bounded coefficient r to Fisher z; FISHERINV goes back. For valid r, the mathematical composition FISHERINV(FISHER(r)) recovers r to ordinary floating-point precision.

Can the input be 2 or −2? Yes, mathematically. Inverse Fisher z is not restricted to the input domain of the forward transform. FISHERINV(2) is approximately 0.964027580.

Why might I use FISHERINV on two numbers? To back-transform the lower and upper z confidence limits separately. A single scalar function call accepts one value at a time; apply it to each corresponding cell.

Is FISHERINV a Fisher F-distribution inverse? No. This is about Fisher z for correlations, not the inverse F probability distribution; see separate F-distribution functions if that is your statistical question.

Does a pooled estimate prove all studies have the same effect? No. Weighting and back-transformation do not remove selection bias, heterogeneity, or dependence. Report those limitations alongside any summary.

Verified official references: Zoho FISHER for the forward transform; Zoho CORREL and Zoho PEARSON for raw correlations; Zoho SUM for the weighted sum. These links point to official references.

Evidence and checks (2026-10-12): Zoho FISHERINV syntax, example and error table directly checked; official Zoho FISHER and CORREL related references checked; Excel and Google Sheets documented comparisons checked independently; mathematical tanh, round-trip, weighted-z and 95% interval outputs independently calculated; actual Zoho Sheet execution 0; screenshots 0.