Statistical and Thurstonian models for the A-not A protocol with and without sureness

Christensen, Rune Haubo Bojesen; Cleaver, Graham; Brockhoff, Per B.

doi:10.1016/j.foodqual.2011.03.003

Cited by 28 publications

(19 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Christensen and Brockhoff ; Brockhoff and Christensen ; Christensen et al . ) and for use in equivalence testing (c.f. Castura ; Meyners ).…”

Section: Resultsmentioning

confidence: 99%

AThurstonian Analysis of theTwo‐Out‐of‐Five Test

Ennis

2013

Journal of Sensory Studies

View full text Add to dashboard Cite

The Two‐Out‐of‐Five test is a method of unspecified difference testing. Although its low guessing probability (1/10) gives promise that it might have high power, the theoretical underpinnings of the method have not yet been investigated. In this article, we offer the first such investigation, via Thurstonian analysis. This investigation reveals that the standard form of the Two‐Out‐of‐Five test is more statistically powerful than the Triangle test, but not as powerful as the Tetrad test. We then propose a new way of scoring Two‐Out‐of‐Five data that yields a test with higher power and lower sample size requirements than the Tetrad test, under the assumption that there is no additional noise from the evaluation of an additional stimulus. This last result is achieved without any experimental modification of the Two‐Out‐of‐Five protocol. Tables for estimating the Thurstonian measure of sensory effect size, δ, for calculating the error in such estimates, and for recommended sample sizes are given. Finally, caution is given against incorrect instructions in the Two‐Out‐of‐Five test – if respondents are asked simply to identify the two most similar samples, the resulting test has almost no power. Practical Applications This article shows that the standard form of the Two‐Out‐of‐Five test is more powerful than the Triangle test, but is not as powerful as the Tetrad test. The article then proposes a new method of scoring Two‐Out‐of‐Five data that requires smaller sample sizes than the Tetrad test, under the assumption that the evaluation of an additional stimulus does not lead to an increase in perceptual noise. When this alternate method of scoring the data is used, the test is called the Two‐Out‐of‐Five test with forgiveness. Tables for estimating δ, the Thurstonian measure of sensory difference, together with B values that allow practitioners to calculate the variance in their estimates are given for both forms of the Two‐Out‐of‐Five test. Tables of recommended sample sizes are also given in each case. Finally, it is noted that care must be taken to give correct instructions to respondents – it is possible to create a test with very low power if respondents are simply asked to identify the two most similar stimuli.

show abstract

“…Christensen and Brockhoff ; Brockhoff and Christensen ; Christensen et al . ) and for use in equivalence testing (c.f. Castura ; Meyners ).…”

Section: Resultsmentioning

confidence: 99%

AThurstonian Analysis of theTwo‐Out‐of‐Five Test

Ennis

2013

Journal of Sensory Studies

View full text Add to dashboard Cite

show abstract

“…The most common overall discrimination test methods using consumer subjects previously reported in experimental situations that have one reference and multiple stimulus types include the triangle (Kuesten, 2001), duo-trio (Kim & Lee, 2012), same-different (Kuesten, 2001), A-Not A (Bi & Ennis, 2001;Christensen, Cleaver, & Brockhoff, 2011;Lee, van Hout, & O'Mahony, 2007) and degree of difference (DOD) tests (Aust, Gacula, Beard, & Washam, 1985;Hahn et al, 2012;Michon & McDonnell, 2008). In these previous studies, with the exception of Kuesten (2001), no empirical comparison of the different methods was performed.…”

Section: Introductionmentioning

confidence: 99%

Sensory discrimination by consumers of multiple stimuli from a reference: Stimulus configuration in A-Not AR and constant-ref. duo-trio superior to triangle and unspecified tetrad?

Jeong

Kang

Jeong

et al. 2016

Food Quality and Preference

View full text Add to dashboard Cite

“…We have shown how cumulative probit models can be used to merge the statistical modeling framework wellknown from ANOVA and multiple linear regression models for normally distributed data with discrimination and preference testing in the 2-AC model. This continues the line of work initiated by Brockhoff and Christensen (2010) where several common discrimination protocols (m-AFC, duo-trio, triangle and A-not A) were identified as generalized linear models and continued by Christensen et al (2011) where the A-not A protocol with sureness was identified as a cumulative probit model. We also proposed a model for replicated 2-AC data that builds on cumulative link mixed models; a class of models that are useful for analyzing categorical ratings data from sensory experiments as shown by Christensen and Brockhoff (2011a).…”

Section: Discussionmentioning

confidence: 63%

“…For example the effect of explanatory variables can be assessed, e.g., the effect of gender or concentration of some additive can be quantified and tested. Christensen, Cleaver, and Brockhoff (2011) continued this line of work and described how the A-not A protocol with sureness can be identified as a cumulative probit model.…”

Section: Introductionmentioning

confidence: 99%