Information loss occurs when continuous data are grouped in discrete intervals. After calculating the squared correlation coefficients between continuous data and corresponding grouped data for four population distributions, the effects of population distribution, number of intervals, and interval width on information loss and recovery were…

An alternative for analyzing responses to Likert Scales is proposed, using additive conjoint measurement. It assumes that subjects can report their attitudes toward stimuli in rank order. Neither within-subject nor between-subject distributional assumptions are made. Nevertheless, interval level stimulus values and response category boundaries are…

Four empirical laws of bibliometrics--anomalous number, Lotka's, Zipf's, and Bradford's--together with Laplace's "law of succession" and de Solla Price's cumulative advantage distribution are shown to be almost identical. A simple model shows that the frequency forms conform with inverse square law over appropriate interval. (Fifteen…

Fleiss' popular multirater kappa is known to be influenced by prevalence and bias, which can lead to the paradox of high agreement but low kappa. It also assumes that raters are restricted in how they can distribute cases across categories, which is not a typical feature of many agreement studies. In this article, a free-marginal, multirater…

During the 1990s, the use of meta-analytic methods in educational research has been widespread, and few aspects of education have escaped the meta-analytic revolution. The acceptance has not been complete, however, and several threats to validity remain. Prominent among these are the "normality" problem and the "independence"…

The purpose of this study was to examine the recovery of item parameters in simulated Automatic Item Generation (AIG) conditions, using Markov chain Monte Carlo (MCMC) estimation methods to attempt to recover the generating distributions. To do this, variability in item and ability parameters was manipulated. Realistic AIG conditions were…

The topic of grade inflation, the awarding of too many "A's" and "B's", is frequently mentioned in the literature on higher education. Many educational philosophies have suggested ways to evaluate students fairly. Some professors have used the bell-shaped curve as a model, giving grades according to the normal distribution curve regardless of the…

Nonparametric procedures are often more powerful than classical tests for real world data, which are rarely normally distributed. However, there are difficulties in using these tests. Computational formulas are scattered throughout the literature, and there is a lack of availability of tables of critical values. This paper brings together the…

Data transformations are commonly used tools in quantitative analysis of data. However, data transformations can be a mixed blessing to researchers, improving the quality of the analysis while at the same time making the interpretation of the results difficult. Few, if any, statistical texts discuss the tremendous influence a distribution's…

Examines the properties of bibliometric distributions (application of mathematics and statistical methods to books and other written communications) in a nontechnical manner, covering similarities of the Lotka, Bradford, and Zipf distributions, the relationship between empirical laws and theories, and bibliometric concepts and theory construction.…

Explains Zipf's Law of Vocabulary Distribution (i.e., relationship between frequency of a word in a corpus and its rank), noting the discovery of the law, alternative forms, and literature relating to the search for a rationale for Zipf's Law. Thirty-eight references are cited. (EJS)

This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments such as might occur in educational research. Three applications illustrate the approach. (SLD)

Responds to an earlier article by the same title in Mathematics in School; v25 n2. Asks the question, Which diagram communicates the nature of the distribution most effectively? Uses debate about the number of angels that can balance on a pin head to illustrate various statistical diagrams and explains problems inherent in each. Concludes with…

Determining whether score distributions differ on two or more test forms administered to samples of examinees from a single population is explored using three statistical tests using loglinear models. Examples are presented of applying tests of distribution differences to decide if equating is needed for alternative forms of a test. (SLD)

Examined the asymptotic distributions of three reliability coefficient estimates: (1) sample coefficient alpha; (2) reliability estimate of a composite score following factor analysis; and (3) maximal reliability of a linear combination of item scores after factor analysis. Findings show that normal theory based asymptotic distributions for these…