R to Z-Score Calculator
Convert correlation coefficients (r) to Fisher's Z-scores for statistical analysis with our precise calculator
Correlation Coefficient
Conversion Results
Enter sample size to calculate confidence intervals.
Interpretation
Your correlation coefficient analysis will appear here.
📊 Correlation Coefficient Guide
| r Value | Strength | Direction | Interpretation |
|---|---|---|---|
| ±0.90 to ±1.00 | Very Strong | Positive/Negative | Nearly perfect linear relationship |
| ±0.70 to ±0.89 | Strong | Positive/Negative | Marked relationship |
| ±0.50 to ±0.69 | Moderate | Positive/Negative | Substantial relationship |
| ±0.30 to ±0.49 | Weak | Positive/Negative | Low association |
| ±0.00 to ±0.29 | Very Weak | Positive/Negative | Little to no association |
Note: Interpretation depends on context and field of study.
📚 Statistical Notes
Fisher's Z Transformation
The Fisher Z-transform converts Pearson's r to a normally distributed variable, enabling more accurate statistical tests.
Formula
Z = 0.5 * ln((1+r)/(1-r)) where ln is the natural logarithm
Standard Error
The standard error of Z is 1/√(n-3), used for confidence intervals and hypothesis testing.
Back Transformation
To convert Z back to r: r = (e2Z-1)/(e2Z+1)
Applications
Used in meta-analysis, comparing correlations, and calculating confidence intervals.
Limitations
Assumes bivariate normality and works best with moderate to large sample sizes (n > 10).
Note: This calculator uses Fisher's Z-transformation for converting Pearson correlation coefficients. Results are approximate and should be verified for critical applications. The transformation assumes bivariate normality.