Many students have difficulty seeing the conceptual link between bivariate data displayed in a scatterplot and the statistical summary of the relationship, "r." This article shows how to teach (and compute) "r" such that each datum's direct and indirect influences are made apparent and used in a new formula for calculating Pearson's "r."

Interest in students who exhibit characteristics with difficulties in learning can be traced as far back as 1800. In order to better understand the complexities and causes of learning disabilities, many researchers (Bannatyne, 1968, 1974; Rugal, 1974) have investigated ways to better identify learners who struggle with academics. A strong argument…

The classical twin study provides a useful resource for testing hypotheses about how the family environment influences children's development, including how genes can influence sensitivity to environmental effects. However, existing statistical models do not account for the possibility that children can inherit exposure to family environments…

In 1897, about half of all American municipalities used lead pipes to distribute water. Employing data from Massachusetts, this paper compares infant death rates in cities that used lead water pipes to rates in cities that used nonlead pipes. In the average town in 1900, the use of lead pipes increased infant mortality by 25 to 50 percent.…

Reforming teacher tenure is an idea that appears to be gaining traction with the underlying assumption being that one can infer to a reasonable degree how well a teacher will perform over her career based on estimates of her early-career effectiveness. Here we explore the potential for using value-added models to estimate performance and inform…

Errors in written multi-digit computation were investigated in children with math difficulties. Third- and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low…

The composite direct product (CDP) model is a multiplicative model for multitrait-multimethod (MTMM) designs. It is extended to incomplete MTMM correlation matrices where some trait-method combinations are not available. Rules for omitting trait-method combinations without resulting in an indeterminate model are also suggested. Maximum likelihood…

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized…

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes in…

This review examined a study designed to evaluate whether playing number board games improved numeracy skills of low-income preschoolers. The study included 136 pre-school children from 10 urban Head Start centers: 72 children were randomly selected to play a number board game with a trained experimenter; the remaining 64 children played a…

This article presents three mathematics lessons in a social justice setting of learning about poverty. Student activities include budgeting, graphic data representation, and linear regression, all in the context of connecting, communicating, and reasoning about poverty. (Contains 1 table, 5 figures and 6 online resources.)

K. Rayner, A. Pollatsek, D. Drieghe, T. J. Slattery, and E. D. Reichle argued that the R. Kliegl, A. Nuthmann, and R. Engbert corpus-analytic evidence for distributed processing during reading should not be accepted because (a) there might be problems of multicollinearity, (b) the distinction between content and function words and the skipping…

In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference…

The hypothesis that a task that increases in complexity (increasing its correlation with a central measure of intelligence) does so by increasing its dimensionality by tapping individual differences or another variable was supported by findings from 46 adults aged 20-70 years performing a mental counting task. (SLD)