Maximum Z Scores and Outliers

1988/02/01 by Ronald E. Shiffler · 12 citations
Mathematics · Decision Sciences · #Advanced Statistical Methods and Models #Multi-Criteria Decision Making

paper · doi:10.1080/00031305.1988.10475530

Abstract

Abstract The magnitude of Z(n), the Z score associated with the largest value of X in a data set of size n, is shown to be bounded above by (n — 1)/√n. As a result, outliers defined as values exceeding four standard deviations from the mean cannot exist for small data sets.

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