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 chi(2) 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.

中文翻译：

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Skillings-Mack 检验（缺失数据时的弗里德曼检验）。

Skillings-Mack 统计量（Skillings 和 Mack，1981，Technometrics 23：171-177）是一种通用的 Friedman 型统计量，可用于几乎任何具有任意缺失数据结构的块设计。缺失数据可能是设计原因缺失，例如不完整的区组设计，或者完全随机缺失。当平衡完整区组设计中没有缺失数据时，Skillings-Mack 检验等效于 Friedman 检验，而 Skillings-Mack 检验等效于 Durbin (1951, British Journal of Psychology, Statistical Section 4) 中建议的检验： 85-90）用于平衡的不完全块设计。Friedman 测试由 Goldstein（1991，Stata Technical Bulletin 3：26-27）在 Stata 中实施，并在 Goldstein（2005，Stata Journal 5：285）中进一步发展。本文介绍了skilmack命令，它执行 Skillings-Mack 检验。 当有很多关系或相等的等级时，skilmack 命令也很有用（注意，弗里德曼统计量与 chi(2) 分布相比将给出保守的结果），以及对于小样本；通过模拟零假设下检验统计量的分布，可以得到合适的结果。