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

Author

Listed:
  • Mark Chatfield

    (Medical Research Council, Cambridge, UK)

  • Adrian Mander

    (Medical Research Council, 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. 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.

Suggested Citation

  • Mark Chatfield & Adrian Mander, 2009. "The Skillings–Mack test (Friedman test when there are missing data)," Stata Journal, StataCorp LP, vol. 9(2), pages 299-305, June.
    • Handle: RePEc:tsj:stataj:v:9:y:2009:i:2:p:299-305
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    Cited by:

    1. Schröter, Iris & Mergenthaler, Marcus, 2020. "Bewertung betrieblicher Maßnahmen für eine tierwohlorientierte landwirtschaftliche Tierhaltung der Zukunft durch Landwirt:innen in Deutschland unter Berücksichtigung von Persönlichkeitsmerkmalen," 60th Annual Conference, Halle/ Saale, Germany, September 23-25, 2020 305594, German Association of Agricultural Economists (GEWISOLA).
    2. M. Lefebvre & C. Biguzzi & E. Ginon & S. Gomez-y-Paloma & S. R. H. Langrell & S. Marette & G. Mateu & A. Sutan, 2017. "Mandatory integrated pest management in the European Union: experimental insights on consumers’ reactions," Review of Agricultural, Food and Environmental Studies, Springer, vol. 98(1), pages 25-54, July.
    3. Schröter, Iris & Mergenthaler, Marcus, 2020. "Bewertung betrieblicher Maßnahmen für eine tierwohlorientierte landwirtschaftliche Tierhaltung der Zukunft durch Landwirt:innen in Deutschland unter Berücksichtigung von Persönlichkeitsmerkmalen," 60th Annual Conference, Halle/ Saale, Germany, September 23-25, 2020 305594, German Association of Agricultural Economists (GEWISOLA).
    4. Geva, Sharon & Fulman, Nir & Ben-Elia, Eran, 2022. "Getting the prices right: Drivers' cruising choices in a serious parking game," Transportation Research Part A: Policy and Practice, Elsevier, vol. 165(C), pages 54-75.
    5. Michelle Colder Carras & Matthew Carras & Alain B. Labrique, 2020. "Stakeholders’ Consensus on Strategies for Self- and Other-Regulation of Video Game Play: A Mixed Methods Study," IJERPH, MDPI, vol. 17(11), pages 1-14, May.

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