Information criteria for pairwise comparisons.

A new approach is presented for the interpretation of differences among means and proportions. Post hoc techniques, such as Tukey's honestly significant difference procedure, have interpretive problems related to intransitive decisions and technical issues arising from unequal sample sizes or heterogeneity of variance. These concerns can be avoided by considering ordered subsets of means and by using information criterion to select among competing models. This paired-comparisons information-criterion (PCIC) approach is wholistic in nature and does not depend on interpreting a series of statistical tests. Simulation results suggest that a protected version of the PCIC procedure is desirable to minimize failures to detect the null case. This technique is illustrated for independent means, proportions, and means from repeated measures.

[1]  J. Rost,et al.  Applications of Latent Trait and Latent Class Models in the Social Sciences , 1998 .

[2]  Scott E. Maxwell,et al.  Designing Experiments and Analyzing Data , 1992 .

[3]  A. Tamhane,et al.  Multiple Comparison Procedures , 1989 .

[4]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[5]  S. Sclove.  Application of model-selection criteria to some problems in multivariate analysis , 1987 .

[6]  A. Scott,et al.  A Cluster Analysis Method for Grouping Means in the Analysis of Variance , 1974 .

[7]  H. Akaike.  A new look at the statistical model identification , 1974 .

[8]  S. G. Carmer,et al.  Evaluation of Cluster Analysis for Comparing Treatment Means1 , 1980 .

[9]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[10]  C. Dayton,et al.  Detecting patterns of bivariate mean vectors using model‐selection criteria , 1995 .

[11]  H. Bozdogan.  Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions , 1987 .

[12]  C. Dayton.  SUBSET: Best Subsets using Information Criteria , 2001 .

[13]  Marie Skodak,et al.  A Final Follow-Up Study of One Hundred Adopted Children , 1949 .

[14]  C. Mitchell Dayton,et al.  Information Criteria for the Paired-Comparisons Problem , 1998 .

[15]  William G. Cochran,et al.  Experimental Designs, 2nd Edition , 1950 .

[16]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[17]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[18]  B. L. Welch.  ON THE COMPARISON OF SEVERAL MEAN VALUES: AN ALTERNATIVE APPROACH , 1951 .

[19]  T. Caliński,et al.  Clustering means in ANOVA by simultanuous testing , 1985 .