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| '''Winsorising''' or '''Winsorization''' (this is also sometimes called Georgization{{citation needed|date=November 2013}}) is the transformation of [[statistic]]s by limiting [[extreme value]]s in the [[statistics|statistical]] data to reduce the effect of possibly spurious [[outliers]]. It is named after the engineer-turned-biostatistician [[Charles P. Winsor]] (1895–1951). The effect is the same as [[clipping (signal processing)|clipping]] in signal processing.
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| The distribution of many [[statistic]]s can be heavily influenced by [[outlier]]s. A typical strategy is to set all outliers to a specified [[percentile]] of the data; for example, a 90% Winsorisation would see all data below the 5th percentile set to the 5th percentile, and data above the 95th percentile set to the 95th percentile.
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| Winsorised [[estimator]]s are usually more [[robust statistics|robust]] to outliers than their more standard forms, although there are alternatives, such as [[Trimmed estimator|trimming]], that will achieve a similar effect.
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| == Example ==
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| Consider the data set consisting of:
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| :<math>\{92, 19, \mathbf{101}, 58, \mathbf{153}, 91, 26, 78, 10, 13, \mathbf{-40}, \mathbf{101}, 86, 85, 15, 89, 89, 25, \mathbf{2}, 41\} \qquad (N = 20)</math>
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| The 5th percentile lies between -40 and 2, while the 95th percentile lies between 101 and 153. (Values shown in bold.)
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| Then a 90% Winsorisation would result in the following:
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| :<math>\{92, 19, \mathbf{101}, 58, \mathbf{101}, 91, 26, 78, 10, 13, \mathbf{2}, \mathbf{101}, 86, 85, 15, 89, 89, 25, \mathbf{2}, 41\} \qquad (N = 20)</math>
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| == Distinction from trimming ==
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| Note that Winsorizing is not equivalent to simply excluding data, which is a simpler procedure, called [[trimmed estimator|trimming]] or [[Truncation (statistics)|truncation]], but is a method of [[Censoring (statistics)|censoring]] data.
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| In a trimmed estimator, the extreme values are ''discarded;'' in a Winsorized estimator, the extreme values are instead ''replaced'' by certain percentiles (the trimmed minimum and maximum).
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| Thus a [[Winsorized mean]] is not the same as a [[truncated mean]].
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| For instance, the 10% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% Winsorised mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. In the previous example the trimmed mean would be obtained from the smaller set:
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| :<math>\{92, 19, \mathbf{101}, 58, \quad 91, 26, 78, 10, 13, \quad \mathbf{101}, 86, 85, 15, 89, 89, 25, \mathbf{2}, 41\} \qquad (N = 18)</math>
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| More formally, they are distinct because the [[order statistics]] are not independent.
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| == References ==
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| * Hasings, C., Mosteller, F., Tukey, J.W., Winsor, C.P. (1947) ''Low moments for small samples: a comparative study of order statistics'', [[Annals of Mathematical Statistics]], 18, 413–426.
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| * W. J. Dixon (1960). ''Simplified Estimation from Censored Normal Samples'', The Annals of Mathematical Statistics, 31, 385–391.
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| * [[John Tukey|J. W. Tukey]] (1962) ''The Future of Data Analysis'', The Annals of Mathematical Statistics, 33, p. 18
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| [[Category:Statistical theory]]
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| [[Category:Robust statistics]]
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| {{Statistics-stub}}
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