We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

Bootstrapping methods and random distribution methods are increasingly recommended as better approaches for teaching students about statistical inference in introductory-level statistics courses. The authors examined the effect of teaching undergraduate business statistics students using random distribution and bootstrapping simulations. It is the…

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

Applications of distribution theory for the squared multiple correlation coefficient and the squared cross-validation coefficient are reviewed, and computer programs for these applications are made available. The applications include confidence intervals, hypothesis testing, and sample size selection. (Contains 2 tables.)

The theoretical framework and conceptual framework help to determine the purpose of scientific research, facilitate the analysis of data, organize the thoughts of researchers, increase the reliability of research, and ensure that research is shared in a wide area. Although these two concepts seem to be basically the same, they have structural…

The Adaption-Innovation Inventory (AII), originally developed by Kirton (1976), is a widely used self-report instrument for measuring problem-solving styles at work. The present study investigates how scores on the AII are affected by different response styles. Data are collected from a combined sample (N = 738) of students, employees, and…

Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate…

The authors conducted 4 experiments to test the decision-bound, prototype, and distribution theories for the categorization of sounds. They used as stimuli sounds varying in either resonance frequency or duration. They created different experimental conditions by varying the variance and overlap of 2 stimulus distributions used in a training phase…

Glass's estimator of effect size, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model. The exact distribution of Glass's estimator is obtained and the estimator is shown to have a small sample bias. Alternatives are proposed and discussed. (Author/JKS)

The robustness of hypothesis tests for the correlation coefficient under varying conditions is discussed. The effects of violations of the assumptions of linearity, homoscedasticity, and kurtosis are examined. (JKS)

Gives a sketch of some topics in distribution theory that is technically simple, yet provides techniques for handling the partial differential equations satisfied by the most important Green's functions in physics. (Author/GA)

Statistical methods are presented for studying "correlates of diversity," defined as characteristics of educational organizations that predict dispersion on the dependent variable. Strategies based on exact distribution theory and asymptotic normal approximation are considered. (TJH)

Outlines a method for comparing completely standardized solutions in multiple groups. The method is based on a correlation structure analysis of equal-size samples and uses the correlation distribution theory implemented in the structural equation modeling program RAMONA. (SLD)

The distribution theory underlying corrections for guessing is analyzed, and the probability distributions of the random variables are derived. The correction in grade, based on random guessing of unknown answers, is compared with corrections based on educated guessing. (Author/MH)

Asymptotic distribution theory of Brogden's form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained. Its relative efficiency to the biserial correlation coefficient is examined. Recommendations for choice of estimator of biserial correlation are presented. (Author/JKS)