The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend…

This paper discusses the issue of multiple testing and overall Type I error rates in contexts other than multiple comparisons of means. It demonstrates, using a 5 x 5 correlation matrix, the application of 5 recently developed modified Bonferroni procedures developed by the following authors: (1) Y. Hochberg (1988); (2) B. S. Holland and M. D.…

Discussion of models for library circulation data highlights a new statistical prediction model that creates a flexible regression curve. Linear graphs that result from previous models are discussed, bivariate discrete distributions are explained, and graphs that show library circulation for one year at a time are presented. (nine references) (LRW)

The adequacy of multidimensional trait and item parameters using multidimensional item response theory analysis was studied through simulation using different degrees of correlation between two trait dimensions and the existence of a restricted trait on the second dimension. Conditions allowing adequate recovery of trait and item parameters are…

Asymptotic distributions of H. Brogden's and F. Lord's modified sample biserial correlation coefficients (SBCCs) are derived. Asymptotic variances of these estimators are evaluated for bivariate normal populations and compared to the maximum likelihood estimator's asymptotic variance. These estimators are less variable than ordinary SBCCs when the…

The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest…

Factor analysis is the traditional method for studying the dimensionality of test data. However, under common conditions, the factor analysis of tetrachoric correlations does not recover the underlying structure of dichotomous data. The purpose of this paper is to demonstrate that the factor analyses of tetrachoric correlations is unlikely to…

This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…

Attitude measures frequently produce distributions of item scores that attenuate interitem correlations and thus also distort findings regarding the factor structure underlying the items. An actual data set involving 260 adult subjects' responses to 55 items on the Love Relationships Scale is employed to illustrate empirical methods for…

The focus of this study is on the estimation procedures implemented in BILOG, a computer program. One purpose is to compare the item parameter estimates produced by various procedures available in BILOG. Four different models are used: the one, two, and three parameter model and a three parameter model with common guessing parameters. The results…