Statistical Methods Guide

Statistical Methods Guide

Univariate Methods

• IQR: robust to non-normal data; configure lower/upper factors.
• Z-score: assumes approximate normality; configurable threshold.
• Modified Z-score: robust via MAD; default threshold 3.5.

Multivariate Methods

• Mahalanobis distance: detects multivariate outliers using covariance structure.
  • chi2_threshold: percentile in (0,1] or absolute chi-square statistic.
  • use_shrinkage=True to enable Ledoit–Wolf covariance if scikit-learn available.

Formal Tests

• Grubbs' test: single outlier detection with p-value and critical value.
• Dixon's Q-test: for small n (<30); approximate p-value reported.

Transformations

• Box-Cox (positive data): optimal lambda estimated; preserves NaNs.
• Log (natural, base 10, base 2): shifts applied for non-positive values.
• Square-root: shifts applied for negatives.

Best practices: drop NaNs before tests where needed; sample large data for Shapiro.

Warning: Dixon’s Q-test is recommended only for small sample sizes (n < 30).

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