COMPARISON OF RATING SCALES: SENSITIVITY, REPLICATES AND RELATIVE MEASUREMENT

The relative sensitivities of four scaling methods were assessed in central location tests with untrained judges. The scales included category scales, line scales, magnitude estimation, and a hybrid of the line and category scales. Approximate parity was observed among category scales, line scales and the hybrid scale in their ability to differentiate small physical differences. Magnitude estimation was used as efficiently as the other methods by a college population, but less efficiently by a heterogeneous sample of consumers. Judges used the scales with greater accuracy as they became familiar with the range of products to be judged. In spite of relatively small physical differences, subjects used wide ranges of the scales, supporting the view that rating scales are relative, not absolute, measuring instruments.     

THE DISRIMINATIVE EFFICIENCY OF COMMON SCALING METHODS

Four types of rating scales, nine-point category scales, line marking, magnitude estimation, and a hybrid of the category and line scale, were employed to assess visual, tactile and olfactory characteristics of products by consumers. The scales were compared for their ability to discriminate differences among products, for variability, for reliability, and for ease of use. All methods were able to generate highly significant differences among products. However, a modest advantage for category scales was observed in almost all comparisons.     

A LABELED AFFECTIVE MAGNITUDE (LAM) SCALE FOR ASSESSING FOOD LIKING/DISLIKING1

The most widely used scale for assessing food liking or disliking is the 9‐pt hedonic scale. Unfortunately, this affective scale suffers from problems related to unequal scale intervals and the underuse of end categories, which results in a reduced ability to differentiate among extremely well liked or extremely disliked foods. Magnitude estimation avoids these problems while enabling ratio statements to be made about the data. However, it does not provide absolute ratings of liking/disliking and can be difficult for some consumers to use. We report here on the development of a labeled affective magnitude scale (LAM) scale that has advantages over both the 9‐pt hedonic scale and magnitude estimation. Forty‐four semantic labels were scaled for their affective meaning by subjects using modulus‐free magnitude estimation. The geometric mean magnitude estimates obtained for each semantic label were used to construct a series of labeled affective magnitude scales by spacing the labels along a visual analogue scale according to their obtained semantic values. Reliability and sensitivity studies were conducted to assess the effects of alternative semantic and numeric labels. The results of these studies led to the choice of a scale format that uses verbal labels that are consistent with the 9‐pt hedonic scale. The labeled affective magnitude (LAM) scale was compared to the hedonic scale and magnitude estimation in several food preference and acceptability tests. The LAM was shown to have equal reliability and sensitivity to the hedonic scale, provided somewhat greater discrimination among highly liked foods, and resulted in data that were similar to magnitude estimation in terms of the obtained ratios among rated stimuli. The LAM scale was also judged by consumers to be as easy to use as the 9‐pt hedonic scale and significantly less difficult than magnitude estimation.     

Contrast and range effects for category, magnitude and labeled magnitude scales in judgements of sweetness intensity

The labeled magnitude scale (LMS) is a verbally anchored quasi-logarithmically spaced response scale with properties similar to magnitude estimation. Three experiments examined whether the LMS showed context effects similar to those found with magnitude estimation and category scales. Two versions of the LMS were used, one anchored at the high end to the strongest imaginable sweetness and the other to the strongest imaginable oral sensation. In a simple contrast experiment, subjects judged the sweetness of a 10% sucrose fruit beverage in the context of a less sweet (5%) beverage or a more sweet (20%) beverage. Consistent with previous literature, the sweetness was judged more intense in the low context and less intense in the high context, for all scaling methods. In a second experiment, this effect persisted (although was smaller) when the contextual item preceded the to-be-rated item, a so-called 'reversed-pair' design. Once again, the effect was highly significant for all scaling methods. In a third experiment, a range effect was examined using wide and narrow ranges of concentration. Psychophysical functions were flatter in a wide context and steeper in a narrow context, consistent with previous observations on range-mapping bias. This result was obtained for all scales. In three common contextual effects, the labeled magnitude scale behaved similarly to other scaling procedures. Its application to comparisons across individuals may be limited if those individuals have different experiential contexts within which they make their judgements.     

EVALUATION OF THREE SCALING METHODS FOR HEDONICS

A collaborative study of twenty-three laboratories was conducted to compare the relative effectiveness of three scales: two forms of magnitude estimation scaling and one form of a category scale in the measurement of hedonic response to a controlled stimulus. Responses from 553 individual judges show that all scales yield hedonic measurements that are very similar in both direction and magnitude of difference between the stimuli. No scale showed any clear superiority in reliability, precision, or discrimination. Selection of a scale must be based on considerations other than the simple form of response.     

