The Annals of Statistics

Paired Comparisons with Order-Effects

Willem Schaafsma

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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.

Article information

Ann. Statist., Volume 1, Number 6 (1973), 1027-1045.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F05: Asymptotic properties of tests
Secondary: 62B99: None of the above, but in this section

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


Schaafsma, Willem. Paired Comparisons with Order-Effects. Ann. Statist. 1 (1973), no. 6, 1027--1045. doi:10.1214/aos/1176342555.

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