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.     

Factors influencing responding under multiple schedules of conditioned and unconditioned reinforcement

Two experiments examined pigeons' responses under multiple schedules of conditioned and unconditioned reinforcement. In one component, responses produced food according to a fixed-interval schedule; in a second component, responses produced brief stimuli according to a fixed-ratio schedule. When brief-stimulus presentations were paired with food in the first component, rates in the second component were usually higher than 10 responses per minute. When pairing in the first component was eliminated, responding continued to be maintained in the second component. Elimination of food presentation from the first component substantially decreased responding in the second component, even though the brief stimulus had not been paired with food. Experiment II demonstrated that response rate was affected by the duration of both the second component and the brief stimulus. The results suggest that three conditions are important in maintaining responding with brief-stimulus presentations: (1) pairing the brief stimulus, at least initially, with food, (2) maintaining unconditioned reinforcement in one component, and (3) employing optimal brief-stimulus and component durations.     

Statistical Significance Levels of Nonparametric Tests Biased by Heterogeneous Variances of Treatment Groups

The statistical significance levels of the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test are substantially biased by heterogeneous variances of treatment groups—even when sample sizes are equal. Under these conditions, the Type I error probabilities of the nonparametric tests, performed at the .01, .05, and .10 significance levels, increase by as much as 40%-50% in many cases and sometimes as much as 300%. The bias increases systematically as the ratio of standard deviations of treatment groups increases and remains fairly constant for various sample sizes. There is no indication that Type I error probabilities approach the significance level asymptotically as sample size increases.     

Redundancy analysis an alternative for canonical correlation analysis

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.A Fortran IV program for the method of redundancy analysis described in this paper can be obtained from the author upon request.     

On the effects of component durations and component reinforcement rates in multiple schedules

Four experiments, each using the same six pigeons, investigated the effects of varying component durations and component reinforcement rates in multiple variable-interval schedules. Experiment 1 used unequal component durations in which one component was five times the duration of the other, and the shorter component was varied over conditions from 120 seconds to 5 seconds. The schedules were varied over five values for each pair of component durations. Sensitivity to reinforcement rate changes was the same at all component durations. In Experiment 2, both component durations were 5 seconds, and the schedules were again varied using both one and two response keys. Sensitivity to reinforcement was not different from the values found in Experiment 1. In Experiment 3, various manipulations, including body-weight changes, reinforcer duration changes, blackouts, hopper lights correlated with keylights, and overall reinforcement rate changes were carried out. No reliable increase in reinforcement sensitivity resulted from any manipulation. Finally, in Experiment 4, reinforcement rates in the two components were kept constant and unequal, and the component durations were varied. Shorter components produced significantly increased response rates normally in the higher reinforcement rate component, but schedule reversals at short component durations eliminated the response rate increases. The effects of component duration on multiple schedule performance cannot be interpreted as changing sensitivity to reinforcement nor to changing bias.     

Principal component analysis of three-mode data by means of alternating least squares algorithms

A new method to estimate the parameters of Tucker's three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.     

The P600 as an indicator of syntactic ambiguity

In a study using event-related brain potentials, we show that the current characterization of the P600 component as an indicator of revision processes (reanalysis and repair) in sentence comprehension must be extended to include the recognition of syntactic ambiguity. By comparing the processing of ambiguous and unambiguous sentence constituents in German, we show that the P600 is elicited when our language processing system has syntactic alternatives at a certain item given in the input string. That the P600 is sensitive to syntactic ambiguity adds crucial evidence to current debates in psycholinguistic modelling, as the results clearly favour parallel models of syntactic processing which assume that ambiguity is recognized and costly.     

Inferential theory for partially disattenuated correlation coefficients

Four measurement designs are presented for use with correlation coefficients corrected, in one variable, for attenuation due to unreliability—coefficients that we term partially disattenuated correlation coefficients. Asymptotic expressions are derived for the variances and covariances of the estimates accompanying each design. Empirical simulation results that bear on the preceding mathematical developments are then presented. In addition to providing insights into the distributions of the estimates, the empirical results demonstrate satisfactory Type I error control for typical inferential applications. Power is shown to be equal to or greater than that of corresponding product-moment correlations in three of the four designs. Implications for practice are discussed.Support for the research reported in this article was provided by the Natural Sciences and Engineering Research Council of Canada. The authors acknowledge with thanks the contributions of Nancy E. Heckman to some of the theoretical aspects of the study.     

Principals versus osmod: A comment on saito and otsu

Saito and Otsu (1988) compared their OSMOD method of nonmetric principal-component analysis to an early and incorrect implementation of the PRINCIPALS algorithm of Young, Takane, and de Leeuw (1978). In this comment we present results from the current, correct implementations of the algorithm.     

ANOVA and ANCOVA of pre- and post-test,ordinal data

With random assignment to treatments and standard assumptions, either a one-way ANOVA of post-test scores or a two-way, repeated measures ANOVA of pre- and post-test scores provides a legitimate test of the equal treatment effect null hypothesis for latent variable . In an ANCOVA for pre- and post-test variablesX andY which are ordinal measures of and , respectively, random assignment and standard assumptions ensure the legitimacy of inferences about the equality of treatment effects on latent variable . Sample estimates of adjustedY treatment means are ordinal estimators of adjusted post-test means on latent variable .