USE OF SENSORY EVALUATION FOR MEASURING DEODORIZING EFFECTS OF AN AIR CONDITIONER

The application of sensory methodology for measuring deodorizing effect of an air conditioner equipped with electric plasma was introduced. Deodorizing effect was measured using chemical and sensory methods at different time (0, 30 and 60 min) and mode (control, blowing and cooling) of an air conditioner. Smoke from a roll of cigarette in a closed room was used as a source of odor and the concentrations of acetic acid and ammonia were measured as odorous chemical components. As one of the sensory methods triangle test was used and as a first step to obtain deodorizing effects by triangle test, the threshold of each panelist was obtained as the log dilution ratio of odor concentration at which the difference from odorless air was detected. The odor concentration at each time and mode was calculated using the threshold of the panel and the deodorizing effect was obtained on the basis of the odor concentration. In addition to a triangle test, scaling methods such as category scaling or magnitude estimation were used to measure deodorizing effect of an air conditioner. Deodorizing effects by scaling methods were calculated based on odor intensity with time at each mode. The regression analysis was done between the efficacy of deodorizing effect by sensory test and those by acetic acid and ammonia, the R² values of the regression equations for triangle test, category scale, and magnitude estimation were 0.84, 0.72 and 0.69, respectively. Deodorizing effect by triangle test explained the decrease of acetic acid and ammonia better than those by category scaling or magnitude estimation while high cost and time consuming labor involved in triangle tests reduced the merit. The results of this study demonstrated that various sensory methods could be used to measure deodorizing effect of air conditioners and further researches on fast and reliable methods are needed to establish the official procedures.     

ALTERNATIVE ANALYSES OF MAGNITUDE ESTIMATION DATA

Three methods of standardizing magnitude estimation data, external calibration, modulus normalization, and equalization were examined using a sensory evaluation data set arising from an incomplete block experiment testing five gels of varying firmness. Both the original data and a logarithmic transformation of the data were analyzed. Instrumental data were also collected. When untransformed data were analyzed the method of standardization profoundly affected tests of significance, coefficients of variation (%CV), and estimation of the power function relating the sensory data to the concentration of the underlying gel. The logarithmically transformed data lead to results independent of the standardizing technique and with higher F-ratios, lower %CV's and normally distributed errors.     

Measurement scale in maximum entropy models of species abundance

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.     

生态学中的尺度问题——尺度上推

尺度推绎是生态学理论和应用的核心。如何在一个异质景观中进行尺度推绎仍然是一个悬而未决的科学难题,是对当今生态学家在全球变化背景下研究环境问题的重大挑战。就目前的研究,一般可分为四大类尺度推绎途径:空间分析法(如分维分析法和小波分析法)、基于相似性的尺度上推方法、基于局域动态模型的尺度上推方法、随机(模型)法。基于相似性的尺度上推方法来源于生物学上的异量关联,可将其思想延伸至空间上,研究物种丰富度、自然河网、地形特征、生态学格局或过程变量和景观指数等。基于局域动态模型的尺度上推方法需要首先确定是否进行跨尺度推绎,以及是否考虑空间单元之间的水平相互作用和反馈,然后再应用具体的方法或途径,如简单聚合法、有效值外推法、直接外推法、期望值外推、显式积分法和空间相互作用模拟法等。随机(模型)法以其它尺度上推方法为基础,根据研究的是单个景观,还是多个景观,采用不同的途径。理解、定量和降低尺度推绎结果的不确定性已经变得越来越重要,但相关研究仍然极少。以上所有有关尺度推绎的方法、途径和结果分析共同构成了尺度推绎的概念框架。     

COMPARISON OF SINGLE PRODUCT SCALING AND RELATIVE-TO-REFERENCE SCALING IN SENSORY EVALUATION OF DAIRY PRODUCTS

Single product scaling and relative-to-reference scaling were compared on the basis of numbers of significant differences among chocolate milks and among vanilla yogurts using both trained and untrained panels. The study involved 920 comparisons among product means with appearance, flavor and mouthfeel attributes. Although there were a greater number of significant t-tests when the relative-to-reference scales were used by both trained and untrained panels, the differences between scale types were minor. Panels showed no advantage with the type of scale they used first. The two methods may be used with equal efficiency for sensory evaluations.     

EVALUATION OF BITTERNESS OF CAFFEINE IN HOT CHOCOLATE DRINK BY CATEGORY, GRAPHIC, AND RATIO SCALING

Perceived intensity of bitterness of caffeine (0.5 - 1.6 g/100 mL) and of quinine HCI (0.5 - 1.6 g/L) added to hot cocoa gave similar response distributions with concentration by category scales (CS) and magnitude estimation (ME). Using caffeine additives, CS and graphic analogue scales (GS) gave similar bitterness response functions. Parabolic functions provided the best fit between concentration and ratings for CS, GS and ME. The data demonstrated no difference for ME of bitterness intensity between free or fixed moduli. Hedonic responses also were not modified by whether the modulus was free or fixed, however, greater ME values were ascribed to lower concentrations in the series when the reference was 4 g/L than when it was 2 g/L caffeine. CS intensity response distributions were similar between a series with a larger number of low levels versus a series with a larger number of high levels across the same concentration range. The results indicate that ME may be inappropriate for scaling of degree of liking, independent of type of modulus.     

