A type of data layout that may be considered as an extension of the two-way random effects analysis of variance is characterized and modeled based on group invariance. The data layout seems to be suitable for several scenarios in psychometrics, including the one in which multiple measurements are taken on each of a set of variables, and the…

This note provides a scheme that can overcome difficulties in calculating statistical quantities using certain formulae because of errors in the means. Specifically the diversions and discrepancies arising from the results obtained from three groups of widely used formulae for computing the estimated regression coefficients, the gradient b and the…

In item-response theory, if a latent-structure model has an ability variable, then elementary information theory may be employed to provide a criterion for evaluation of the information the test provides concerning ability. This criterion may be considered even in cases in which the latent-structure model is not valid, although interpretation of…

It is common to assume during statistical analysis of a multiscale assessment that the assessment has simple structure or that it is composed of several unidimensional subtests. Under this assumption, both the unidimensional and multidimensional approaches can be used to estimate item parameters. This paper theoretically demonstrates that these…

The statistician has n independent estimates of a parameter he knows is positive, but, as is the case in components-of-variance problems, some of the estimates may be negative. If the n estimates are to be combined into a single number, we compare the obvious rule, that of averaging the n values and taking the positive part of the result, with…

This paper outlines some common applications of the statistical method of linear least-squares and examines the statistical significance of the results. (BB)

It is shown that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Analysis of several thousand solutions to Bayesian problems showed that when information was presented in frequency formats, statistically naive participants derived up to 50% of inferences by Bayesian…

There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean [mu] and variance [sigma][superscript 2], the expected value of the sample variance is [sigma][superscript 2]. The generalization justifies the use of the usual standard error of the sample mean in possibly…

In this paper, we consider some combinatorial and statistical aspects of the popular "Powerball" lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the "jackpot" in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the…

An obstacle to broader acceptability of effect sizes in single case research is their lack of intuitive and useful interpretations. Interpreting Cohen's d as "standard deviation units difference" and R[superscript 2] as "percent of variance accounted for" do not resound with most visual analysts. In fact, the only comparative analysis widely…

Sequential probability ratio testing (PRT), which usually is applied in situations requiring a decision between two simple hypotheses or a single decision point, is extended to include situations involving k decision points and [(k + 1)-choose-2] sets of simultaneous, simple hypotheses, where k>1. The multiple-decision point or…

Students in two biostatistics courses at the Cornell Medical College and in a course in applications of computer science given in Cornell's School of Industrial Engineering were given access to an interactive package of computer programs enabling them to perform statistical analysis without the burden of hand computation. After a general…

This note presents the results of a survey of the power of statistical tests appearing in the Journal Of Educational Measurement from winter, 1969 through fall, 1971. (Author)

A bias-corrected estimator of noncentrality parameters of covariance structure models is discussed. The approach represents an application of the bootstrap methodology for purposes of bias correction, and utilizes the relation between average of resample conventional noncentrality parameter estimates and their sample counterpart. The…

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter…