Outlier Tests

Hampel Identifier

Robust Z-score replacement using median and MAD — resistant to masking.

Statusvalidated

Version1.0.0

Minitab equivalent—

Description

The Hampel identifier replaces mean and standard deviation in the classical Z-score by median and scaled MAD. Both estimators have a 50 % breakdown point, so they are not distorted by genuine outliers. Threshold k = 3 corresponds to ≈ ±3σ under normality (via the 1.4826 scale).

Formulas

MAD

MAD = median (∣ x_{i} - median (x) ∣)

Median Absolute Deviation

Schwelle

∣ x_{i} - median (x) ∣ > k \cdot 1.4826 \cdot MAD

Flags outliers (default k = 3)

Assumptions

No distributional assumption — robust to skew and heavy tails

Limitations

When MAD = 0 (more than half of values identical) the method yields no result
Produces no p-value

References

Hampel, F. R. (1974), The influence curve and its role in robust estimation, JASA 69(346), 383–393
Pearson, R. K. (2002), Outliers in process modeling and identification, IEEE Trans. Control Syst. Technol. 10(1), 55–63