PlanMaker FISHERINV: Inverse Transformation and Interval Shape
Reverse the Fisher transformation in PlanMaker with complete round-trip examples, exponential checks and an asymmetric interval illustration.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
FISHERINV reverses the Fisher transformation. Its input is already on the transformed scale, so it need not lie between −1 and 1. The output returns to the coefficient scale; inverse does not mean one divided by the input.
Availability and version history
- Introduced: Documented by the PlanMaker 2010 manual; the first introduction release and date are not established.
- Availability: Documented in PlanMaker 2026; this is not a final working-version endpoint.
- Scope: The reference belongs to the 2026/NX manual family. FreeOffice and individual mobile-build availability remains unverified.
- Checked: October 14, 2026, against the official function reference and historical entry. Examples were independently calculated; no native PlanMaker test was performed.
Syntax and the inverse relationship
=FISHERINV(Number)
The PlanMaker reference identifies this one-argument function as the inverse of FISHER. It does not list optional arguments or a separate finite numeric input interval.
For a mathematical transformed value z, the inverse is:
=(EXP(2*z)-1)/(EXP(2*z)+1)
SAS’s statistical reference gives this back-transformation. It is the independent model used to check the following outputs, rather than a claim about PlanMaker’s implementation or extreme-input precision.
A reproducible inverse table
Create InverseValues with Transformed value, FISHERINV and Exponential check in A1:C1. Enter the five inputs in A2:A6.
| Row | A: transformed input | Expected B and C, approximately |
|---|---|---|
| 2 | -1.5 | -0.9051482536 |
| 3 | -0.75 | -0.6351489524 |
| 4 | 0 | 0 |
| 5 | 0.75 | 0.6351489524 |
| 6 | 1.5 | 0.9051482536 |
Enter =FISHERINV(A2) in B2 and =(EXP(2*A2)-1)/(EXP(2*A2)+1) in C2. Fill through row 6. The ordinary finite mathematical results lie strictly between −1 and 1. Finite-precision display can require extra care near those limits.
Put Forward check in D1, enter =FISHER(B2) in D2 and fill through D6. Expected targets are −1.5,−0.75,0,0.75,1.5, matching the original transformed inputs.
For a reciprocal comparison, put =1/A6 in F2 and =FISHERINV(A6) in F3. The targets are approximately 0.6666666667 and 0.9051482536. They perform different operations. At an input of zero, the inverse Fisher model gives zero, whereas division by zero is mathematically undefined.
Round-trip coefficients without retyping displayed values
Create CoefficientCheck with Coefficient, Transformed and Recovered in A1:C1. Enter 0.1,0.5,0.9 in A2:A4. In B2 enter =FISHER(A2) and in C2 enter =FISHERINV(B2); fill through row 4.
The transformed B targets are approximately 0.1003353477,0.5493061443,1.4722194896. The recovered C targets are 0.1,0.5,0.9.
Keep C linked to B’s formula result. Changing display precision does not ordinarily replace the stored number, while copying a shortened display into a new numeric input loses information. This matters most when a later calculation depends on small differences.
A symmetric transformed interval can become asymmetric
This is an algebraic illustration, not a confidence interval. Create IntervalShape and use these cells:
| Cell | Input or formula | Expected result, approximately |
|---|---|---|
| B2 | 0.6 | 0.6 |
| B3 | =FISHER(B2) |
0.6931471806 |
| B4 | 0.25 | 0.25 |
| B6 | =FISHERINV(B3-B4) |
0.4162497345 |
| B7 | =FISHERINV(B3+B4) |
0.7366648767 |
| D6 | =B2-B6 |
0.1837502655 |
| D7 | =B7-B2 |
0.1366648767 |
The two transformed endpoints are equally spaced around B3 by 0.25. After inversion, the distances below and above 0.6 differ. Applying ±0.25 directly to the original coefficient would give different endpoints and would not invert the transformed interval.
The half-width here was chosen for demonstration. No confidence level, sample size or standard-error model has been supplied, so the numbers should not be labelled as statistical confidence bounds.
Limits and related functions
Large transformed inputs can make exponential reconstructions numerically difficult or produce displays very close to an endpoint. The short PlanMaker page does not specify a safe magnitude threshold, exact error labels or all text/array conversion rules. No unobserved boundary result is promised here.
Negative output is valid on the coefficient scale. Do not treat the inverse as a probability function or transfer FISHER’s strict input interval to FISHERINV merely because the names are related.