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Biometrika 1976 63(2):255-262; doi:10.1093/biomet/63.2.255
© 1976 by Biometrika Trust
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Treatment contrasts in paired comparisons: Basic procedures with application to factorials

RALPH A. BRADLEY and ABDALLA T. EL-HELBAWY

Department of Statistics, Florida State University Tallahassee
Institute of Statistical Studies and Research, University of Cairo

A simple procedure for consideration of specified treatment contrasts or sets of contrasts in a paired comparisons experiment is developed. General likelihood estimation and likelihood ratio tests are given. Specified treatment comparisons as appropriate in a particular experiment may be made. The procedure may be used for consideration of factor effects and interactions when the treatments in paired comparisons are factorial treatment combinations. An example is given of a taste preference experiment on coffee with factors, brew strength, roast colour and brand, each at two levels. Results are summarized in an analysis of chi-squared table very analogous to the typical analysis of variance summary.

Key Words: Factorials • Iterative solution of likelihood equations • Maximum likelihood estimation • Paired comparison • Treatment contrasts


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