## The Annals of Statistics

### Paired Comparisons with Order-Effects

Willem Schaafsma

#### Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176342555

Digital Object Identifier
doi:10.1214/aos/1176342555

Mathematical Reviews number (MathSciNet)
MR381089

Zentralblatt MATH identifier
0277.62057

JSTOR