Outlier Tests

Z-Score (Outliers)

Flags points with |Z| > threshold using mean and standard deviation.

Statusvalidated

Version1.0.0

Minitab equivalent—

Description

The simplest outlier detector: standardise every value and flag those whose magnitude exceeds a threshold (typically 3). Caveat — mean and standard deviation are themselves distorted by outliers (masking), so the Modified Z-score (MAD-based) is more reliable on contaminated data.

Formulas

Z-Score

Z_{i} = \frac{x _{i} - x ˉ}{s}

Standardised value

Schwelle

∣ Z_{i} ∣ > z_{thr}

Default z_thr = 3 (≈ 99.7 % under normality)

Assumptions

Data approximately normal
Sample size: n ≥ 30 for stable s

Limitations

Masking effect with multiple outliers
Produces no p-value

References

NIST/SEMATECH e-Handbook of Statistical Methods, Section 1.3.5.17.1