The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

The article first summarizes the assumptions of Luce (2004, 2008) for inherently binary (2-D) stimuli (e.g., the ears and eyes) that lead to a "p-additive," order-preserving psychophysical representation. Next, a somewhat parallel theory for unary (1-D) signals is developed for intensity attributes such as linear extent, vibration to finger, and…

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution that need not be centered row-wise. The results bear directly on several types of preprocessing methods in Parafac/Candecomp. (Author/TJH)

This note shows that the formula suggested by N. D. Bryant and S. Gokhale (1972) for correcting indirectly restricted correlations when no information is available on the third (directly restricted) variable is accurate only in one special instance. A more general correction formula is illustrated. (SLD)

A summary and a unified treatment of fully general computational solutions for two criteria for transforming two or more matrices to maximal agreement are provided. The two criteria--Maxdiff and Maxbet--have applications in the rotation of factor loading or configuration matrices to maximal agreement and the canonical correlation problem. (SLD)

The phimax adjustment to phi (Pearson's product moment correlation applied to binary data) is explored. Phi/phimax is shown to be a measure of relationship apart from its affiliation with phi. The relations between phi/phimax and kappa and limitations of phi/phimax are discussed. (SLD)

Rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, is discussed. Rowwise and columnwise indices are particularly suited for evaluating different types of conjectures of a similar pattern of entries across the two matrices. (SLD)

A family of coefficients of relational agreement for numerical scales is proposed, generalizing to multiple judges the theory of F. E. Zegers and J. M. F. ten Berge (1985) of association coefficients for two variables, using the premise that choice of coefficient depends on scale type of the variables. (SLD)

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

A theoretical framework is developed in which the effects of some common forms of violation of assumptions of linearity of regression and homoscedasticity can be investigated. Simple expressions are derived for the restricted and corrected correlations in terms of the target (unrestricted) correlation in these situations. (SLD)

New methods of analysis--equations and graphs for iso-r(sup 2) contours--were introduced and used to illustrate location effects for pooled data sets. The "r(sup 2)" is the coefficient of determination. Results are used to highlight imprecise statements in the literature about the behavior of the correlation coefficient for pooled data…

Point-estimate and confidence-interval procedures are proposed for the (1) combined Mann-Whitney U test; (2) combined two-sample normal-scores test; (3) combined matched-pair Wilcoxon signed-ranks test; and (4) combined matched-pair normal-scores test. The four techniques are illustrated with hypothetical examples and are considered either…

A causal model of halo error (HE) is derived. Three hypotheses are formulated to explain findings of negative HE. It is suggested that apparent negative HE may have been misinferred from existing correlational measures of HE, and that positive HE is more prevalent than had previously been thought. (SLD)

The problem of combining information to estimate standardized partial regression coefficients in a linear model is considered. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. This estimate can be generalized to address situations in which not every study measures every…

Conditions necessary and sufficient for the determination of LISREL model solutions are identified. The reasons for indeterminacy of LISREL solutions are discussed, and an index of determinacy is presented and related to the covariance matrix of latent variables. (SLD)