Sample size determination for matched-pair equivalence trials using rate ratio

In this article, we compare Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point. These statistics can be implemented through sample-based, constrained least squares estimation and constrained maximum likelihood (CML) estimation methods. Sample size formulae based on the CML estimation method are developed. We consider formulae that control a prespecified power or confidence width. Our simulation studies show that statistics based on the CML estimation method generally outperform other statistics and methods with respect to actual type I error rate and average width of confidence intervals. Also, the corresponding sample size formulae are valid asymptotically in the sense that the exact power and actual coverage probability for the estimated sample size are generally close to their prespecified values. The methods are illustrated with a real example from a clinical laboratory study.     

FURTHER EVIDENCE FOR ANOMALOUS SIZE SCALING OF RESPIRATION IN PHYTOPLANKTON1

Respiration per unit mass decreases as organism size increases among metazoans and heterotrophic unicells. The rate of decrease is described by a power function of organism mass; the exponent of the power function is 0.75 (Three-fourths Rule). Previously unanalyzed respiration rates for 11 species of phytoplankton ranging in size over four orders of magnitude show a size-scaling exponent of 1.13 (SE, ±0.15), which is statistically different from 0.75. This result confirms the result of an earlier study of eight phytoplankton species indicating that size scaling of respiration is absent or minimal in phytoplankton, in contrast to the pattern of heterotrophic unicells. The size-related range of respiration rates per unit mass across the full size spectrum of phytoplankton would be approximately 18–fold if respiration were scaled according to the Three-fourths Rule. If respiration does not scale with size or scales minimally with size, as suggested by present evidence, the size-related range of rates will be much smaller or negligible. The apparent anomaly of size scaling for phytoplankton respiration is potentially of great ecological and adaptive significance in unicellular algae.     

生态学中的尺度及尺度转换方法

尺度作为生态学的重要范式,已经引起了广泛重视,但对尺度问题的研究还不够成熟.尺度具有多维性特点,即功能尺度、空间尺度、时间尺度等,但生态学研究的重点是空间和时间尺度.并且时空尺度还具有复杂性、变异性特征.尺度研究的根本目的在于通过适宜的空间和时间尺度来揭示和把握复杂的生态学规律.为此,科学有效的尺度选择和尺度转换方法不可或缺.常见的尺度转换方法有图示法、回归分析、变异函数、自相关分析、谱分析、分形和小波变换,同时遥感和地理信息系统技术在尺度研究中也发挥着重要作用.结合实例对上述方法进行了分析和论述,认为各种方法都有其内在的优势和不足,新方法的引入和应用对于尺度转换方法体系的充实和完善非常重要.有关尺度的研究将进一步加强,研究的重点是尺度变异性、不同尺度间的相互作用机制以及尺度转换方法等.     

RATIO SCALES AND CATEGORY SCALES OF ODOUR INTENSITY

The relation between a ratio scale obtained by magnitude estimationand a category scale of the odour intensity of 1-butanol wasstudied, together with individual variations in the ratio scale.Series of solutions of butanol in water in small bottles werepresented to a panel for judgement, half using the method ofmagnitude estimation, the other half a category scale. Plotswere made of the category scale against the ratio scale, andthe ratio scales of individual members of the panel were analysed.A power function exponent of 0.48 was found for the panel'sratio scale, with individual values ranging from 0.25 to 0.49.The category scale was curved relative to the ratio scale; variabilityof the magnitude estimates was approximately proportional tothe magnitude estimates; and a small time-order error was found.Odour intensity exhibits the three tested characteristics ofa prothetic continuum, and the variability of individual exponentswas not as great as sometimes suggested.     

Perception of effort in isometric and dynamic muscular contraction.

The perception of muscular effort was studied using estimation and production methods in the adductor pollicis and quadriceps. A psychometric scale (percentage magnitude) was used. Static contractions were studied in the adductor pollicis, and both dynamic (isokinetic) and static contractions were studied in quadriceps. Linear and logarithmic equations were fitted for the perceived effort as a percentage of the maximum in relation to the produced percentage maximal force or torque. The logarithmic exponent was around or above 1.0. No significant difference was found between mean exponent and intercept values for the adductor pollicis and the quadriceps, or when estimated or produced values for the two muscles were compared. There was no difference in the same subjects between the equations for static and dynamic contractions with low angular velocity of the quadriceps.     

Unanticipated consequences of logarithmic transformation in bivariate allometry

Parameters in the two-parameter allometric equation are commonly estimated by fitting a straight line to logarithmic transformations of the original data and by back-transforming the resulting model to the arithmetic scale. However, log transformation distorts the relationship between the predictor and response variables, and this distortion may be sufficient to lead unsuspecting investigators to analyze data that actually are unsuited for allometric research. Two data sets from the current literature are re-examined here to illustrate instances in which log transformation caused ugly data to look deceptively good. One of the investigations focused on the scaling of metabolism to body mass in evolutionary transitions from prokaryotic to protistan to metazoan levels of organization whereas the other addressed the scaling of intestines to body size in rodents. In both instances investigators were led to conclusions that are not supported by the original data. Problems of the sort described here can readily be avoided simply by performing preliminary graphical analysis of observations expressed in the original units and by validating the final model in the arithmetic domain.