The Annals of Statistics

The Analysis of Sequential Experiments with Feedback to Subjects

Persi Diaconis and Ronald Graham

Full-text: Open access

Abstract

A problem arising in taste testing, medical, and parapsychology experiments can be modeled as follows. A deck of $n$ cards contains $c_i$ cards labeled $i, 1 \leq i \leq r$. A subject guesses at the cards sequentially. After each guess the subject is told the card just guessed (or at least if the guess was correct or not). We determine the optimal and worst case strategies for subjects and the distribution of the number of correct guesses under these strategies. We show how to use skill scoring to evaluate such experiments in a way which (asymptomatically) does not depend on the subject's strategy.

Article information

Source
Ann. Statist., Volume 9, Number 1 (1981), 3-23.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345329

Digital Object Identifier
doi:10.1214/aos/1176345329

Mathematical Reviews number (MathSciNet)
MR600529

Zentralblatt MATH identifier
0478.62064

JSTOR
links.jstor.org

Subjects
Primary: 62K99: None of the above, but in this section
Secondary: 62E15: Exact distribution theory

Keywords
Partial randomization card-guessing experiments combinatorics martingales feedback design

Citation

Diaconis, Persi; Graham, Ronald. The Analysis of Sequential Experiments with Feedback to Subjects. Ann. Statist. 9 (1981), no. 1, 3--23. doi:10.1214/aos/1176345329. https://projecteuclid.org/euclid.aos/1176345329


Export citation