The mixed model analysis of variance assumes a mathematical property known as sphericity. Several preliminary tests have been proposed to detect departures from the sphericity assumption. The logic of the preliminary testing procedure is to conduct the mixed model analysis of variance if the preliminary test suggests that the sphericity assumption…

The objective of this paper is to examine the relationship between the unreliability of difference scores and the power of tests of significance in an attempt to determine the validity of the paradox for the measurement of change presented by Overall and Woodward: that the power of tests of significance is maximum when the reliability of the…

Faced with a nonstandard, complicated practical problem in statistical inference, the applied statistician sometimes must use asymptotic approximations in order to compute standard errors and confidence intervals and to test hypotheses. This usually requires that he derive formulas for one or more asymptotic sampling variances (and covariances)…

Tests the "holistic construal" method of validating constructs and testing organizational hypotheses, using examples from organizational theory and data on wholesale distribution companies. Holistic construal is meant to explicitly represent theoretical and empirical concepts, nonobservational hypotheses, and correspondence rules and…

A probabilistic hypothesis testing procedure to assess the fit of hypothesized hierarchical structures for test item data is discussed. Statistical procedures are presented which are useful for evaluating the fit of data of a certain class of probabilistic models. These models apply to sets of dichotomous (O,1) responses for which there are…

A general Computer program is described that will compute asymptotic standard errors and carry out significance tests for an endless variety of (standard and) nonstandard large-sample statistical problems, without requiring the statistician to derive asymptotic standard error formulas. The program assumes that the observations have a multinormal…

The validity of various reliability-corrected procedures for adjusting for initial differences between groups in uncontrolled studies is established for subjects exhibiting linear fan-spread growth. The results are then extended to a nonlinear model of growth. (Author)

We concern ourselves with the hypothesis that two variables have a perfect disattenuated correlation, hence measure the same trait except for errors of measurement. This hypothesis is equivalent to saying, within the adopted model, that true scores of two psychological tests satisfy a linear relation. Statistical tests of this hypothesis are…

Textbook calculations of statistical power or sample size follow from formulas that assume that the variables under consideration are measured without error. However, in the real world of behavioral research, errors of measurement cannot be neglected. The determination of sample size is discussed, and an example illustrates blocking strategy.…

The effects of the violation of the assumption of normality coupled with the condition of multicollinearity upon the outcome of testing the hypothesis Beta equals zero in the two-predictor regression equation is investigated. A monte carlo approach was utilized in which three differenct distributions were sampled for two sample sizes over…

In a multiple (or multivariate) regression model where the predictors are subject to errors of measurement with a known variance-covariance structure, two-sample hypotheses are formulated for (i) equality of regressions on true scores and (ii) equality of residual variance (or covariance matrices) after regression on true scores. The hypotheses…

This study investigated seven methods for analyzing multivariate group differences. Bonferroni t statistics, multivariate analysis of variance (MANOVA) followed by analysis of variance (ANOVA), and five other methods were studied using Monte Carlo methods. Methods were compared with respect to (1) experimentwise error rate; (2) power; (3) number…

The statistical properties of two methods of estimating gain scores for groups in quasi-experiments are compared: (1) gains in scores standardized separately for each group; and (2) analysis of covariance with estimated true pretest scores. The fan spread hypothesis is assumed for groups but not necessarily assumed for members of the groups.…

The study examines the rule space model, a probabilistic model capable of measuring cognitive skill acquisition and of diagnosing erroneous rules of operation in a procedural domain. The model involves two important components: (1) determination of a set of bug distributions (bug density functions representing clusters around the rules); and (2)…