Correlation Analysis
Pearson and Spearman correlation on scatter and regression charts: primary selection from residual Shapiro-Wilk, confidence intervals, effect-size benchmarks, Inspector fields, and limitations.
Correlation analysis measures the strength and direction of the linear relationship between two continuous variables. Licklider calculates both Pearson (parametric) and Spearman (non-parametric) correlations automatically when a scatter or regression chart includes a linear regression run.
Pearson and Spearman
Pearson correlation (r) measures the linear relationship between two variables. It assumes that both variables are approximately normally distributed.
Spearman correlation (ρ) measures the monotonic relationship between two variables using ranks. It does not assume normality and is appropriate when the data contains outliers or non-linear but monotonic trends.
How Licklider selects the primary correlation
Licklider runs both Pearson and Spearman on every eligible scatter or regression chart. The primary correlation — the one highlighted in the Inspector and marked in the Statistical Results Table — is selected based on the normality of the regression residuals:
- Residuals pass Shapiro-Wilk: Pearson is primary
- Residuals fail Shapiro-Wilk: Spearman is primary
This selection is automatic and recorded in the analysis record. Both coefficients are always available regardless of which is primary.
Confidence intervals
Pearson confidence intervals are calculated using the Fisher z-transformation. Spearman confidence intervals use the same Fisher z-approximation, which is standard practice for moderate to large samples.
Effect size interpretation
| Absolute r or rho | Interpretation |
|---|---|
| < 0.10 | Negligible |
| 0.10 – 0.30 | Small |
| 0.30 – 0.50 | Medium |
| ≥ 0.50 | Large |
These thresholds follow Cohen (1988). Hemphill (2003) provides empirical benchmarks from psychology suggesting that correlations above 0.20 represent meaningful effects in many applied contexts.
Reading the output
The Correlation panel in the Inspector reports:
| Field | What it means |
|---|---|
| r | Pearson correlation coefficient |
| ρ | Spearman correlation coefficient |
| 95% CI | Confidence interval (Fisher z) |
| p | p-value for the correlation test |
| n | Number of complete pairs |
| Primary | Which correlation is recommended |
Current limitations
- Correlation is only available alongside linear regression on scatter and regression charts
- Partial correlation is not yet supported
- Correlation matrices (all pairwise) are not yet available
- Kendall's tau is not yet available