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The ranking and selection problem has been well-studied in the case of continuous responses. In this paper, we address the situation in which continuous responses are replaced by discrete orderings. When individuals in the population provide exhaustive rank-orderings of the alternatives, two common decision rules are the majority rule and the rank-sum method. In the former case, the alternative receiving the most first-place votes is declared superior, while in the latter, the alternative with the smallest rank-sum is deemed the best. Both the Pitman efficiencies and the lower bounds on Bahadur efficiencies of the majority rule relative to the rank-sum method are derived, assuming that the rank data are generated from either the Plackett–Luce or the translative strengths models. In addition, finite sample properties of the two methods are compared with the maximum likelihood approach through simulation studies. Our results suggest two things. First, when it is substantially more difficult to obtain a complete rank-ordering than simply the top choice, the majority rule performs adequately and efforts would be better spent asking many voters to provide top choice rather than fewer voters to provide complete orderings. Second, the rank-sum rule compares favorably to, and is substantially more robust than, the maximum likelihood approach.

Maximum likelihood estimation for exponential families depends exclusively on the first two moments of the data. Recognizing this, Wedderburn [1974. Quasi-likelihood functions, generalized linear models, and the Gauss–Newton method. Biometrika 61, 439–447] proposed estimating regression parameters based on a quasi-likelihood function requiring only the relationship between the mean and variance. We extend quasi-likelihood to situations in which there exists vague prior information on the mean parameters. It is shown when data are exponential family with quadratic variance functions, maximum a posteriori inference under a conjugate prior relies solely on two moments of the data and the prior distribution. This result suggests a Bayesian analog of quasi-likelihood for which only two moments of the data and two moments of the prior need be specified.

In the minimum inhibitory concentration (MIC) test literature, discussion concerning the effect of laboratory-to-laboratory variation is lacking. We present 2 sets of drug dilution test quality control data that illustrate considerable laboratory differences in measured MIC. In both isolates (Escherichia coli, ATCC 25922; Staphylococcus aureus, ATCC 29213) the laboratory-to-laboratory variability accounts for approximately half of the total variability. We illustrate the impact of this variability on the probability of correctly classifying the susceptibility level of an isolate and on the estimation of resistance prevalence. For example, we show that laboratory differences in the probability of correctly classifying the isolate (specifically near the lower breakpoint) can vary up to 80%.

College students enrolled in various kinds of philosophy courses and in a nonphilosophy control group were tested at the beginning and end of the term with different forms of the Watson-Glaser Critical Thinking Appraisal in order to determine the effect of course content on growth in critical thinking. It was found that Logic had a consistent impact on certain aspects of critical thinking, while other philosophy courses when compared to the control group did not have this consistent effect. It was also found that student sex interacts with number of previous philosophy courses for at least one aspect of critical thinking, with females scoring lower than males when both have no previous courses in philosophy and higher than males when both sexes have had previous philosophy courses. Implications of these findings for increasing the growth of critical thinking in other disciplines are discussed.