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The Stata Journal
Volume 9 Number 2: pp. 299-305

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The Skillings–Mack test (Friedman test when there are missing data)

Mark Chatfield
Medical Research Council
Human Nutrition Research
Cambridge, UK
Adrian Mander
Medical Research Council
Human Nutrition Research
Cambridge, UK
Abstract.  The Skillings–Mack statistic (Skillings and Mack, 1981, Technometrics 23: 171–177) is a general Friedman-type statistic that can be used in almost any block design with an arbitrary missing-data structure. The missing data can be either missing by design, for example, an incomplete block design, or missing completely at random. The Skillings–Mack test is equivalent to the Friedman test when there are no missing data in a balanced complete block design, and the Skillings–Mack test is equivalent to the test suggested in Durbin (1951, British Journal of Psychology, Statistical Section 4: 85–90) for a balanced incomplete block design. The Friedman test was implemented in Stata by Goldstein (1991, Stata Technical Bulletin 3: 26–27) and further developed in Goldstein (2005, Stata Journal 5: 285). This article introduces the skilmack command, which performs the Skillings–Mack test.
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