14 Paired comparisons: Some basic procedures and examples

Publisher Summary This chapter describes some basic procedures and examples related to paired comparisons. The chapter presents the methods for the examination of specified treatment contrasts and the analysis of factorial paired comparison experiments together with examples. These methods provide much new flexibility. Several applications are arisen in many areas, but most notably in food technology, marketing research, and sports competition. Probabilistic models for paired comparisons may be devised to represent the experimental situation and permit appropriate data analysis. The models provide probabilities of possible choices of items or treatments from pairs of items and hence depend on orderings. Then extensions of the method are developed for factorial treatment combinations and for multivariate responses, responses on several attributes for each paired comparison. Multivariate responses to paired comparisons are obtained. For example, this happens in consumer testing where, on paired samples, preferences on a number of characteristics are solicited. The chapter concludes with comments on additional methods of analysis.

[1]  R. A. Bradley.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS: III. SOME LARGE-SAMPLE RESULTS ON ESTIMATION AND POWER FOR A METHOD OF PAIRED COMPARISONS , 1955 .

[2]  K. L. Mehra,et al.  Rank Tests for Paired-Comparison Experiments Involving Several Treatments , 1964 .

[3]  F. Mosteller.  Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations , 1951 .

[4]  Ralph A. Bradley,et al.  Treatment Contrasts in Paired Comparisons: Large-Sample Results, Applications, and Some Optimal Designs , 1978 .

[5]  Robert J. Beaver,et al.  On Extending the Bradley-Terry Model to Incorporate Within-Pair Order Effects , 1977 .

[6]  Ralph A. Bradley,et al.  A 2 X 2 Factorial with Paired Comparisons , 1954 .

[7]  N. T. Gridgeman.  Pair Comparison, with and without Ties , 1959 .

[8]  R. A. Bradley.  Incomplete Block Rank Analysis: On the Appropriateness of the Model for a Method of Paired Comparisons , 1954 .

[9]  Pranab Kumar Sen,et al.  On the asymptotic theory of rank order tests for experiments involving paired comparisons , 1969 .

[10]  Ralph A. Bradley,et al.  Multivariate paired comparisons: The extension of a univariate model and associated estimation and test procedures , 1969 .

[11]  Roger R. Davidson,et al.  A Bibliography on the Method of Paired Comparisons , 1973 .

[12]  Teh-Hsing Wei,et al.  The algebraic foundations of ranking theory , 1952 .

[13]  E. Zermelo.  Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung , 1929 .

[14]  Louis Guttman,et al.  An Approach for Quantifying Paired Comparisons and Rank Order , 1946 .

[15]  R. A. Bradley.  The rank analysis of incomplete block designs. II. Additional tables for the method of paired comparisons. , 1954 .

[16]  O. Dykstra.  A Note on the Rank Analysis of Incomplete Block Designs -- Applications beyond the Scope of Existing Tables , 1956 .

[17]  H. Scheffé.  An Analysis of Variance for Paired Comparisons , 1952 .

[18]  M. Kendall.  Further contributions to the theory of paired comparisons , 1955 .

[19]  R A Bradley.  Science, statistics, and paired comparisons. , 1976, Biometrics.

[20]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[21]  G. T. Park.  Sensory Testing by Triple Comparisons , 1961 .

[22]  H. A. David,et al.  The method of paired comparisons , 1966 .

[23]  William P. Harris,et al.  A revised law of comparative judgment , 1957 .

[24]  R. A. Bradley,et al.  Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons , 1952 .

[25]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.

[26]  W. H. Clatworthy.  Partially balanced incomplete block designs with two associate classes and two treatments per block , 1955 .

[27]  Ralph A. Bradley,et al.  A regression relationship for multivariate paired comparisons , 1971 .

[28]  H. A. David,et al.  Ties in Paired-Comparison Experiments Using a Modified Thurstone-Mosteller Model , 1960 .

[29]  Ralph A. Bradley,et al.  MULTIVARIATE PAIRED COMPARISONS: SOME LARGE-SAMPLE RESULTS ON ESTIMATION AND TESTS OF EQUALITY OF PREFERENCE. , 1969 .

[30]  M. Kendall,et al.  ON THE METHOD OF PAIRED COMPARISONS , 1940 .

[31]  D. V. Gokhale,et al.  A model to incorporat within-pair order effects in paired comparisons , 1975 .

[32]  D. Raghavarao.  Constructions and Combinatorial Problems in Design of Experiments , 1971 .

[33]  Daniel L. Solomon,et al.  A Bayesian approach to paired comparison experimentation , 1973 .

[34]  P. V. Rao,et al.  Ties in Paired-Comparison Experiments: A Generalization of the Bradley-Terry Model , 1967 .

[35]  S. Fienberg,et al.  Log linear representation for paired and multiple comparisons models , 1976 .

[36]  J. Hemelrijk,et al.  A theorem on the sign test when ties are present , 1952 .

[37]  Ralph A. Bradley,et al.  Treatment contrasts in paired comparisons: convergence of a basic iterative scheme for estimation , 1977 .

[38]  G. SadasIvan,et al.  A thurstone-type model for paired comparisons with unequal numbers of repetitions , 1982 .

[39]  Ralph A. Bradley,et al.  Treatment contrasts in paired comparisons: Basic procedures with application to factorials , 1976 .

[40]  L. R. Ford.  Solution of a Ranking Problem from Binary Comparisons , 1957 .

[41]  O. Dykstra.  Rank Analysis of Incomplete Block Designs: A Method of Paired Comparisons Employing Unequal Repetitions on Pairs , 1960 .

[42]  C. I. Bliss,et al.  A Rankit Analysis of Paired Comparisons for Measuring the Effect of Sprays on Flavor , 1956 .

[43]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[44]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[45]  Ralph A. Bradley,et al.  RANKING IN TRIPLE COMPARISONS , 1959 .

[46]  R. Davidson.  On Extending the Bradley-Terry Model to Accommodate Ties in Paired Comparison Experiments , 1970 .

[47]  R. A. Bradley.  SOME STATISTICAL METHODS IN TASTE TESTING AND QUALITY EVALUATION (a, b) , 1953 .