A simple test for heterogeneity of variance in complex factorial designs

A simple procedure for testing heterogeneity of variance is developed which generalizes readily to complex, multi-factor experimental designs. Monte Carlo Studies indicate that the Z-variance test statistic presented here yields results equivalent to other familiar tests for heterogeneity of variance in simple one-way designs where comparisons are feasible. The primary advantage of the Z-variance test is in the analysis of factorial effects on sample variances in more complex designs. An example involving a three-way factorial design is presented.     

Comment on Levy's “an empirical comparison of the Z-variance and Box-Scheffé tests for homogeneity of variance”

An alternative selection of subsample sizes for the Box-Scheffé test is compared to the singlem used in Levy, An empirical comparison of the Z-variance and Box-Scheffé tests for homogeneity of variance. Use of the alternative subsample sizes is shown to suggest greater power for the Box-Scheffé test, although the test would still be less powerful than the Z-variance test. Because of the nonrobustness of the Z-variance test and the robustness of the Box-Scheffé test, the latter is recommended as a general technique unless an experimenter has assurance that all populations in the experiment are normal. Alternative techniques are also considered.The opinions expressed do not necessarily reflect the position or policy of the U. S. Civil Service Commission.     

Some approximate tests for repeated measurement designs

Four approximate tests are considered for repeated measurement designs in which observations are multivariate normal with arbitrary covariance matrices. In these tests traditional within-subject mean square ratios are compared with critical values derived fromF distributions with adjusted degrees of freedom. Two of them—the approximate and the improved general approximate (IGA) tests—behave adequately in terms of Type I error. Generally, the IGA test functions better than the approximate test, however the latter involves less computations. In regards to power, the IGA test may compete with one multivariate procedure when the assumptions of the latter are tenable.The author wishes to thank Garrett K. Mandeville for his careful reading of the final version of the paper.     

Repeated measurements analysis of variance when the correlations have a certain pattern

Consider a repeated measurements study in which a single observation is taken at each oft(t > 2) equally spaced time points for each ofn subjects. This paper uses a result of Box to find the appropriate multiplicative correction term for the degrees of freedom in the analysis of variance table for the case when there is equal variability per time point, and when the correlation between observationsu time units apart is equal to ^u . For large values oft, the multiplicative correction has a lower bound approximately equal to 2.5/(t – 1).Dr. Fleiss is also with the Biometrics Research Unit of the New York State Psychiatric Institute. This work was supported in part by grant DE 04068 from the National Institute of Dental Research.     

The effects on the predictive variance of a new subject’s score for a new test

Abstract: It is often required to predict the scores or their variations under interest. Ishii and Watanabe (2001) investigated, in the context of psychological measurement, the Bayesian predictive distribution of a new subject’s scores for tests and subjects’ scores for a new test. In this paper, the Bayesian posterior predictive distribution of a new subject’s scores for a new parallel test were considered. And the effects of the number of subjects, the number of the tests, and the test reliability were investigated. Then, it was found that, under assumptions that (co)variance parameters are known, the predictive variance of a new subject’s score for a new test was equal to the predictive variances of the new subject’s scores for the existent tests. It was also found that the effect of the number of subjects was relatively large and the effect of the number of tests was relatively small, when a new subject’s scores for existent tests were not observed.     

Robust estimation of ability in the Rasch model

Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. This noise can be caused by guessing, inattention to easy questions, and other factors which are unrelated to ability. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. It was found that although no one of the tested schemes is uniformly superior to all others, a modified jackknife stood out as the best one in general, it was also super efficient (more efficient than the asymptotically optimal estimator) for tests with forty or fewer items. It is proposed that this sort of jackknifing scheme for estimating ability be considered for practical work.This research was funded through a grant from the Law Enforcement Assistance Administration (78-NI-AX-0047) to the Bureau of Social Science Research, Howard Wainer, Principal Investigator. We would like to thank Ronald Mead, Anne Morgan and James Ramsay for kind, generous, and invaluable help at various stages of the project.     

Identification of cognitive profiles among women considering BRCA1/2 testing through the utilisation of cluster analytic techniques

Based on the cognitive-social health information processing model, we identified cognitive profiles of women at risk for breast and ovarian cancer. Prior to genetic counselling, participants (N?=?171) completed a study questionnaire concerning their cognitive and affective responses to being at genetic risk. Using cluster analysis, four cognitive profiles were generated: (a) high perceived risk/low coping; (b) low value of screening/high expectancy of cancer; (c) moderate perceived risk/moderate efficacy of prevention/low informativeness of test result; and (d) high efficacy of prevention/high coping. The majority of women in Clusters One, Two and Three had no personal history of cancer, whereas Cluster Four consisted almost entirely of women affected with cancer. Women in Cluster One had the highest number of affected relatives and experienced higher levels of distress than women in the other three clusters. These results highlight the need to consider the psychological profile of women undergoing genetic testing when designing counselling interventions and messages.     

