COMPARISON OF CORRELATED PROPORTIONS IN REPLICATED PRODUCT TESTS

Product testing with multiple matched samples is often encountered. If the response for each sample is binary, the test involves comparison of multiple proportions of dependent samples. In the paper, a test statistic due to Bennett (1967, 1968) is discussed and extended to the replicated testing situation. An adjusted Bennett's statistic is proposed based on the Dirichlet-multinomial distribution. The conventional and adjusted Bennett's statistics are illustrated by a numerical example in product testing.     

COMPARISON OF THE EFFICIENCY OF PAIR, DUO-TRIO AND TRIANGLE TESTS

The pair, duo-trio and triangle tests were compared, using three levels of instructions with orange drink as medium and sucrose as stimulus. If the subjects know only the nature of the test, the pair test cannot be performed and the frequencies of correct responses above chance of the two other tests do not differ significantly, in this case the triangle test is the more efficient. If the subjects know the nature of the test and the nature of the stimulus, the frequency of correct responses above chance obtained for the pair test is significantly higher than those of the two other tests, in this case the pair test is more efficient. Finally, if the subjects know the nature of the test, the nature of the stimulus and whether or not the sample to be selected contains the stimulus, the conclusions are more difficult to achieve but the triangle test seems to be the more efficient.     

COMPARISON OF METHODS FOR ANALYZING REPLICATED PREFERENCE TESTS

Preference testing is commonly used in consumer sensory evaluation. Traditionally, it is done without replication, effectively leading to a single 0/1 (binary) measurement on each panelist. However, to understand the nature of the preference, replicated preference tests are a better approach, resulting in binomial counts of preferences on each panelist. Variability among panelists then leads to overdispersion of the counts when the binomial model is used and to an inflated Type I error rate for statistical tests of preference. Overdispersion can be adjusted by Pearson correction or by other models such as correlated binomial or beta‐binomial. Several methods are suggested or reviewed in this study for analyzing replicated preference tests and their Type I error rates and power are compared. Simulation studies show that all methods have reasonable Type I error rates and similar power. Among them, the binomial model with Pearson adjustment is probably the safest way to analyze replicated preference tests, while a normal model in which the binomial distribution is not assumed is the easiest.     

EFFECT OF ASSESSORS EXPERTISE LEVEL ON EFFICIENCY OF WARM-UP FOR TRIANGLE TESTS

The effect of warm-up on performance for repeated triangle tests is studied according to assessors' expertise level for both triangle test strategy and the pair of products to compare. Three experiments performed with orange flavored soft drinks show that the effect of warm-up depends on the assessors' expertise: (1) naive assessors do not increase their performance with warm-up; (2) assessors with a moderate practice of both triangle tests and the pair of products improve their performance with warm-up; (3) assessors with a moderate practice of triangle tests, but not familiar with the pair of products, improve their performance with warm-up too; and (4) assessors highly experienced for both triangle tests and products do not improve their performance with warm-up. These results support the idea that the positive effect of warm-up is due to an attentional process: Warm-up seems to help assessors focusing their attention on the dimension on which the two products are actually different and ignoring the other dimensions. Thus, results show that assessors are able to learn the difference between the two products and to learn to focus their attention on this difference at any time. They also suggest that prior knowledge of the triangle test scheme is required to benefit from warm-up.     

THE DESIGN OF REPLICATED DIFFERENCE TESTS

We show that adding replications in replicated difference tests results in larger power and smaller variance when the number of assessors is fixed. On the other hand, when the number of total assessments is fixed, the power usually decreases and the variability increases whenever replications are considered instead of different assessors. The appropriate numbers of assessor needed to gain the same power and variability, respectively, when replications are used will be given. It is shown that the number of assessors might indeed be reduced, but this has to be paid for by an increasing total number of assessments. We show that two key models, namely the mixture binomial and a corrected version of the Beta-binomial model, are quite similar with respect to the properties of interest. We provide tables from which, according to her/his requirements, the investigator might find an appropriate setting with respect to the number of assessors and replications.     

