While researching student assumptions for the development of the Biology Concept Inventory (BCI; http://bioliteracy.net), we found that a wide class of student difficulties in molecular and evolutionary biology appears to be based on deep-seated, and often unaddressed, misconceptions about random processes. Data were based on more than 500…

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of…

Recent work has shown that multidimensionally scoring responses from different tests can provide better ability estimates. For educational assessment data, applications of this approach have been limited to binary scores. Of the different variants, the de la Torre and Patz model is considered more general because implementing the scoring procedure…

The Monte Carlo study compared the performance of predictive discriminant analysis (PDA) and that of logistic regression (LR) for the two-group classification problem. Prior probabilities were used for classification, but the cost of misclassification was assumed to be equal. The study used a fully crossed three-factor experimental design (with…

The Johnson-Neyman (J-N) technique (P. Johnson and N. Neyman, 1936) is used to determine areas of significant difference in a criterion variable between two or more groups in situations of linear regression. In using this technique, researchers have encountered difficulties with results, possibly related to the J-N technique's sensitivity to…

Accurate classification in discriminant analysis and the value of prediction are discussed, with emphasis on the uses and key aspects of prediction. A brief history of discriminant analysis is provided. C. J. Huberty's discussion of four aspects of discriminant analysis (separation, discrimination, estimation, and classification) is cited.…

A recent survey of simulation studies concluded that an overwhelming majority of papers do not report a rationale for the number of iterations carried out in Monte Carlo robustness (MCR) experiments. The survey suggested that researchers might benefit from adopting a hypothesis testing strategy in the planning and reporting of simulation studies.…

This paper studies the general theory of Akaike's Information Criterion (AIC) and provides two analytical extensions. The extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the two models. The criteria are applied in two Monte Carlo experiments. (Author/GDC)

Recent research using single-stage procedures to test the equality of the means of J independent normal distributions when variances are unequal have proven unsatisfactory in controlling Type I errors and power. A method for dealing with the problem of unequal sample sizes while implementing two-stage procedures is discussed. (TJH)

We consider the problem of classifying an unknown observation into one of several populations using tree-structured allocation rules. Although many parametric classification procedures are robust to certain assumption violations, there is need for discriminant procedures that can be utilized regardless of the group-conditional distributions that…

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are…

Eta-Squared (ES) is often used as a measure of strength of association of an effect, a measure often associated with effect size. It is also considered the proportion of total variance accounted for by an independent variable. It is simple to compute and interpret. However, it has one critical weakness cited by several authors (C. Huberty, 1994;…

Monte Carlo methods were used to investigate the effects of removing extreme data points identified by five indices of influence. Multivariate normal data were simulated and observations were removed from samples if they exceeded the criteria suggested in the literature for each influence statistic. Factors included in the design of the Monte…

This study compared the effectiveness of 10 methods of determining the number of factors to retain in exploratory common factor analysis. The 10 methods included the Kaiser rule and a modified Kaiser criterion, 3 variations of parallel analysis, 4 regression-based variations of the scree procedure, and the minimum average partial procedure. The…

Many multivariate statistical methods call upon the assumption of multivariate normality. However, many applied researchers fail to test this assumption. This omission could be due to ignorance of the existence of tests of multivariate normality or confusion about which test to use. Although at least 50 tests of multivariate normality exist,…