PLACE:  321 Snedecor

SPEAKER:
Joachim Kunert
Fachbereich Statistik, University of Dortmund, Germany

TITLE:
On Repeated Difference Tests

ABSTRACT:

If the number of assessors in a difference test is not large enough to ensure the desired power of the testing procedure, then it is often advised to use assessors repeatedly. That is, each assessor performs the testing not just once but several times.

A commonly used test statistic for repeated difference tests is the sum of  all correct assessments, summed over all assessors. Several authors (e.g. o'Mahony, 1982, Brockhoff and Schlich, 1998) argue that the binomial distribution cannot be used to analyse this kind of data. Brockhoff and Schlich (1998) propose an alternative model, where the assessors have different probabilities to correctly identify the odd sample even if the products are identical.

This is criticised by Kunert and Meyners (1999) who agree that assessors will have different probabilities of correct assessment if there are true differences, but do not think that Brockhoff and Schlich's model makes sense under the null hypothesis of product equality. They show that all assessments are independent and all have the same success probability c, if the null hypothesis is true and the experiment is properly randomised and properly carried out. This implies that the sum of all correct assessments is binomial with parameter p = c. Therefore the usual test based on this sum and the critical values of the binomial distribution is a level a test for the null hypothesis of equality of the products, even if there are replications.

The present paper discusses the distribution of the sum of all correct assessments if there are differences between the products and the probabilities for correct assessment are not all equal to c. We use this statistic to derive a confidence interval for the probability that a randomly
selected assessor at a given experiment gives a correct answer.
 

COFFEE
12:45 p.m., 104 Snedecor