THE EFFECT OF 40 HOURS OF CONSTANT WAKEFULNESS ON NUMBER COMPARISON PERFORMANCE

We investigated the effects of sleep loss and circadian rhythm on number comparison performance. Magnitude comparison of single-digits is robustly characterized by a distance effect: Close numbers (e.g., 5 versus 6) produce longer reaction times than numbers further apart (e.g., 2 versus 8). This distance effect is assumed to reflect the difficulty of a comparison process based on an analogous representation of general magnitude. Twelve male participants were required to stay awake for 40?h in a quasi-constant-routine protocol. Response speed and accuracy deteriorated between 00:00 and 06:00?h but recovered afterwards during the next day, indicating a circadian rhythm of elementary cognitive function (i.e., attention and speed of mental processing). The symbolic distance effect, however, did not increase during the nighttime, indicating that neither cumulative sleep loss nor the circadian clock prolongs numerical comparison processes. The present findings provide first evidence for a relative insensitivity of symbolic magnitude processing against the temporal variation in energy state. (Author correspondence: michael.steinborn@uni-tuebingen.de)     

BETA-BINOMIAL TABLES FOR REPLICATED DIFFERENCE AND PREFERENCE TESTS

Ennis and Bi (1998) discussed the beta-binomial (BB) model for replicated difference and preference tests. Based on the BB model, tables of the minimum number of choice responses to achieve significance at α≦ 0.05 are provided for replicated 2-AFC, Duo-Trio, 3-AFC and Triangular tests. The theory underlying the tables, how to use the tables, as well as some examples to illustrate their use are given. The tables can be used to evaluate the results of replicated difference and preference tests using forced choice methods.     

THE POWER OF SENSORY DISCRIMINATION METHODS USED IN REPLICATED DIFFERENCE AND PREFERENCE TESTS

Research on the power of discrimination methods in difference and preference tests has both theoretical and practical significance. Power is important to evaluate the sensitivities of tests and determine sample size. Ennis and Bi (1998, 1999) proposed the beta-binomial distribution to model replicated difference and preference tests with inter-trial variation and analyzed in general the power of the tests. In this paper, the power of discrimination methods for replicated difference and preference tests is discussed further. The equations for calculating power for methods based on the BB model are given. Examples with tables and charts for calculating and comparing the power of the methods are also given.     

POWER AND SENSITIVITY OF THE SAME-DIFFERENT TEST: COMPARISON WITH TRIANGLE AND DUO-TRIO METHODS

Same-different, duo-trio and triangle discrimination methods were compared using vanilla flavored yogurt with and without added sugar as the medium. Two experiments were performed, one in controlled laboratory conditions and the other in conditions approximating more to consumer testing. A modification of the same-different test had greater power than the duo-trio of triangle tests. At higher sugar concentrations, d'values for the three methods were equivalent. Yet, at lower sugar concentrations, the same-different d'tended to be higher. The results are discussed in terms of Sequential Sensitivity Analysis, memory effects and changes between β and criteria.     

EFFECT OF TEMPERATURE AND DESICCATION ON THE PHOTOSYNTHETIC PERFORMANCE OF PORPHYRA PERFORATA

Porphyra perforata is a common seaweed inhabiting the upper intertidal zone, and as a consequence it experiences great fluctuations in tissue temperature and desiccation. The objective of this work was to evaluate the effect of ambient temperature and the tissue desiccation status on the photosynthetic performance of P. perforata. Photosynthetic performance was evaluated polarographically after the temperature or desiccation treatments. Maximum photosynthesis (P_max) occurred between 25 and 30° C and decreased at higher and lower temperatures, however, no significant differences were observed in the initial slope of photosynthesis (α) from 10 to 30° C. This suggests that the photosynthetic efficiency of this species does not decrease as a result of fluctuating temperatures during tidal emergence/submergence. P_max and α were relatively constant in tissue of P. perforata with 5 to 100% relative water content. This also suggests that natural desiccation rates during low tides do not decrease photosynthetic rates in this species. Variations in the synthesis of specific proteins as a result of fluctuations in temperature and relative water content in the tissue of P. perforata are being studied.     

