Are extreme scores "out", "way out" or "far out" and what should we do with them?

Abstract

INTRODUCTION: One of the key foundations of statistics, is the representation of many observations by summary measures. Summaries include the median or middle value, the mean, and measures of variation such as the standard deviation. Unfortunately, the actual data that we collect often contain extreme or unusual values, known as "outliers". these values may be "out", or "far out" in relation to other values, depending upon the distribution. Outliers aren't necessarily a negative thing. For example, evolutionary biologist Stephen Jay Gould was diagnosed with one type of cancer, with a median survival time of 8 months, but died 20 years later from an unrelated form of cancer. Summary measures such as the mean and standard deviation may be highly affected by extreme scores, and so may bias the results. Although the median is less affected by extreme score, we still need to carefully inspect the distribution of the data, using techniques such as histograms and density plots. AIMS: To better summarise, and identify possible outliers in, data - such as length of stay in hospital or operating theatre, improvement in quality of life, or overall functioning - in reports, presentations and scientific publications. METHODOLOGY: Choosing the best ways to summarise data, as well as to identify and handle possible outliers, generally requires researchers and biostatisticians working together. However, simple graphical techniques such as the boxplot are readily available in Microsoft Excel 2016 and statistical packages. RESULTS: Illustrative data and graphs, including new developments in boxplots, will be presented. CONCLUSIONS: Data are valuable, and need to be summarised to as to represent what is actually happening, without losing sight of the individuals. While needing to be careful about "rules of thumb", we must be alert (but not alarmed) for the possibility of outliers and what they may mean.