RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS .1. THE METHOD OF PAIRED COMPARISONS
RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS .1. THE METHOD OF PAIRED COMPARISONS
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DOI：
10.1093/biomet/39.3-4.324
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发表时间：
1952-01-01
期刊：
影响因子：
2.7
通讯作者：
TERRY, ME
中科院分区：
文献类型：
--
作者：
BRADLEY, RA;TERRY, ME
配对比较实验的分析在统计方法学中受到了相当大的关注。瑟斯顿（Thurstone，1927）在考虑这一问题时，假设涉及一个线性变量，并且在用于比较的项目之间存在明显的差异。最近，Mosteller（1951 a，B）详细阐述了Thurstone的方法，并假设了一个感觉连续体，在该连续体上感觉是联合正态分布的，并在观察变量的变换之后发展了ax 2检验。Kendall和Babington Smith（1940）提出了一种用于配对比较的分析方法，该方法不依赖于线性变量或正态性的假设，并且该过程可以被描述为组合类型测试。它们形成了一个一致性系数，基本上衡量了与完全一致性的差异，尽管测试中使用的模型没有明确制定。在主观测试中，裁判的一致性是用循环三和弦来衡量的。我们注意到，当已知存在差异时，一致性检验和一致性检验也可以被认为是基于不存在差异的假设的零假设检验。Guttman（1946）提出了一种量化配对比较的方法。他的问题是确定一个数值为每一个项目的数量将最好地代表比较在某种意义上。这个问题可以被认为是一个与检验假设的问题不同的估计问题。当在排序实验中只比较两个项目时，它们之间在某些特征上无差异的假设的检验可以基于二项分布。在给定的比较中，可以完成对项目是最优的概率的估计，并且这些估计提供了对项目进行评级的方法或量化的方法。本文给出了二项模型和分布的推广。
The analysis of experiments involving paired comparisons has received considerable attention in statistical methodology. Thurstone (1927) has considered the problem on the assumptions that a linear variate is involved and that perceptible differences exist among the items presented for comparison. More recently, Mosteller (1951 a, b) has elaborated upon Thurstone's method and, having postulated a sensation continuum over which sensations are jointly normally distributed, has developed ax2 test following transformation of the observed variates.Kendall & Babington Smith (1940) proposed a method of analysis for paired comparisons which does not depend on assumptions of a linear variate or of normality, and the procedure may be described as a combinatorial type test. They form a coefficient of agreement which essentially measures discrepancies from perfect agreement, although the model used in the test is not explicitly formulated. In subjective tests the consistency of a judge is measured in terms of circular triads. We note that tests of consistency and tests of agreement, when differences are known to exist, may also be considered to be tests of null hypotheses upon the postulation of absence of differences. Guttman (1946) has developed a method of quantifying paired comparisons. His problenm was to determine a numerical value for each of a number of items which will best represent the comparisons in some sense. The problem may be considered to be one of estimation as distinct from the problem of testing hypotheses. When only two items are to be compared in a ranking experiment, a test of the hypothesis of no-difference between them on some characteristic may be based on the binomial distribution. The estimation of the probabilities that the items are stuperior in a given comparison may be accomplished, and these estimates afford a method of rating the items or a method of quantification. In the present paper a generalization of the binomial model and distribution is obtained.