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Ennis J.M.,The Institute for Perception
Journal of Sensory Studies | Year: 2012

Tetrad testing is theoretically more powerful than Triangle testing, yet the addition of a fourth stimulus raises questions - it is possible that the addition of a fourth stimulus places such an additional demand on subjects that the theoretical advantage of the Tetrad test is lost. In this paper, we provide a guideline to compare results of Tetrad and Triangle. Specifically, it is roughly correct to say that as long as the effect sizes do not drop by more than one third for the same stimuli, then the Tetrad test remains more powerful than the Triangle test. We explain this guideline in terms of perceptual noise, illustrate its use in several examples and discuss the statistical considerations that accompany its use. To assist with statistical evaluation, we provide a table for finding the variance in the Tetrad-based measurement of the effect size. Finally, we show how the Thurstonian framework helps us to improve discrimination testing efficiency even when we do not seek additional power. © 2012 Wiley Periodicals, Inc.


Ennis J.M.,The Institute for Perception
Journal of Sensory Studies | Year: 2013

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. © 2013 Wiley Periodicals, Inc.


Ennis J.M.,The Institute for Perception | Christensen R.H.B.,Technical University of Denmark
Food Quality and Preference | Year: 2014

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. © 2013 Elsevier Ltd.


Ennis J.M.,The Institute for Perception | Jesionka V.,O. P. and P. Product Research B.V.
Journal of Sensory Studies | Year: 2011

"The power of sensory discrimination methods" (PSDM) was published in this journal in 1993. PSDM clarified the need for power considerations in the interpretation of testing results while providing a series of sample size tables. Despite the fact that the data considered in PSDM were binomially distributed, a normal approximation was used that both overestimated power and underestimated sample sizes. Although exact power functions have been examined in the sensory literature, the unusual behavior of these functions has not been embraced; the fact that increasing sample size can decrease power has not yet been incorporated into stable sample size recommendations. In this paper, we provide sample size recommendations with the property that any larger sample sizes also have the desired level of power. These recommendations are given in the form of tables updating those found in PSDM. In addition, a relatively new discrimination testing method known as the tetrad test has grown in popularity recently and this test now needs to be examined from a power perspective. We show that the tetrad test is remarkably powerful for an unspecified test and in some cases only requires one third the sample size as that required by the triangle test. PRACTICAL APPLICATIONS: This paper contains three main practical applications. First, we provide sample size recommendations, including tables, based on the exact power function as determined by the binomial distribution. In particular, this paper is the first to provide exact sample size recommendations such that all larger sample sizes continue to have the desired level of power. Next, we use the exact power analysis to recommend that only the 2-alternative forced choice (AFC); instead of, for example, the 3-AFC or the specified tetrad test be used for forced choice testing in which an attribute of interest is specified to distinguish the samples. Finally, we provide a power analysis of the unspecified tetrad test for the first time in the sensory literature and show that in some cases, the tetrad test only requires one third the sample size as the triangle test. This last point could lead to both significant resource savings and improved confidence for researchers throughout sensory science. © 2011 Wiley Periodicals, Inc.


Ennis J.M.,The Institute for Perception | Ennis D.M.,The Institute for Perception
Journal of Sensory Studies | Year: 2012

The treatment of no preference votes continues to be an issue in sensory science, especially as the proper treatment of these votes has recently gained importance in advertising claims support. There are currently three main methods in common use: dropping the no preference votes, splitting the votes equally and splitting the votes proportionally according to the results among those who expressed a preference. The analyses then proceed as if the data were binomially distributed. In this paper, we compare these methods with respect to power and type I error. We show that proportional splitting returns more false alarms than expected and hence should not be used. We then discuss the meaningful interpretation of statistical significance in the presence of large numbers of no preference votes before providing general recommendations and indicating a promising direction of future research in this area. © 2012 Wiley Periodicals, Inc.

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