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arXiv · 1601.07521

Multiple Outliers in Small Samples

Mark Chamness·Rachel Traylor
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Abstract

Z-scores are often employed in outlier detection in a dataset. For small samples, the presence of multiple outliers forces a finite supremum on the absolute value of possible z-scores that decreases with an increasing number of outliers, creating a "masking effect" that hinders identification of true outliers. We give an illustrative case study in which the accurate detection of the number of outliers is critical, and provide a closed form expression of the maximum possible z-score in terms of the sample size and number of outliers. In addition, a corresponding analysis on the $t-$statistic is performed.

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Mark Chamness, Rachel Traylor. 2016-03-14. Multiple Outliers in Small Samples. https://arxiv.org/abs/1601.07521

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