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November, 1973 Paired Comparisons with Order-Effects
Willem Schaafsma
Ann. Statist. 1(6): 1027-1045 (November, 1973). DOI: 10.1214/aos/1176342555


Suppose $n$ tea-tasting ladies are asked to compare two brands of brandy. Each lady drinks two cups, one of each brand. The order is determined by coin-tossing. The lady is forced to state whether she prefers the first or the second cup. Thus each lady provides one out of four possible outcomes: which brand did she try first, did she prefer the first or the last cup. One usually summarizes this information by telling for each lady which of the brands she preferred. This paper shows that by doing so some relevant information is lost. One obtains a theory for a $2 \times 2$-table where no UMP unbiased test exists. Several modifications and generalizations are considered.


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Willem Schaafsma. "Paired Comparisons with Order-Effects." Ann. Statist. 1 (6) 1027 - 1045, November, 1973.


Published: November, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0277.62057
MathSciNet: MR381089
Digital Object Identifier: 10.1214/aos/1176342555

Primary: 62F05
Secondary: 62B99

Keywords: A $2 \times 2$ table where no UMP unbiased test exists , an incomplete necessary and sufficient statistic

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 6 • November, 1973
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