Statistical inference concerning the parameters of k multivariate normal populations is considered. Several models in which the parameters have certain hierarchical relationships are discussed, in particular as related to testing the hypothesis that k psychological tests are parallel forms of the same test. The report contains the following…

The logic and procedures underlying a disturbance term regression test of logical consistency for structural models are reviewed for recursive and nonrecursive designs. It is shown that in a simple three-variable, complete mediational case the test procedure is mathematically equivalent to a part correlation. (Author/LMO)

Correct simple formulas are provided for the value of phi needed to use the commonly available Pearson and Hartley power charts in determining the power of hypothesis tests involving simple degree-of-freedom comparisons in the fixed effects analysis of variance. (LMO)

Fifteen examples using different formulas for calculating degrees of freedom for power analysis of multiple regression designs worked out by Cohen are presented, along with a more general formula for calculating such degrees of freedom. (Author/JKS)

The properties of nonmetric multidimensional scaling one explored by specifying statistical models, proving statistical consistency, and devloping hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. (Author/LMO)

This study is an analysis of the robustness of the Box-Tiao integrated moving averages model for analysis of time series quasi experiments. One of the assumptions underlying the Box-Tiao model is that all N values of alpha subscript t come from the same population which has a variance sigma squared. The robustness was studied only in terms of…

Conjunctive item response models are introduced such that: (1) sufficient statistics for latent traits are not necessarily additive in item scores; (2) items are not necessarily locally independent; and (3) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are…

A five by five covariance matrix representing longitudinal measurements at five occasions is used to illustrate that markedly different types of learning curves may generate indistinguishable covariance structures. An excellent fit of a simplex structure can be misleading. Common uses of covariance structure models for growth studies are…

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…

A solution is proposed for analysis of variance procedures with missing cells, such as may occur when a control group is not assigned to any of the rows or columns of the various experimental groups. Mathematical models for two-way design are presented which define several variables; as well as row effect, column effect, and row and column…

The testing of a priori contrasts, post hoc contrasts, and experimental error rates are discussed. Methods for controlling the experimental error rate for a set of a priori contrasts tested simultaneously have been developed by Dunnett, Dunn, Sidak, and Krishnaiah. Each of these methods is discussed and contrasted as to applicability, power, and…

A procedure was developed within hypothesis-testing logic that allows researchers to support a hypothesis that has traditionally been the statistical or null hypothesis. Four activities involved in attainment of this goal were discussed: (1) development of statistical logic needed to define the sampling distribution associated with the hypothesis…

The results of reanalyses of statistical procedures used in the class-size meta-analyses by Glass and Smith are reported. The analyses suggest that the use of suboptimal statistical methods did not greatly affect the results of the meta-analyses by Glass and Smith. (Author/PN)

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are…

Intraclass correlation reliability estimates are based on the assumption that the various measures are equivalent. Joreskog's (1970) general model for the analysis of covariance structures can be used to test the validity of this assumption. (For related document, see TM 002 301.) (Author)