FISHERINV function

The FISHERINV function in Excel is the inverse of the Fisher transformation. It is used to convert a transformed correlation coefficient back into the original correlation coefficient (a value between -1 and 1). This is particularly useful when you have applied the Fisher transformation to a correlation coefficient and need to reverse it to its original scale.

Syntax:

FISHERINV(z)

Arguments:

• z: The transformed value (result of the Fisher transformation), which is the value that you want to convert back to the original correlation coefficient.

Formula:

The inverse Fisher transformation formula is:

$$r = \frac{e^{2z} – 1}{e^{2z} + 1}$$

Where:

• $z$ is the Fisher transformed value.
• $e$ represents the base of the natural logarithm.

Example:

If you have a Fisher-transformed value of 1.0986 (which corresponds to a transformed correlation coefficient of 0.8), you can reverse this transformation to obtain the original correlation coefficient:

=FISHERINV(1.0986)

This will return approximately 0.8, which is the original correlation coefficient.

Key Points:

• The FISHERINV function is used to reverse the Fisher transformation and return the original correlation coefficient.
• The Fisher transformation is used to make correlation coefficients more suitable for statistical analysis, and the inverse function is used to interpret those results in their original scale (from -1 to 1).
• The inverse Fisher transformation is useful when working with confidence intervals or hypothesis tests that involve the Fisher-transformed values.

Use Cases:

• Restoring Original Correlation: After applying the Fisher transformation to a correlation coefficient for statistical analysis, you can use FISHERINV to get the original value.
• Confidence Intervals for Correlations: After calculating confidence intervals for the Fisher-transformed correlation, you can reverse the transformation to get the interval in terms of the original correlation coefficient.
• Hypothesis Testing: Used in situations where you have transformed correlation coefficients and need to interpret the results in the context of the original scale.

Example Workflow:

1. Apply the FISHER transformation to a correlation coefficient (e.g., 0.8) to stabilize its variance.
2. Perform statistical analysis on the transformed value (e.g., test significance, calculate confidence intervals).
3. Use FISHERINV to reverse the transformation and interpret the results in the context of the original correlation coefficient.