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.     

Robust techniques for testing heterogeneity of variance effects in factorial designs

Several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequaln are compared using both theoretical and Monte Carlo results. Two types of spread variables, (1) the jackknife pseudovalues ofs ² and (2) the absolute deviations from the cell median, are shown to be robust and relatively powerful. These variables seem to be generally superior to the Z-variance and Box-Scheffé procedures.This research was sponsored by Public Health Service Training Grant MH-08258 from the National Institute of Mental Health. The author thanks Mark I. Appelbaum, Elliot M. Cramer, and Scott E. Maxwell for their helpful criticisms of this paper. An earlier version of this work was presented at the Annual Meeting of the Psychometric Society, Murray Hill, New Jersey, April, 1976.     

On Bayesian estimation in unrestricted factor analysis

It is shown that the common and unique variance estimates produced by Martin & McDonald's Bayesian estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. This fact is used to justify a suggested simple alternative method of specifying the Bayesian parameters required by the procedure.     

Multiple schedule component duration: a reanalysis of Shimp and Wheatley (1971) and Todorov (1972)

The tendency for relative response rate to approach matching as multiple schedule component duration decreases has been interpreted as confirming a prediction of Herrnstein's multiple schedule equation. However, the equation predicts that absolute response rate will decrease in both multiple schedule components as component duration decreases. The absolute response-rate data of two studies of component duration do not support this prediction; absolute rate either increased or remained relatively constant.     

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.     

Effects of dialect on merger perception: ERP and behavioral correlates

Native speakers of a language are often unable to consciously perceive, and have altered neural responses to, phonemic contrasts not present in their language. This study examined whether speakers of dialects of the same language with different phoneme inventories also show measurably different neural responses to contrasts not present in their dialect. Speakers with (n=11) and without (n=11) an American English I/E (pin/pen) vowel merger in speech production were asked to discriminate perceptually between minimal pairs of words that contrasted in the critical vowel merger and minimal pairs of control words while their event-related potential (ERPs) were recorded. Compared with unmerged dialect speakers, merged dialect speakers were less able to make behavioral discriminations and exhibited a reduced late positive ERP component (LPC) effect to incongruent merger vowel stimuli. These results indicate that between dialects of a single language, the behavioral response differences may reflect neural differences related to conscious phonological decision processes.     

A Preliminary Investigation of the Relationship Between Fluency and Application for Multiplication

Research suggests component skill performance has a strong positive relationship with composite skill performance. This study examined the association between accuracy and fluency for the component-composite relationship within multiplication. One hundred and fifty-seven fifth-graders did one-minute assessments for single-digit, and multi-digit multiplication problems. The results demonstrated the students achieved high levels of accuracy but low levels of fluency. Strong correlations between the component-composite skill fluency suggest that fluent component skills may have a significant role in composite skill performance. Moderate/low correlations between component and composite skill accuracy indicate that more than one skill component may contribute to composite skill acquisition.     

WEIRDness abounds! Sample characteristics,restricted variance,and why they matter for international selection and assessment research

There is increasing awareness that reliance on samples from Western, Educated, Industrialized, Rich, Democratic (WEIRD) countries may have skewed our view of human phenomena. Nowhere is this more true than in international selection and assessment (ISA) research. In the present paper, we describe a way of understanding the impact of WEIRDness on ISA phenomena: restricted variance (RV). The WEIRDness problem is usually one of cross level interactions in which a country-level variable (e.g., individualism/collectivism) might moderate the relationship between two individual-level variables. RV can help to see not only where such cross level interactions might exist, but also provide a specific, mathematical reason for their existence. We use several examples from IJSA and related sources to illustrate the role of RV in ISA-based WEIRDness.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

USE OF COMPONENT ANALYSES TO IDENTIFY ACTIVE VARIABLES IN TREATMENT PACKAGES FOR CHILDREN WITH FEEDING DISORDERS

We evaluated the separate components in treatment packages for food refusal of 4 young children. First, treatment packages were implemented until food acceptance improved. Next, a component analysis was conducted within a multielement or reversal design to identify the active components that facilitated food acceptance. The results indicated that escape extinction was always identified as an active variable when assessed; however, other variables, including positive reinforcement and noncontingent play, were also identified as active variables for 2 of the children. The results suggest that the component analysis was useful for identifying variables that affected food acceptance.