Showing papers on "Pairwise comparison published in 1973"

An Evaluation of Ten Pairwise Multiple Comparison Procedures by Monte Carlo Methods

Abstract: Computer simulation techniques were used to study the Type I and Type III error rates and the correct decision rates for ten pairwise multiple comparison procedures. Results indicated that Scheffe's test, Tukey's test, and the Student-Newman-Keuls test are less appropriate than either the least significant difference with the restriction that the analysis of variance F value be significant at α = .05, two Bayesian modifications of the least significant difference, or Duncan's multiple range test. Because of its ease of application, many researchers may prefer the restricted least significant difference.

Estimating the weights for multiple attributes in a composite criterion using pairwise judgments

Abstract: This paper presents a new methodology for estimating the weights or saliences of subcriteria (attributes) in a composite criterion measure. The inputs to the estimation procedure consist of (i) a set of stimuli or objects with each stimulus defined by its subcriteria profile (set of attribute values) and (ii) the set of paired comparison dominance (e.g., preference) judgments on the stimuli made by a single judge (expert) in terms of the global criterion. A criterion of fit is developed and its optimization via linear programming is illustrated with an example. The procedure is generalized to estimate a common set of weights when the pairwise judgments on the stimuli are made by more than one judge. The procedure is computationally efficient and has been applied in developing a composite criterion of managerial success yielding high concurrent validity. This methodology can also be used to perform ordinal multiple regression—i.e., multiple regression with an ordinally scaled dependent variable and a set of intervally scaled predictor variables. The approach is further extended to “internal analysis” (unfolding) using the vector model of preference and to the additive model of “conjoint measurement.”

Pairwise nonmetric multidimensional scaling

Abstract: A method of nonmetric multidimensional scaling is described which minimizes pairwise departures from monotonicity. The procedure is relatively simple, both conceptually and computationally. Experience to date suggests that it produces solutions comparable to those of other methods.

On the construction of weak orders from fragmentary information

Abstract: An iterative method is proposed for constructing a weak order from a partial order on a set of stimuli that is based on individual pairwise comparison data. The method generalizes Duncan Luce's construction of the weak order induced by a semiorder. Various aspects of the iterative procedure are discussed, including its rationale, the number of iterations required to obtain a weak order, and the extent to which the data support additions to the initial partial order as a function of the number of iterations performed before the additions occur.

A pairwise probability approach to the likelihood of the paradox of voting

Abstract: The paradox of voting (transitive individual preferences resulting in intransitive group preferences) is concealed by typical voting rules even when it exists. Consequently, researchers have developed theoretical solutions for the likelihood of the paradox which are based on the probability of individual preference orders. Here we develop a pairwise probability approach which depends only on the probability that one alternative is preferred to another; the likelihood of individual preference orders need not be specified. The results make the probability model more meaningful by establishing broad conditions under which the probability of the paradox is limited rather than varying between zero to one as in the unrestricted case. In addition, the maximum limiting probability of the paradox is shown to be smallest in the neutral case when all pairwise probabilities equal. 5.