Ethical considerations in the testing of biopharmaceuticals for adventitious agents

Safety testing of biological pharmaceuticals is often carried out by contract testing laboratories which perform these tests on behalf of the drug’s developer. These laboratories are confronted with a number of ethical issues related to selling their services, maintaining confidentiality, and the handling of results. This paper outlines these issues, and, by way of illustration, discusses how one such laboratory addresses them.     

Overcoming overconfidence in learning from video-recorded lectures: Implications of interpolated testing for online education

The video-recorded lecture represents a central feature of most online learning platforms. Nonetheless, little is known about how to best structure video-recorded lectures in order to optimize learning. Here, we focused on the tendency for high school and college students to be overconfident in their learning from video-recorded modules, and demonstrated that testing could be used to effectively improve the calibration between predicted and actual performance. Notably, interpolating a lecture with repeated tests helped to boost actual performance to the level of predicted performance, whereas a single test following the lecture served to lower unrealistic judgments of learning. The value of improving performance to match predictions of learning and other avenues for future research regarding meta-comprehension of video-recorded lectures is discussed.     

The exchangeable multinomial model as an approach to testing deterministic axioms of choice and measurement

The multinomial (Dirichlet) model, derived from de Finetti's concept of exchangeability, is proposed as a general Bayesian framework to test axioms on data, in particular, deterministic axioms characterizing theories of choice or measurement. For testing, the proposed framework does not require a deterministic axiom to be cast in a probabilistic form (e.g., casting deterministic transitivity as weak stochastic transitivity). The generality of this framework is demonstrated through empirical tests of 16 different axioms, including transitivity, consequence monotonicity, segregation, additivity of joint receipt, stochastic dominance, coalescing, restricted branch independence, double cancellation, triple cancellation, and the Thomsen condition. The model generalizes many previously proposed methods of axiom testing under measurement error, is analytically tractable, and provides a Bayesian framework for the random relation approach to probabilistic measurement (J. Math. Psychol. 40 (1996) 219). A hierarchical and nonparametric generalization of the model is discussed.     

Hemispheric asymmetry effects in children studied by dichotic listening and visual half-field testing

Dichotic listening (DL) and visual half-field (VHF) testing were used to study hemisphere asymmetry in a developmental perspective. Five-, 8-, and 11-year-old children were presented lists of fused words using a DL technique in Experiment 1, and 8- and 11-year-old children were presented pictures of common objects using a VHF technique in Experiment 2. In both experiments, measures of identification, free recall, and recognition of the words/pictures were employed. The results revealed effects of ear input (right-ear advantage) and half-field presentation (right visual half-field advantage) for all age groups, although the magnitude of this lateralization effect differed between the three memory measures. The results are discussed in relation to developmental aspects of language laterality, and in relation to the clinical utility of non-invasive lateralization techniques.     

A parametric characterization of mean–variance efficient solutions for general feasible action sets

In this paper we show how the mean–variance efficient solution problem may be converted to a parametric efficient solution problem with objective functions affine in the mean and second moment of the random variable of concern. Some potential uses are considered, the relationship with some other work is examined and two potential applications are given. © 1998 John Wiley & Sons, Ltd.     

The ubiquity of common method variance: The case of the Big Five

The factor structures of the International Personality Item Pool (IPIP) and NEO-FFI Big Five questionnaires were examined via confirmatory factor analyses. Analyses of IPIP data for five samples and NEO data for one sample showed that a CFA model with three method bias factors, one influencing all items, one influencing negatively worded items, and one influencing positively worded items fit the data significantly better than models without method factors or models with only one method factor . With the method factors estimated, our results indicated that the Big Five dimensions may be more nearly orthogonal than previously demonstrated. Implications of the presence of method variance in Big Five scales are discussed.     

Statistical inference for false positive and false negative error rates in mastery testing

This paper describes an asymptotic inferential procedure for the estimates of the false positive and false negative error rates. Formulas and tables are described for the computations of the standard errors. A simulation study indicates that the asymptotic standard errors may be used even with samples of 25 cases as long as the Kuder-Richardson Formula 21 reliability is reasonably large. Otherwise, a large sample would be required.This work was performed pursuant to Grant No NIE-G-78-0087 with the National Institute of Education, Department of Health, Education and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE position or policy and no official endorsement should be inferred. The editorial assistance of Joseph C. Saunders is gratefully acknowledged.