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Estimating departure from normality
Author(s) -
Royston Patrick
Publication year - 1991
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780100811
Subject(s) - normality , statistics , statistic , plot (graphics) , mathematics , interpretation (philosophy) , normal distribution , test statistic , econometrics , statistical hypothesis testing , computer science , programming language
Departure of a sample from a normal distribution should be assessed by a quantity that is meaningful in terms of the data, rather than merely by the P ‐value from a test statistic. Indices of departure based on the Shapiro‐Francia W ′ and the Shapiro‐Wilk W statistics are derived, and shown to have a natural interpretation in relation to the normal probability plot. A new diagnostic plot is proposed. An example is given which shows the relationship between one of the new indices and errors in calculated reference ranges due to non‐normality of the data.