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

Mark David Chatfield and Adrian Paul Mander ()

Stata Journal, 2009, vol. 9, issue 2, pages 299-305

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. The skilmack command is also useful when there are many ties or equal ranks (N.B. the Friedman statistic compared with the χ2 distribution will give a conservative result), as well as for small samples; appropriate results can be obtained by simulating the distribution of the test statistic under the null hypothesis.

Keywords: skilmack; Skillings – Mack; Friedman; block design; nonpara- metric; unbalanced; missing data; ties (search for similar items in EconPapers)
Date: 2009

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