Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units…

Correlation analysis has been used widely by researchers and analysts when analyzing large-scale assessment data. Limit research provided reliable methods to estimate various correlations and their standard errors with the complex sampling design and multiple plausible values taken into account. This report introduces the methodology used by the…

Data collected from online learning and tutoring systems for individual students showed strong autocorrelation or dependence because of content connection, knowledge-based dependency, or persistence of learning behavior. When the response data show little dependence or negative autocorrelations for individual students, it is suspected that…

Measurement in geometry is one of the key areas of school mathematics, however, pupils make serious mistakes when solving problems involving measurement and hold misconceptions. This article focuses on the possible links between lower secondary pupils' (n = 870) success in solving non-measurement tasks and calculations tasks on area and volume and…

One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous…

To rule out the need for a two-parameter item response theory (IRT) model during item analysis by Rasch models, it is important to check the Rasch model's assumption that all items have the same item discrimination. Biserial and polyserial correlation coefficients measuring the association between items and restscores are often used in an informal…

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."

A common mistake in analysis of cluster randomized trials is to ignore the effect of clustering and analyze the data as if each treatment group were a simple random sample. This typically leads to an overstatement of the precision of results and anticonservative conclusions about precision and statistical significance of treatment effects. This…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…

A table is presented that directly converts any known point biserial coefficient to the biserial coefficient, providing the largest proportion of the dichotomous variable is also known. (Author)

The method of least squares enables the determination of an estimate of the slope and intercept of a straight line relationship between two quantities or variables X and Y. Although a theoretical relationship may exist between X and Y of the form Y = mX + c, in practice experimental or measurement errors will occur, and the observed or measured…

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…

In this article, the author takes up the special trinomial (1 + x + x[squared])[superscript n] and shows that the coefficients of its expansion are entries of a Pascal-like triangle. He also shows how to calculate these entries recursively and explicitly. This article could be used in the classroom for enrichment. (Contains 1 table.)

The National Center for Education Statistics (NCES) commissioned the papers in this publication to address advances in measuring education inflation and adjusting for it, as well as to examine the emergence of a new focus on school spending, rather than school district spending, as well as new, private sources of funding for public education, and…