Skillings-Mack Statistic: Computer-Intensive Methods

Authors

  • Patchanok Srisuradetchai
  • Nantapath Trakultraipruk

Keywords:

block designs, Monte Carlo method, missing values

Abstract

The Skillings-Mack statistic is the appropriate statistic when missing observations occur randomly in a block design. In this paper, the exact randomization test and the Monte Carlo method are applied for the Skilling-Mack test statistic. We found that when there is more missing data, the chi-squared distribution is worse for being a reference distribution to calculate critical values even for significance levels near .10. Furthermore, for some designs with two missing values it is impossible to reject the null hypothesis when using the chi-squared distribution. Also, we have developed the R package named Skillings.Mack to calculate the Skillings-Mack statistic as well as produce p-values based on the Monte Carlo method. Our R package is very useful when there are many ties and/or small designs are conducted. Finally, we present tables of critical values for block designs with two missing observations.

Author Biographies

Patchanok Srisuradetchai

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University

Nantapath Trakultraipruk

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University

References

1. Friedman, M.: The use of ranks to the avoid the assumption of normality Implicit in the analysis of variance. Journal of the American Statistical Association. 32, 675-701 (1937)

2. Durbin, J.: Incomplete blocks in Ranking Experiment. British Journal of Statistical Psychology. 4, 85-90 (1951)

3. Benard, A. and Van Elteren, P.: A generalization of the method of m rankings. In: Koninklijke Akademie van Wetenschappen. International Mathematical Congress Amsterdam, Series A. 56, 358-369 (1954)

4. Brunden, M.N. and Mohberg, N.R.: The Benard-Van Elteren statistic and nonparametric computation. Communications in Statistic-Simulation and Computation. 5, 155-162 (1976)

5. Skillings, J.H. and Mack, G.A.: On the use of a Friedman-type statistic in balanced and unbalanced block designs. Journal of the Royal Statistical Society. 23, 171-177 (1981)

6. Chatfield, M. and Mander, A.: The Skillings-Mack test (Friedman test when there are missing data). The Stata journal. 9, 299-305 (2009)

7. Cunningham, M.: A nonparametric method to assess treatment effects for unbalanced designs using SAS/IML. SAS Global Forum (2010)

8. Bi, J.: Computer-intensive methods for sensory data analysis, exemplified by Durbins rank test. Food Quality and Preference. 20, 195-202 (2009)

9. Fawcett, R.F. and Salter, K.C.: Distributional studies and the computer: An analysis of Durbin’s rank test. The American Statistician. 41, 81-83 (1987)

10. R Core Team. R: A language and environmental for statistical computing (2015)

11. Srisuradetchai, P.: Skillings.Mack: The Skillings.Mack test statistic for block designs with missing observations. R package version 1.10 (2015), http://CRAN.R-project.org/package=Skillings.Mack

12. Fisher, R.A.: The design of experiments. 9th ed. Macmillan Pub Co (1971)

13. Pitman, E.J.G.: Significance tests which may be applied to samples from any populations. Technometrics. 4, 119-130 (1937)

14. Kennedy, P.E.: Randomization tests in econometrics. Journal of Business & Economic Statistics. 13, 85-94 (1995)

15. Kalos, M.H. and Whitlock, P.A.: Monte Carlo methods. 2nd ed. Darmstadt, Wiley-VCH Verlag GmbH & Co (2008)

16. Hubbard, D.W.: How to measure anything: Finding the Value of “Intangibles” in Business. Hoboken. John Wiley & Sons Inc (2010)

17. Metropolis, N. and Ulam, S.: The Monte Carlo method. Journal of the American Statistical Association. 44, 335-341 (1949)

18. Metropolis, N.: The beginning of the Monte Carlo method. Los Alamos Science, 125 (1987)

19. Hartley, H.O.: The impact of computers on statistics. In: D.B. Owens, ed. 1976. On the history of statistics and probability, pp. 421-442. Marcel Dekker, New York (1976)

20. North, B.V., Curtis, D. and Sham, P.C.: A note on the calculation of empirical P values from Monte Carlo procedures. American journal of human genetics. 71, 439-441 (2002)

21. Broman, K.W., Caffo, B.S.: Simulation-based P values: response to North et al.. American journal of human genetics. 72, 496 (2003)

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Published

2016-12-31

How to Cite

Srisuradetchai, P., & Trakultraipruk, N. (2016). Skillings-Mack Statistic: Computer-Intensive Methods. Journal of Applied Statistics and Information Technology, 1(2), 33–45. Retrieved from https://ph02.tci-thaijo.org/index.php/asit-journal/article/view/164759

Issue

Vol. 1 No. 2 (2016): Journal of Applied Statistics and Information Technology Vol1 No2 (July - December 2016)

Section

Research Articles

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เนื้อหาและข้อมูลที่ปรากฏในบทความที่ตีพิมพ์ในวารสารสถิติประยุกต์และเทคโนโลยีสารสนเทศถือเป็นความคิดเห็นส่วนบุคคลของผู้เขียนแต่ละท่าน ความผิดพลาดของข้อความและผลที่อาจเกิดจากนำข้อความเหล่านั้นไปใช้ผู้เขียนบทความจะเป็นผู้รับผิดชอบแต่เพียงผู้เดียว บทความ ข้อมูล เนื้อหา รูปภาพ ฯลฯ ที่ได้รับการตีพิมพ์ในวารสารถือเป็นลิขสิทธิ์ของวารสาร หากบุคคลหรือหน่วยงานใดต้องการนำทั้งหมดหรือส่วนหนึ่งส่วนใดไปเผยแพร่ต่อหรือเพื่อกระทำการใดๆ จะต้องได้รับอนุญาตเป็นลายลักอักษรณ์จากวารสาร ก่อนเท่านั้น