HOW TO ESTIMATE AND USE THE VARIANCE OF d’ FROM DIFFERENCE TESTS

Abstract

d' is an estimate of 6, a measure of the degree of sensory difference between two products, that can be obtained easily using tables, from the proportion of difference tests peformed correctly. Tables of 6 are available for the 2-AFC, 3-AFC, triangular and duo-trio tests. Tables for calculating the variance of d' for these tests are provided in this paper. n e y can be used for comparison of d 's, especially for those obtained from different difference tests. A simple procedure is described here for computing values for the variance of d I . Having obtained the variance, confidence intervals for d' can be obtained, tests of significance ford' can be made as well as tests of whether two or more d's are sign@cantly different. The formula and tables for the number of judgments required for the estimation of 6 are given also in this paper.

The variance of d′ estimates obtained in yes—no and two-interval forced choice procedures

“…This factor contributes to a further reduction in the value ofV d¢ in the conditions in whichV d¢ would otherwise be the greatest. The interaction of these effects results in the pattern shown in Figure 5, where the large values ofV d¢ in 2IFC predicted by Bi et al (1997) are not obtained using Miller's approach. For values of N Ͼ 80, there are in fact values of true d¢ for which the variance ind¢ obtained with 2IFC is greater than that with yes-no, but the effect never grows large because the variance associated withd¢ in either procedure decreases as a function of N.…”

“…This review has been included because the standard ÷2 correction described here plays a critical role in the relation between values ofV d¢ for yes-no and 2IFC. Bi et al (1997) presented a derivation ofV d¢ for 2IFC for the case of equal numbers of Interval 1 and Interval 2 trials and lack of response bias, the same assumptions used above. Their approach is comparable to Gourevitch and Galanter (1967), with the addition of a standard ÷2 correction in the conversion from true d¢ to expected proportion correct.…”

“…Macmillan and Creelman (1991, p. 274) suggested that confidence intervals ford¢ obtained with 2IFC could be arrived at by reducing confidence intervals ford¢ obtained with yes-no (computed using the Gourevitch and Galanter approximation) by a factor of ÷2. Approximations of the variance ofd¢ in 2IFC and other multiple-interval procedures provided by Bi, Ennis, and O'Mahony (1997) suggest that the approach proposed by Macmillan and Creelman is correct when true d¢ is small, but not when true d¢ is greater than about 2.5. The approximation formula derived by Bi et al is based on assumptions identical to those used by Gourevitch and Galanter.…”

“…The Bi et al formula for 2IFC, however, yields values for the variance ofd¢ that increase rapidly with true This work was supported by Grant DC 006648 from the National Institutes of Health. Neil Macmillan pointed out the work by Bi, Ennis, and O'Mahony (1997) and the lack of agreement between that work and the approach to estimatingV d¢ described by Macmillan and Creelman. This work benefited from data analysis software written by Hongyang Tan and Thomas Creutz and from helpful comments by anonymous reviewers.…”

Evaluation of a simple and sensitive sensory method for measuring rancidity in soybean oils

“…These data were combined over the eight judges (6 pairings x 8 judges) giving a total proportion of correct tests for each oil pairing (from 48). From these proportions, d' values were obtained using tables (Bi et al, 1997). Testing whether the differences in perceived rancidity between the oils were statistically significant can be accomplished using binomial statistics.…”