Precision of measurement in Tetrad testing

• The variance of d’ is compared for the Tetrad, Triangle, and 2-AFC tests.
• The expected widths of the likelihood-based confidence intervals for these tests are compared.
• The advantage of the Tetrad over the Triangle and 2-AFC for equivalence testing is examined.

Interest in the Tetrad test has increased recently as it has become apparent that this methodology can be a more powerful alternative to the Triangle test within the standard difference testing paradigm. But when products are tested following an ingredient or process change, a pressing question is whether a sensory difference is large enough to be meaningful. To this end, in this paper we examine the precision of measurement offered by the Tetrad test as compared to two other standard forced-choice discrimination testing procedures – the Triangle and 2-AFC tests. This comparison is made from a Thurstonian perspective. In particular, for all three methods we compare: (1) The variances in the maximum-likelihood estimates of the Thurstonian measure of sensory difference, (2) The expected widths of the corresponding likelihood-based confidence intervals, and (3) The power of the tests when used for equivalence testing. We find that the Tetrad test is consistently more precise than the Triangle test and is sometimes even more precise than the 2-AFC. As a result of this precision, we discover that the Tetrad test is typically more powerful than the Triangle test for equivalence testing purposes and can, under certain conditions, even be more powerful than the 2-AFC.