The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students'…

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

Many of us in the social sciences deal with data that do not conform to assumptions of normality and/or homoscedasticity/homogeneity of variance. Some research has shown that parametric tests (e.g., multiple regression, ANOVA) can be robust to modest violations of these assumptions. Yet the reality is that almost all analyses (even nonparametric…

This short article gives a geometrical interpretation of the relationship between the harmonic mean, the arithmetic mean and the self-weighted mean. (Contains 1 figure.)

It is argued that ordinal statistical methods are often more appropriate than their more common counterparts because conclusions will be unaffected by monotonic transformation of the variables; they are more statistically robust when used appropriately; and they often correspond more closely to the researcher's goals. (SLD)

The main purpose of this paper consists in deriving means for making statistical inferences about the distribution of u under the conditions of sigma' is equal to sigma" and sigma' is not equal to sigma". An application of the results to coefficient alpha is appended as an illustration. (CK)

Four types of metric scales are distinguished: absolute, ratio, difference, and interval. A general coefficient of association for two variables of the same scale type is developed which reduces to specific coefficients of association for each scale type. (NSF)

The problem of correlating variables from different scale types is discussed. A general correlation coefficient, based on symmetrization theory, is derived. The coefficient is invariant over permitted transformations of the variables for their respective (possibly nonequivalent) scale types. (Author/JKS)

A Monte Carlo simulation was used to investigate the effect of data transformation on average correlations between Job Descriptive Index scores. In general, results indicate that transformation of scores did not result in marked changes in the correlations and that such transformation may not be worthwhile. (SLD)

Relations between maximum likelihood factor analysis and factor indeterminacy are discussed. (CK)

In the family of correlation suggested by Janson and Vegilius, some coefficients are generalized squared product-moment correlations and some are not. This paper advocates a family of correlations for variables of mixed scale types in which all members are generalized squared product-moment correlations. Practical advantages are explained.…

Three factors that increase score variability yet can be associated with an increase, a decrease, or no change in Pearson's correlation coefficient (r) are discussed (restriction of range, errors of measurement, and linear transformations of data). The connection between changes in variability and r depends on how changes occur. (SLD)

Prediction for a number of criteria from a set of predictor variables in a system of regression equations is studied with the possibilities of linear transformations applied to both the criterion and predictor variables. Predictive composites representing a battery of predictor variables provide identical estimates of criterion scores as do the…

To study the applicability of simple structure logic for factorial data from scientific disciplines outside psychology, four correlation matrices from each of six scientific areas were factor analyzed by five factoring methods. Resulting factor matrices were compared on two objective criteria of simple structure before and after rotation.…