In today's era of large-scale data, academic institutions, businesses, and government agencies are increasingly faced with heterogeneous datasets. Consequently, there is a growing need to develop effective methods for extracting meaningful insights from this type of data. Quantile, expectile, and expected shortfall regression methods offer useful…

In regression analysis courses, there are many settings in which the response variable under study is continuous, strictly positive, and right skew. This type of response variable does not adhere to the normality assumptions underlying the traditional linear regression model, and accordingly may be analyzed using a generalized linear model…

This paper describes a method for pooling grouped, ordered-categorical data across multiple waves to improve small-sample heteroskedastic ordered probit (HETOP) estimates of latent distributional parameters. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in each of a small…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

Whenever you think you have an idea of how something works, you have a mental model. That is, in effect, a layman's way of talking about having an hypothesis. The hypothesis needs to be tested for how closely it fits reality--and reality is the data collected from an experiment. So the data is collected on the few and compared with a few…

Researchers suggest that certain supportive behaviors of mentors could increase the benefits of school-based mentoring for youth. However, the literature contains few validated instruments to measure these behaviors. In our present study, we aimed to construct and validate a tool to measure the supportive behaviors of mentors participating in…

This article is concerned with the question of whether the missing data mechanism routinely referred to as missing completely at random (MCAR) is statistically examinable via a test for lack of distributional differences between groups with observed and missing data, and related consequences. A discussion is initially provided, from a formal logic…

Previous research suggested that candidates from some black and minority ethnic groups were less likely to receive an offer of a place from an "old" university. These findings were disputed in a re-analysis carried out for HEFCE which found that only Pakistani candidates were significantly less likely to receive offers (from both…

Value-added models have been widely used to assess the contributions of individual teachers and schools to students' academic growth based on longitudinal student achievement outcomes. There is concern, however, that ignoring the presence of missing values, which are common in longitudinal studies, can bias teachers' value-added scores.…

Using a national database, this study uses discriminant analysis to explore the role of citizenship status in determining intent to leave for pre-tenure faculty members at 4-year research universities. Of the 3 possible responses (intend to stay, intend to leave, and undecided), 2 functions emerged. The first function differentiates between those…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

Outliers, extreme data values relative to others in a sample, may distort statistics that assume internal levels of measurement and normal distribution. The outlier may be a valid value or an error. Several procedures are available for identifying outliers, and each may be applied to errors of prediction from the regression lines for utility in a…

Explains two basic exploratory techniques for displaying and summarizing data--the stem and leaf diagram and the box and whiskers plot--and applies them to a data set consisting of federal allotments and state and local matching funds. One table, three figures, and seven sources are included. (Author/RBF)

The primary purpose of this study was to examine significant differences, if any, in student achievement in the area of math and science of students taught by traditionally certified teachers and alternatively certified teachers. This study examined alternatively certified teachers, as identified from through the Georgia TAPP (Teacher Alternative…

This set of activity sheets requires students to organize and display data with a box-and-whiskers graph. Students use the plot as a summary display to detect patterns and to highlight the important features of the data for purposes of comparison. (PK)