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Variance of d′ for the Tetrad Test and Comparisons with Other Forced-Choice Methods

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Abstract

Tetrad tests are forced-choice discrimination methods that have received comparatively little attention in the past. However, recently, their relatively large statistical power has stimulated interest in these methods. In this paper, some historical notes for the tetrads are presented along with some recent developments in the use of the tetrads. Tables of B are presented for the specified and unspecified tetrad tests. R/S-Plus codes are provided for calculating d′s and variances of d′s for the tetrads. The paper notices that the psychometric function for the unspecified tetrad given by Ennis et al. can be expressed as closed forms. The influential psychometric function for the triangle method can also be expressed as closed forms, which are similar to those of the unspecified tetrad. The latter part of the paper pulls together tables of d and B scattered throughout the literature into single tables for ease of comparison with those values for the tetrad test. In the same spirit, power curves scattered across the literature are also pulled together in a single figure for ease of comparison.

Practical Applications

Thurstonian discriminal distance d′ is a first appropriation, method-independent measure of sensory differences and treatment effects. Estimations of d′ and variance of d′ for the tetrads can be used to compare treatment effects evaluated using the tetrads and other discrimination methods.

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