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A T hurstonian Model and Statistical Inference for the 2‐Alternative Choice Test with Both Test Pairs and Placebo Pairs
Author(s) -
Bi Jian,
Lee HyeSeong,
O'Mahony Michael
Publication year - 2015
Publication title -
journal of sensory studies
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 53
eISSN - 1745-459X
pISSN - 0887-8250
DOI - 10.1111/joss.12132
Subject(s) - mathematics , estimator , statistics , preference , test (biology) , resampling , statistical hypothesis testing , inference , computer science , artificial intelligence , paleontology , biology
Abstract For the paired difference or preference test applied to consumer research, the 2‐Alternative Choice (2‐ AC ) method that allows a “no difference” or “no preference” option is more suitable. For this method, using both test and placebo pairs is useful for estimating the degree of response bias among the consumers using the test and accurately estimating the degree of difference or preference between the test pairs. This paper proposes a T hurstonian model for the 2‐ AC for both test pairs and placebo pairs in a test method. Maximum likelihood estimations are used for the parameters: d′ , a perceived distance of difference or preference, and τ, a criterion and a decision parameter. Three methods are used for estimations of the covariance matrix for the parameter estimators: (1) using the built‐in functions in the S ‐ P lus and R packages, which are based on maximum likelihood and observed F isher information; (2) the delta method, which is based on the T aylor series approximation; and (3) the bootstrap method, which is computer‐intensive with resampling. Statistical tests are discussed for d′ and vectors of responses for test pairs and placebo pairs in both a monadic design and a paired design. R/S ‐ P lus codes are developed and provided for the calculations. Practical Applications This paper proposes a T hurstonian model for the 2‐Alternative Choice (2‐ AC ) difference test or preference test method with both test pairs and placebo pairs. This test method provides more information than the 2‐ AC method without an embedded placebo pair control. Applying this model, especially for the paired preference test method with a “no‐preference” option can be accurately and readily used for consumer research to achieve various business objectives such as reformulation and claim substantiation. Using R/S ‐ P lus and built‐in functions and codes developed and provided in the paper, maximum likelihood estimation of parameters in the model, covariance matrix of the parameter estimators and statistical tests can be obtained and conducted easily and quickly.