A significance test for multisample sphericity

The paper obtains a maximum likelihood criterion test for multisample sphericity. The test contains Mauchly's sphericity test as a special case.I would like to thank Professor R. E. Bargmann for his most valuable help.     

A statistical test for means of samples from skew populations

This paper presents a test for determining significance of differences between means of samples which are drawn from positively skewed populations, more specifically, those having a Pearson Type III distribution function. The quantity 2npx _g /x _p (wherep equals the mean squared divided by the variance andn is the number of cases in the sample), which distributes itself as Chi Square for 2np degrees of freedom, may be referred to the tables of Chi Square for testing hypotheses about the value of the true mean. For two independent samples, the larger mean divided by the smaller mean, which distributes itself asF for 2n ₁ p ₁ and 2n ₂ p ₂ degrees of freedom, may be referred to theF distribution tables for testing significance of difference between means. The test assumes that the range of possible scores is from zero to infinity. When a lower theoretical score limit (c) exists which is not zero, the quantity (Mean —c) should be used instead of the mean in all calculations.     

A sensible formulation of the significance test

The conventional procedure for null hypothesis significance testing has long been the target of appropriate criticism. A more reasonable alternative is proposed, one that not only avoids the unrealistic postulation of a null hypothesis but also, for a given parametric difference and a given error probability, is more likely to report the detection of that difference.     

A k-sample significance test for independent alpha coefficients

The earlier two-sample procedure of Feldt [1969] for comparing independent alpha reliability coefficients is extended to the case ofK 2 independent samples. Details of a normalization of the statistic under consideration are presented, leading to computational procedures for the overallK-group significance test and accompanying multiple comparisons. Results based on computer simulation methods are presented, demonstrating that the procedures control Type I error adequately. The results of a power comparison of the case ofK=2 with Feldt's [1969]F test are also presented. The differences in power were negligible. Some final observations, along with suggestions for further research, are noted.The authors gratefully acknowledge the assistance of Michael E. Masson, in the computations performed, and of Leonard S. Feldt, in suggesting the data generation procedures used in the study. In addition, the authors thank James Zidek and the Institute of Applied Mathematics and Statistics, University of British Columbia, for advice concerning some of the theoretical development.     

A significance test for one parameter isosensitivity functions

A large-sample test for the significance of the difference between two detection data points is developed based upon the assumptions of a one-parameter signal detectability model. In essence, the null hypothesis tested is that two observed data points belong to the samed' function.Portions of this research were supported by Contract DA-49-193-MD-2713 between the University of Washington and the U. S. Army Medical Research and Development Command.Now at Teachers College, Columbia University.     

A statistical test of a prediction from information theory in a card-sorting situation

Previous work with cards left the joint effects of varying entropy and discriminability on choice-reaction times somewhat in doubt. A card-sorting situation is here constructed in which entropy and discriminability can be varied independently. Two experiments are described with naive subjects and two different treatments of the practice effect. The effect of varying entropy with discriminability held constant is. shown to be significantly non-linear, contrary to the prediction from information theory. Finally a statistical model is proposed which shows at least, qualitative agreement with the results of these experiments.     

A significance test for minimum rank in factor analysis

This paper presents a new method of determining the minimum rank in factor analysis, appropriate to the principal axes solution. The new method is compared with a former method which, with some adjustment, is more convenient for the centroid approach. Both methods are applied to two familiar examples.     

Clinical significance methods: a comparison of statistical techniques

Clinically significant change refers to meaningful change in individual patient functioning during psychotherapy. Following the operational definition of clinically significant change offered by Jacobson, Follette, and Revenstorf (1984), several alternatives have been proposed because they were thought to be either more accurate or more sensitive to detecting meaningful change. In this study, we compared five methods using a sample of 386 outpatients who underwent treatment in routine clinical practice. Differences were found between methods, suggesting that the statistical method used to calculate clinical significance has an effect on estimates of meaningful change. The Jacobson method (Jacobson & Truax, 1991) provided a moderate estimate of treatment effects and was recommended for use in outcome studies and research on clinically significant change, but future research is needed to validate this statistical method.     