A THURSTONIAN VARIANT OF THE BETA-BINOMIAL MODEL FOR REPLICATED DIFFERENCE TESTS

The beta-binomial model is combined with a Thurstonian psychometric function to obtain estimates of the parameters of a distribution applicable to replicated difference tests. A method of estimating the variance of d'obtained from these tests is provided. A formula for determining sample size, which is composed of the number of trials (or panelists) and the number of replications, to determine d'is also given.     

THE BETA-BINOMIAL MODEL: ACCOUNTING FOR INTER-TRIAL VARIATION IN REPLICATED DIFFERENCE AND PREFERENCE TESTS

Binomial tests are commonly used in sensory difference and preference testing under the assumptions that choices are independent and choice probabilities do not vary from trial to trial. This paper addresses violations of the latter assumption (often referred to as overdispersion) and accounts for variation in inter-trial choice probabilities following the Beta distribution. Such variation could arise as a result of differences in test substrate from trial to trial, differences in sensory acuity among subjects or the existence of latent preference segments. In fact, it is likely that overdispersion occurs ubiquitously in product testing. Using the Binomial model for data in which there is inter-trial variation may lead to seriously misleading conclusions from a sensory difference or preference test. A simulation study in this paper based on product testing experience showed that when using a Binomial model for overdispersed Binomial data, Type I error may be 0.44 for a Binomial test specification corresponding to a level of 0.05. Underestimation of Type I error using the Binomial model may seriously undermine legal claims of product superiority in situations where overdispersion occurs. The Beta-Binomial (BB) model, an extension of the Binomial distribution, was developed to fit overdispersed Binomial data. Procedures for estimating and testing the parameters as well as testing for goodness of fit are discussed. Procedures for determining sample size and for calculating estimate precision and test power based on the BB model are given. Numerical examples and simulation results are also given in the paper. The BB model should improve the validity of sensory difference and preference testing.     

EFFECT OF MUSIC ON ANAEROBIC EXERCISE PERFORMANCE

For years, mostly the effects of music on cardiorespiratory exercise performance have been studied, but a few studies have examined the effect of music on anaerobic exercise. The purpose of this study was to assess the effect of listening to music and its rhythm on anaerobic exercise: on power output, heart rate and the concentration of blood lactate. 28 male subjects were required to visit the laboratory on 6 occasions, each separated by 48 hours. Firstly, each subject performed the Running-based Anaerobic Sprint Test (RAST) under 3 conditions on separate days: while listening to “slow rhythm music”, “fast rhythm music” or “no music”. 48 hours after the subjects completed RAST under 3 conditions, Wingate Anaerobic Power (WAN) tests were performed under 3 music conditions. The order of the 3 conditions (slow music, fast music and no music) was selected randomly to prevent an order effect. Results showed no significant differences between 3 conditions in anaerobic power assessments, heart rate or blood lactate (p > 0.05). On the basis of these results it can be said that music cannot improve anaerobic performance. The type of music had no impact on power outputs during RAST and WAN exercise. As a conclusion, listening to music and its rhythm cannot enhance anaerobic performance and cannot change the physiological response to supramaximal exercise.     

INVESTIGATION OF THE DUAL-PAIR METHOD AS A POSSIBLE ALTERNATIVE TO THE TRIANGLE AND SAME-DIFFERENT TESTS

Previous experiments have shown that the same-different test, because of its more suitable cognitive strategy and lower memory requirements, is a more powerful and sensitive alternative to the triangle and duo-trio tests. This project describes an experiment conducted in order to investigate ways to improve further the performance of the same-different test. Three protocols were compared using orange flavored beverages and 24 judges: the same-different method, the triangle test and the dual-pair paradigm. The latter protocol could improve the same-different's performance by preventing the spontaneous variations of the judges'τ criterion. While no significant differences were detected among the d' values obtained with each procedure, a trend was observed for the same-different and dual-pair test to be slightly more sensitive (higher d' values) than the triangle test. Since the same-different test is statistically more powerful, it is a preferable choice over the triangle, duo-trio and dual-pair tests.