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Fisher inv

FISHERINV Function

The FISHERINV function in Excel calculates the inverse Fisher transformation of a given number. This function is often used in statistics to revert a Fisher-transformed value (produced by the FISHER function) back to its original, untransformed scale.

Key Features of FISHERINV:

  • Computes the inverse Fisher transformation for a given input value.
  • Useful for converting Fisher-transformed values back into correlation coefficients or other original data scales.
  • Frequently applied in statistical analysis, particularly when dealing with correlations and their normalized values.

Syntax:

FISHERINV(y)
  • y: The Fisher-transformed value to be converted back to the original scale.

Formula:

The FISHERINV function implements the following mathematical transformation:

FISHERINV(y) = (e^(2y) - 1) / (e^(2y) + 1)

Where e represents the base of the natural logarithm.

Examples:

  1. Revert the Fisher-transformed value:

    =FISHERINV(0.54931)

This calculates the inverse Fisher transformation of the value 0.54931 and returns the original correlation coefficient (~0.5).

  1. Analyze transformed data:

Suppose you have a Fisher-transformed value stored in cell B1:

```excel
=FISHERINV(B1)
```

This reverts the Fisher-transformed value in B1 back to its original scale.

  1. Combine FISHER and FISHERINV:

To verify that the FISHER and FISHERINV functions are inverse operations:

```excel
=FISHERINV(FISHER(0.5))
```

This returns the original value 0.5.

Notes:

  • The FISHERINV function is defined for all real numbers, as Fisher-transformed values can range from -∞ to ∞.
  • This function is commonly paired with the FISHER function to move back and forth between transformed and original scales.

Applications:

  • Statistical Analysis of Correlations: Convert normalized Fisher-transformed values back into correlation coefficients.
  • Hypothesis Testing: Interpret results of statistical tests relying on Fisher-transformed values by reverting them to their original context.
  • Reversing Fisher Transformations: Use the inverse transformation to interpret normalized correlation values in their original scale.

Tip: Use FISHERINV to easily interpret Fisher-transformed results in the context of the original data.