The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

Propensity score analysis (PSA) is a methodological technique which may correct for selection bias in a quasi-experiment by modeling the selection process using observed covariates. Because logistic regression is well understood by researchers in a variety of fields and easy to implement in a number of popular software packages, it has…

We estimate the trend in the transitory variance of male earnings in the United States using the Michigan Panel Study of Income Dynamics from 1970 to 2004. Using an error components model and simpler but only approximate methods, we find that the transitory variance started to increase in the early 1970s, continued to increase through the…

Extracting and representing semantic information from large scale corpora is at the crux of computer-assisted knowledge generation. Semantic information depends on collocation extraction methods, mathematical models used to represent distributional information, and weighting functions which transform the space. This dissertation provides a…

Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)

Box's method of approximation for the null distributions of likelihood criteria is described. It simplifies the formulas, describes a method of obtaining f, phi, and rho directly from given values, and provides two illustrations of the method. (DJ)

In the traditional Guttman-Harris type image analysis, a transformation is applied to the data matrix such that each column of the transformed data matrix is the best least squares estimate of the corresponding column of the data matrix from the remaining columns. The model is scale free. However, it assumes (1) that the correlation matrix is…

Recent theoretical analyses of the concept of suppression are identified and discussed. A generalized definition of suppression is presented and the conditions for suppressor structures in the context of the General Linear Model are derived. (Author)

An integrated overview is provided of selected multiple comparison methods, with an emphasis on the sequentially rejective Bonferroni (SRB) test and its modifications. Multiple comparisons of means is a frequently used, and yet confusing, method in educational and psychological research. Seven multiple comparison methods are reviewed: (1) the…

The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how…

Lord's Paradox is analyzed in terms of a simple mathematical model for causal inference. The resolution of Lord's Paradox from this perspective has two aspects. First, the descriptive, non-causal conclusions of the two hypothetical statisticians are both correct. They appear contradictory only because they describe quite different aspects of the…

Emphasizing the measurement of causal effects to arrive at a better understanding of the causal mechanisms involved in statistical theory, a mathematical model for causal inferences in prospective studies is developed and then applied to retrospective case-control studies. Before developing the model, causal agents are delineated, and causal…

CERTAIN SPECIFIC ASPECTS OF HYPOTHESIS TESTS USED FOR ANALYSIS OF RESULTS IN RANDOMIZED EXPERIMENTS WERE STUDIED--(1) THE DEVELOPMENT OF THE THEORETICAL FACTOR, THAT OF PROVIDING INFORMATION ON STATISTICAL TESTS FOR CERTAIN EXPERIMENTAL DESIGNS AND (2) THE DEVELOPMENT OF THE APPLIED ELEMENT, THAT OF SUPPLYING THE EXPERIMENTER WITH MACHINERY FOR…