Outlier Tests

Modified Z-Score

Robust Z-score variant by Iglewicz & Hoaglin (1993) — based on median and MAD.

Statusvalidated

Version1.0.0

Minitab equivalent—

Description

Modified Z-score swaps mean for median and SD for raw MAD. The 0.6745 factor makes it asymptotically consistent with the classical Z-score under normality. Default threshold |M| > 3.5.

Formulas

Modified Z

M_{i} = \frac{0.6745 ( x _{i} - median ( x ))}{MAD}

Robust standardisation

Assumptions

No distributional assumption — robust to outlier-induced bias

Limitations

MAD = 0 → no result possible
Produces no p-value

References

Iglewicz, B. & Hoaglin, D. C. (1993), How to detect and handle outliers, ASQ Quality Press