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 the significance of a coefficient of reproducibility

Under the assumption that responses to different dichotomous items are statistically independent, exact distributions for coefficients of reproducibility, CR, are derived. These distributions are useful in testing whether an observed coefficient of reproducibility differs significantly from chance expectations and whether further scaling manipulations are warranted. The effects of purification on sampling distributions of errors are calculated to demonstrate a relationship between scaling operations and expected chance values of the CR.     

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 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.     

Observer states and traits and the imitative process: A test of a new formulation

In three studies the formulation was tested that characteristics of the observer have an effect on imitation only in situations which provide little information concerning appropriate or expected behaviors. In Experiment I, female college students of high, medium, and low need for social approval underwent either a high or low arousal manipulation. Subjects observed a videotaped model who engaged in a size judgment task. For half the subjects the model received verbal reward (high information); for the other half the model received no feedback (low information). Subsequently, the model and subject responded alternately in the task during which no feedback was given. Neither need for social approval nor manipulated arousal was found to be systematically related to imitation in either information condition. However, the hypothesized relationships were found when subjects' arousal or anxiety levels were determined by self ratings. These results were replicated in a second, similar experiment. In a third experiment, which involved an improved arousal manipulation, the hypothesized relationships were confirmed.     

The significance test controversy

Summary The pre-designationist, anti-inductivist and operationalist tenor of Neyman-Pearson theory give that theory an obvious affinity to several currently influential philosophies of science, most particularly, the Popperian. In fact, one might fairly regard Neyman-Pearson theory as the statistical embodiment of Popperian methodology. The difficulties raised in this paper have, then, wider purport, and should serve as something of a touchstone for those who would construct a theory of evidence adequate to statistics without recourse to the notion of inductive probability.     

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.     

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.     

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.     

Perception naturalised: relocation and the sensible qualities

This paper offers a partial defence of a Sellarsian-inspired form of scientific realism. It defends the relocation strategy that Sellars adopts in his project of reconciling the manifest and scientific images. It concentrates on defending the causal analysis of perception that is essential to his treatment of sensible qualities. One fundamental metaphysical issue in perception theory concerns the nature of the perceptual relation; it is argued that a philosophical exploration of this issue is continuous with the scientific investigation of perceptual processes. Perception, it is argued, can, and should, be naturalised. A challenge for any account of perception arises from the fact that a subject’s experiences are connected with particular objects. We need to supply principled grounds for identifying which external physical object the subject stands in a perceptual relation to when they have an experience. According to the particularity objection presented in the paper, naive realism (or disjunctivism) does not constitute an independently viable theory since, taken on its own, it is unable to answer the objection. In appealing to a ‘direct experiential relation’, it posits a relation that cannot be identified independently of the underlying causal facts. A proper understanding of one central function of perception, as guiding extended patterns of actions, supports a causal analysis of perception. It allows us to draw up a set of necessary and sufficient conditions for perceiving that avoids well-known counterexamples. An analysis of this kind is congruent with the scientific account, according to which experiences are interpreted as inner states: sensible qualities, such as colours, are in the mind (but not as objects of perception). A Sellarsian version of the relocation story is thus vindicated.

     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.     

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.     

Remarks on the test of significance for the method of paired comparisons

A three-component model for comparative judgment which allows for individual differences in preference is proposed. An implication of the model is that errors in the observed proportions due to sampling individuals in paired comparisons experiments are correlated. By neglecting this correlation, Mosteller's test for the method of paired comparisons tends to accept falsely the goodness of fit of the Case V solution. It is shown that bounds may be set for the correlation effect which make a valid test possible in some cases and provide useful standard errors for the estimated affective values.Preparation of this paper has been supported in part by the Quartermaster Food and Container Institute for the Armed Forces. Views and conclusions expressed herein are those of the author and do not necessarily reflect the views or endorsement of the Department of Defense. Comments of one of the reviewers, which substantially improved an earlier version of this paper, are gratefully acknowledged.     

A significance test for the hypothesis that two variables measure the same trait except for errors of measurement

The likelihood-ratio significance test is derived for the hypothesis that after correction for attenuation two variables have a perfect correlation in the population from which the sample is drawn.The writer is indebted to Professor John W. Tukey for his valuable suggestions on an earlier draft.     

A Bayesian formulation of behavioral control

Helplessness, a belief that the world is not subject to behavioral control, has long been central to our understanding of depression, and has influenced cognitive theories, animal models and behavioral treatments. However, despite its importance, there is no fully accepted definition of helplessness or behavioral control in psychology or psychiatry, and the formal treatments in engineering appear to capture only limited aspects of the intuitive concepts. Here, we formalize controllability in terms of characteristics of prior distributions over affectively charged environments. We explore the relevance of this notion of control to reinforcement learning methods of optimising behavior in such environments and consider how apparently maladaptive beliefs can result from normative inference processes. These results are discussed with reference to depression and animal models thereof.     

A new formulation of discussive logic

S. Jakowski introduced the discussive prepositional calculus D ₂as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa and L. Dubikajtis, On Jakowski's discussive logic, in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37–56). D ₂has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the quoted paper). In this paper we present a natural version of D ₂, in the sense of Jakowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented.     

A biopsychosocial formulation of pain communication

We present a detailed framework for understanding the numerous and complicated interactions among psychological and social determinants of pain through examination of the process of pain communication. The focus is on an improved understanding of immediate dyadic transactions during painful events in the context of broader social phenomena. Fine-grain consideration of social transactions during pain leads to an appreciation of sociobehavioral events affecting both suffering persons as well as caregivers. Our examination considers knowledge from a variety of perspectives, including clinical health psychology, social and developmental processes, evolutionary psychology, communication studies, and behavioral neuroscience.