On determining the reliability and significance of a tetrachoric coefficient of correlation

In this note are presented facilitating tables for the estimation of the standard error of a tetrachoric and also tables providing significant and very significant tetrachoric coefficients for various sizes of samples and various combinations of proportions in the dichotomized distributions.The task of computing the values in the accompanying tables should be credited to Mr. Lyons.     

A graphical test for the significance of differences between frequencies from different samples

For testing the significance of differences between frequencies from different samples, an ellipse can easily be constructed on the basis of a formula developed on the assumption that both observed samples are random samples from the same parent population and that the best estimate of the true proportion is the weighted mean proportion of the two samples. The ellipse provides a very rapid method for testing pairs of frequencies.The opinions expressed in this paper are those of the authors and are not to be construed as those of the Navy Department.     

A monte carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure

Recent advances in computer based psychometric techniques have yielded a collection of powerful tools for analyzing nonmetric data. These tools, although particularly well suited to the behavioral sciences, have several potential pitfalls. Among other things, there is no statistical test for evaluating the significance of the results. This paper provides estimates of the statistical significance of results yielded by Kruskal's nonmetric multidimensional scaling. The estimates, obtained from attempts to scale many randomly generated sets of data, reveal the relative frequency with which apparent structure is erroneously found in unstructured data. For a small number of points (i.e., six or seven) it is very likely that a good fit will be obtained in two or more dimensions when in fact the data are generated by a random process. The estimates presented here can be used as a bench mark against which to evaluate the significance of the results obtained from empirically based nonmetric multidimensional scaling.A preliminary version of this paper was presented at the International Federation for Information Processing Congress 68 in Edinburgh, Scotland, August 5–10, 1968.     

A simple and effective decision rule for choosing a significance test to protect against non-normality

There is no formal and generally accepted procedure for choosing an appropriate significance test for sample data when the assumption of normality is doubtful. Various tests of normality that have been proposed over the years have been found to have limited usefulness, and sometimes a preliminary test makes the situation worse. The present paper investigates a specific and easily applied rule for choosing between a parametric and non-parametric test, the Student t test and the Wilcoxon-Mann-Whitney test, that does not require a preliminary significance test of normality. Simulations reveal that the rule, which can be applied to sample data automatically by computer software, protects the Type I error rate and increases power for various sample sizes, significance levels, and non-normal distribution shapes. Limitations of the procedure in the case of heterogeneity of variance are discussed.     

Extensions of the significance test for one-parameter signal detection hypotheses

The basic models of signal detection theory involve the parametric measure,d, generally interpreted as a detectability index. Given two observers, one might wish to know whether their detectability indices are equal or unequal. Gourevitch and Galanter (1967) proposed a large sample statistical test that could be used to test the hypothesis of equald values. In this paper, their large two sample test is extended to aK-sample detection test. If the null hypothesisd ₁=d ₂=...=d _K is rejected, one can employ the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences. In addition, it is shown how one can use the Gourevitch and Galanter statistics to testd=0 for a single individual.This paper was written while the author was associated with the Institute of Human Learning at the University of California at Berkeley.     

Error of measurement and the sensitivity of a test of significance

Implications of random error of measurement for the sensitivity of theF test of differences between means are elaborated. By considering the mathematical models appropriate to design situations involving true and fallible measures, it is shown how measurement error decreases the sensitivity of a test of significance. A method of reducing such loss of sensitivity is described and recommended for general practice.I wish to express my thanks in acknowledgement that the present form of this paper has benefited from editorial comment, and from the advice of Dr. H. Mulhall of the Department of Mathematics, University of Sydney.     

Use of the test scoring machine and the graphic item counter for statistical work

The graphic item-counter is described and its use as a statistical device is explained. Procedures are presented for obtaining Pearson product-moment correlations by means of the graphic item-counter.