The Skillings–Mack test (Friedman test when there are missing data)
Mark Chatfield
Medical Research Council
Human Nutrition Research
Cambridge, UK
[email protected]
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Adrian Mander
Medical Research Council
Human Nutrition Research
Cambridge, UK
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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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Mark Chatfield, Adrian Mander
View all articles with these keywords:
skilmack, Skillings–Mack, Friedman, block design, nonparametric, unbalanced, missing data, ties
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