FISHERINV Function in Excel
The FISHERINV function returns the inverse of the Fisher transformation, converting normalized values back to correlation coefficients for statistical analysis.
Excel
Google SheetsExcelGoogle Sheets=FISHERINV(y)Quick Answer
FISHERINV function FISHERINV function is a statistical function in Excel and Google Sheets that returns the inverse of the Fisher transformation. It converts Fisher-transformed values back to correlation coefficients, enabling statistical analysis of relationships between variables. This function returns a numeric value between -1 and 1 and is commonly used for hypothesis testing, confidence interval construction, and statistical inference on correlation data.
=FISHERINV(y)- `y` - the Fisher-transformed value to convert back to a correlation coefficient
Practical Examples
Basic Inverse Transformation
Converting a single Fisher-transformed value back to correlation coefficient
Confidence Interval Construction
Building 95% confidence interval for a correlation coefficient
Hypothesis Testing Result Interpretation
Converting test statistic back to correlation for research reporting
Array-Based Batch Conversion
Converting multiple Fisher values simultaneously using array formulas
Round-Trip Verification
Testing Fisher transformation accuracy with inverse transformation
Common Errors and Solutions
FISHERINV returns #NUM! error
The input value is outside the practical range for Fisher-transformed values. While mathematically FISHERINV can accept any numeric value, extremely large values (e.g., >10 or <-10) may cause numerical overflow since they correspond to correlations asymptotically approaching ±1.
1. Verify your input is a valid Fisher z-value (typically between -3 and 3) 2. Check that you're not accidentally using a correlation coefficient instead of a Fisher z-value 3. For extreme values, verify your data preprocessing and transformation steps 4. Ensure the original FISHER transformation was applied correctly
Always validate that input values are Fisher-transformed results (z-values) not raw correlations. Use data validation or IF statements to check input ranges.
Example:
FISHERINV cannot process the input
The input parameter contains non-numeric data (text, blank cells, logical values, or error values from previous calculations). FISHERINV requires a numeric value representing a Fisher-transformed correlation.
1. Check that the input cell contains a number, not text or formula error 2. Use ISNUMBER() to verify data type before applying FISHERINV 3. Clean the data to remove text entries or convert them appropriately 4. Use IFERROR to handle upstream calculation errors gracefully
Implement data validation to ensure only numeric values are used. Wrap in error handling functions for production spreadsheets.
Example:
Results are outside expected correlation range
User is inputting raw correlation coefficients instead of Fisher-transformed values. Since FISHERINV expects z-values (typically -3 to 3), inputting correlations (-1 to 1) produces incorrect results. For example, FISHERINV(0.8) = 0.664, not 0.8.
1. Understand that FISHERINV is the *inverse* transformation - it converts z-values TO correlations 2. If you have correlations and want z-values, use FISHER function instead 3. Review your workflow: correlation → FISHER → z-value → FISHERINV → correlation 4. Check documentation to ensure you're using the correct transformation direction
Document your analysis workflow clearly. Label columns as 'Fisher z' vs 'Correlation r' to avoid confusion. Use consistent naming conventions.
Example:
Advanced Tips and Best Practices
Always Use with FISHER for Complete Workflow
FISHERINV should be used as part of a complete transformation workflow: start with correlation coefficients, apply FISHER for statistical analysis in z-scale, then use FISHERINV to convert results back for interpretation. Never use FISHERINV in isolation without understanding the Fisher transformation context. This ensures mathematically sound statistical inference on correlations.
Combine with Confidence Interval Formulas
For research-grade analysis, use FISHERINV to construct confidence intervals around correlation estimates. Transform to z-scale, compute CI using standard error formula 1/sqrt(n-3), then transform bounds back with FISHERINV. This method respects the -1 to 1 bounds of correlations and provides statistically valid confidence intervals for any sample size >3.
Leverage Array Formulas for Efficiency
In Excel 365 or Google Sheets, use dynamic arrays to process multiple Fisher z-values simultaneously. A single formula like =FISHERINV(A2:A100) can convert an entire column of transformed values instantly, dramatically reducing formula complexity and improving spreadsheet performance. This is particularly valuable for large-scale statistical analysis projects.
Beware of Extreme Values
While FISHERINV can theoretically accept any numeric input, values beyond ±3 are rare in practice and may indicate data errors. Fisher z-values beyond ±3 correspond to correlations very close to ±1 (>0.995), which are unusual in real-world data and should be verified. Always investigate extreme values before proceeding with analysis.
Understanding Asymmetry After Transformation
Note that while confidence intervals are symmetric in Fisher z-space, they become asymmetric when converted back to correlation scale using FISHERINV. This is mathematically correct and reflects the bounded nature (-1 to 1) of correlation coefficients. Don't attempt to 'correct' this asymmetry - it's a natural consequence of the transformation and ensures valid statistical inference.
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