outlier

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An observation that is very different to other observations in a set of data. Since the most common cause is recording error, it is sensible to search for outliers (by means of summary statistics and plots of the data) before conducting any detailed statistical modelling.

Outlier. A small data set showing an obvious outlier. Whenever feasible, data should be plotted, since including an outlier will usually make nonsense of any calculations.
Various indicators are used to identify outliers. One is that an observation has a value that is more than 2.5 standard deviations from the mean. Another is that an observation has a value that lies more than 1.5I beyond the upper or the lower quartile, where I is the interquartile range (see boxplot).

If there is only a single outlier present, then an effective test is the Dixon test. Denoting the kth largest observation by y_(k), the test statistic is either


depending on whether y_(n) appears unusually large, or y₍₁₎ appears unusually small. Special tables are required in order to determine significance.

For data from a normal distribution, the test statistic of the Grubbs test, suggested by Grubbs in 1969, is G, given by
where y̅ and s are the sample mean and standard deviation.

The Rosner test for multiple outliers relies on ordering the n observations in terms of their distance from the overall mean, y̅. Let y_m be the observation that is the mth closest to y̅ and let the mean and standard deviation of the m−1 observations closest to the overall mean be y̅_m−1 and s_m−1. The decision as to whether y_m is an outlier is based on the value of

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1. An example of something (e.g. a site or object) found a long way detached from the main distribution of similar things.

2. A standing stone outside and some distance apart from a stone circle.

(in statistics) a data point that falls far outside the values of others in a data set. The nature of outliers should be understood prior to further analysis: those arising from measurement errors will distort the statistics and hence interpretation of the data; those that are genuine, however, may point to unexpected and hence highly interesting results.

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An extremely high or low value lying beyond the range of the bulk of the data.

See words rhyming with "outlier."