Equations are derived for product correlation between variables derived from two or fewer original variables. Index correlation and spurious index correlation are briefly discussed. Exact equations for product correlation are derived, and spurious product correlation is demonstrated under various conditions. (RC)

This paper is written with the underlying philosophy that any theory aimed at understanding the functional organization of the brain must begin with an analysis of perception and must also be firmly based on experimental evidence. (Author)

The possibility of using component analysis for nominal data is discussed. Two nominal scale correlation coefficients are applicable. Tschuprow's coefficient and the J index. The reason is that they satisfy the requirements of a scalar product between normalized vectors in a Euclidean space. Some characteristics of these coefficients are…

Estimates of the mean and standard deviation of the tetrachoric correlation are compared with their expected values in several two by two tables. Significant bias in the mean is found when the minimum cell frequency is less than five. Three formulas for the standard deviation are discussed. (Author/JKS)

Coefficient Alpha can be used to estimate the reliability of a test when the test is split into several parts. It is known that alpha can severly underestimate test reliability when the parts have an unequal number of items. A generalization of alpha is proposed to correct this defect. (Author/JKS)

Two models for scaling of paired comparison data are compared to the Thurstone case III model. Two goodness of fit indices are presented for each model for five data sets. The results illustrate the inability of the Thurstone model to adequately account for data when the scale includes extreme stimuli. (Author)

Two forms of stationarity prior to criterion in absorbing Markov chains are examined. Both forms require that the probability of a particular response on a particular trial before absorption be independent of trial number. Simple, necessary and sufficient conditions for both forms are developed and applied to several examples. (Author)

One of the innovative approaches in the use of hierarchical linear models (HLM) is to use HLM for Slopes as Outcomes models. This implies that the researcher considers that the regression slopes vary from cluster to cluster randomly as well as systematically with certain covariates at the cluster level. Among the covariates, group indicator…

Item response theory (IRT) is a useful and effective tool for item response measurement if used in the proper context. This paper discusses the sets of assumptions under which responses can be modeled while exploring the framework of the IRT models relative to response testing. The one parameter model, or one parameter logistic model, is perhaps…

The entire article is in German with no English abstract. (5 references) (NH)

Applies mathematical models to the concepts of ecological dominance and ecological niche. Considers niche width, the addition of new species to a community, and the evolution of dominant and subordinate species within a community. Analyzes data from other studies to support the models. (EB)

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of dichotomous items. The algorithms presented, and three competing deterministic algorithms are compared using computer-generated data. (Author/JKS)

The model presented involves the concept of "mathematical quotient." It is intended that the model be used by the classroom teacher in developing mathematical instructional sequences. (MK)

The relationship between hierarchical linear modeling (HLM) notation and mixed model notation is illustrated by explicitly mapping the parameters across notations for a concrete example involving the hierarchical modeling of change. (Author/SLD)