Outlier Tests

Tukey IQR Rule

Distribution-free outlier flagging via boxplot whisker fences.

Statusvalidated

Version1.0.0

Minitab equivalentGraph > Boxplot (whiskers identify the same fences)

Description

Tukey's rule marks every value below Q1 − k·IQR or above Q3 + k·IQR. Default k = 1.5 highlights potential outliers, k = 3.0 extreme ones. The rule is distribution-free and matches the whiskers of a Tukey boxplot.

Formulas

Untere Schranke

L = Q_{1} - k \cdot IQR

Lower whisker fence (k = 1.5 default)

Obere Schranke

U = Q_{3} + k \cdot IQR

Upper whisker fence

IQR

IQR = Q_{3} - Q_{1}

Interquartile range

Assumptions

No distributional assumption
Sample size: n ≥ 4 (for stable quartiles)

Limitations

Heavy/skewed tails flag many "outliers" that are merely natural tail observations
Produces no p-values or significance statements

References

Tukey, J. W. (1977), Exploratory Data Analysis, Addison-Wesley