Kurtosis provides a good omnibus test for outliers in small samples.
OBJECTIVE
To compare the power of the Healy, single-outlier Grubbs, skewness and kurtosis tests for outliers and their applicability to quality control (QC).


METHODS
Power to detect outliers was calculated in simulated samples of twenty normal variates, one or two of which were shifted in mean or increased in variance.


RESULTS
All tests showed similar power against a single outlier. For two outliers shifted in the same direction, skewness then kurtosis were the most powerful; for outliers shifted in opposite directions, Healy's method was just superior to kurtosis. For two outliers of increased variance, these two methods were first equal.


CONCLUSIONS
Where the number of outliers is unknown the kurtosis test for outliers is more versatile than the Grubbs test as it has greater power where there is more than one outlier, a similar power when there is just one outlier, and a similar performance in QC.
Livesey
John H
JH
Endolab, 21 St. Asaph St., Christchurch Hospital, Private Bag 4710, Christchurch, New Zealand. john.livesey@cdhb.govt.nz
D000465:Algorithms; D019411:Clinical Laboratory Techniques / Q000592:standards / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D011786:Quality Control; D015203:Reproducibility of Results; D018401:Sample Size