The object of this study is to relate qualitative and quantitative ratings as expressed by judges and to relate sensory responses to physical measurements and gas chromatograms. Judges were asked to rate acceptability, flavor, and mouthfeel of blueberries on a five-point scale in a darkened room. With another specimen, they were asked to judge appearance and color without, however, tasting these berries. The judges were also asked to complete a questionnaire describing, in qualitative terms, the characteristics of each specimen. Varieties were subjected to analysis by physical and chemical measurements, and gas chromatograms were prepared. Contingency analysis and analysis of variance were performed to relate qualitative and quantitative ratings. The relationship between physical measurements or chromatograms and ratings is displayed in tables of means; although these numbers can be expressed as single correlations, using a random model, a single measure based on just four products was deemed to be less informative than a tabulation of correspondence.

ABSTRACTComponent and factor analysis were compared as means of reducing scaled values for 10 descriptors of tea to two dimensions so that relations among the attributes could be visualized. The association diagrams yielded by the two methods were generally similar, and there were significant differences between the diagrams for English Breakfast, an 80:20 blend of English Breakfast and Sencha teas, Ceylon and Darjeeling teas. Bartlett's test for equality ofvariance‐covariance matrices was significant. When tea was equivalently sweetened with sucrose and with saccharin, the association diagrams were different. Preference and sweetness were highly correlated with each other and they had high com‐munality with the other attributes when saccharin was the sweetening agent. When sucrose was the agent, sweetness still had high communality with the other attributes, but preference did not, indicating preference was the result of interplay of all the attributes rather than a dominant one. The correlation matrices were not significantly at p= 0.05, but they were at 0.10.

The purpose of this study was to prepare computational tools, particularly for a microcomputer, to permit application of the unbiased testing technique in standard testing situations. Each situation has been illustrated by comparative studies of point testing and interval testing. A package of programs has been established to facilitate applications. In the testing of hypotheses, a logical null-region should be an interval instead of a point. Measurements on a continuous random variable cannot be recorded with arbitrary precision. There is always some error (rounding, uncertainty). We express our interval hypotheses in standardized form and restrict the discussion to the normal case. In many standard testing situations such as those for means, linear model parameters, correlations, etc., unbiased tests do exist for both point and interval testing. The formulation of point-hypothesis and interval-hypothesis regions (e.g., in one-way analysis of variance) is as follows: H:$\mu\sb1$ = $\mu\sb2$ = dots = $\mu\sb{\rm k}$ versus K:not H (traditional), and H:$\rm\sum\sbsp{i=1}{k} p\sb{i}(\mu\sb{i}$ $-$ $\mu)\sp2/\sigma\sp2$ $\le$ $\delta\sp2$ versus K:$\rm\sum\sbsp{i=1}{k} p\sb{i}(\mu\sb{i}$ $-$ $\mu)\sp2/\sigma\sp2$ $>$ $\delta\sp2,$ where $\rm p\sb{i}$ is $\rm n\sb{i}$/N (sample size of group i over total sample size), $\mu\sb{\rm i}$'s are treatment means, and $\mu$ = $\rm\sum n\sb{i}\mu\sb{i}$/N. Under the normal assumption, the test statistics are subject to noncentral distributions (noncentral chi-square, t, F, beta, etc.). Although tables or charts for these distributions are available in the literature, their use is limited. Thus, computer programs (programs to find the cumulative distribution functions and inversion programs to find the percentage points and the noncentrality parameters) are desirable to facilitate the evaluation of the noncentral distributions and are developed in this dissertation. In one-way analysis of variance with equal sample sizes, one can also express an interval hypothesis as H:${\rm Max\atop i,j}\vert(\alpha\sb{\rm i}$ $-$ $\alpha\sb{\rm j})/\sigma\vert\le\delta$ versus K:${\rm Max\atop i,j}\vert(\alpha\sb{\rm i}$ $-$ $\alpha\sb{\rm j})/\sigma\vert$ $>$ $\delta$, (where $\alpha\sb{\rm i}$ = $\mu\sb{\rm i}$ $-$ $\mu$; thus $\sum\alpha\sb{\rm i}$ = 0), and perform range tests when $\sigma\sp2$is known and studentized range tests when $\sigma\sp2$ is unknown. The distributions of the test statistics are noncentral range and noncentral studentized-range distributions, respectively. They are not functions of ${\rm n}\sum\alpha\sbsp{\rm i}{2}/\sigma\sp2$ alone, but functions of any k $-$ 1 of the $\alpha$'s. Furthermore, the tests are not unbiased. However, comparative studies have been included and computer programs have been provided.

Union-intersection is a heuristic method of test construction developed by S. N. Roy. Among the well-known applications of this principle is the test for independence between two sets of variates which leads directly to the concept of canonical correlation. Another multivariate application of considerable importance is the test of internal independence. In this article we consider the structure of a correlation matrix and derive a union-intersection test statistic for internal independence. This statistic will be shown to be a function of the maximum eccentricity of the p-dimensional correlation ellipsoid x′R−1x = 1. The statistic will be applied to problems in factor analysis and categorical scaling.

A mathematical model of radionuclide kinetics in a laboratory microcosm was built by systems identification techniques. Insight into the functioning of the system was obtained from analysis of the model. Methods employed have allowed movements of radioisotopes not directly observable in the experimental system to be distinguished. Results are generalized to whole ecosystems.

For decades, substantial effort has been expended to develop sound objective methods for quality evaluation of foods. Considerable success has been achieved for color measurement; and for texture, moderate success. As was pointed out by Powers and Quinlan (1), part of this success has come about because some of the same forces or properties that cause us humans to respond to the food could be utilized in developing objective tests. Before the origin of gas-liquid chromatography (GLC) two decades ago, objective measurements of the numerous compounds that make up flavor was nigh impossible. Actually, not until a decade ago when Powers and Keith (2) and Dravnieks et al. (3) described practical means of analyzing GLC patterns could GLC measurements be efficiently correlated with flavor (4, 5). Quinlan et al. (6) and Powers (7) have reviewed most of the literature through early 1974. Recent papers are those of Galleto and Bednarczyk

Abstract : Many experiments involve measuring a number of response variables simultaneously. As a result of giving one stimulus to an experimental unit, what the author obtains is not just one response but several responses. In statistical language, one deals with a multivariate situation as opposed to univariate situations. Usually, many stimuli, called factors, are considered at many levels in the same experiment. Many statistical techniques are available to analyze this type of data and to draw conclusions therefrom. The present work considers one such technique, the identification of subgroups of individuals on the basis of responses, i.e., a special case of cluster analysis. Many different algorithms proposed for detecting clusters have been reviewed. These fall into two classes-- those which detect clusters of variables--factor analysis--and those which detect clusters of experimental units--cluster analysis. What the author has done in the present work lies in between these two techniques.

: The report contains algorithms and computer programs used for the identification and statistical testing of virtual clusters. Virtual clusters are described in the report as alternatives to the hypothesis of random directions in a p-dimensional space. The report includes an example of application to simulated data.