Relates Thurstonian models for paired comparisons data to Thurstonian models for ranking data and proposes an intermediate model for paired comparisons data that assigns nonzero probabilities to all transitive patterns and to some, but not all, intransitive patterns. Conducted a simulation study to investigate the performance of three alternative…

Bootstrap methodology is presented that yields approximations of the sampling variation of redundancy estimates while assuming little a priori knowledge about the distributions of these statistics. Results of numerical demonstrations suggest that bootstrap confidence intervals may offer substantial assistance in interpreting the results of…

The biases and mean squared errors of the sample squared multiple correlation coefficient and five adjusted estimators of the population squared multiple correlation are examined. A quadratic estimator and the minimum variance unbiased estimator are also examined. These estimators are compared in terms of absolute bias and mean squared error.…

The primary objective of this study was to investigate how incorporating prior information improves estimation of item parameters in two small samples. The factors that were investigated were sample size and the type of prior information. To investigate the accuracy with which item parameters in the Law School Admission Test (LSAT) are estimated,…

Studied three procedures for estimating the standard errors of school passing rates using a generalizability theory model and considered the effects of student sample size. Results show that procedures differ in terms of assumptions about the populations from which students were sampled, and student sample size was found to have a large effect on…

Explains how the Gibbs sampler can be applied to obtain a sample from the posterior distribution over the parameters of a structural equation model. Presents statistics to use to summarize marginal posterior densities and model checks using posterior predictive p-values. (SLD)

Investigated the item-parameter recovery characteristics of a Gibbs sampling method (J. Albert, 1992) for item-response theory item-parameter estimation and compared them to those from the BILOG computer program. Item-parameter recoveries were similar for both approaches for larger data sets, but overall, BILOG performance was superior. (SLD)

The sampling interpretation of confidence intervals and hypothesis tests is discussed in the context of conditional maximum likelihood estimation. Three different interpretations are discussed, and it is shown that confidence intervals constructed from the asymptotic distribution under the third sampling scheme discussed are valid for the first…

When the same parameters are estimated by data from several independent samples, it may happen that, for any pair of samples, even though the test for parameter discrepancy is statistically significant, the two individual confidence intervals overlap. To overcome this potential contradiction, a new type of one-sample confidence intervals is…

A method is presented for approximating the amount of bias in estimators with complex sampling distributions that are influenced by a variety of properties. The model is illustrated in the contexts of the bootstrap method and redundancy analysis. (SLD)

Illustrates that sampling variance can be very large when a three-wave quasi simplex model is used to obtain reliability estimates. Also shows that, for the reliability parameter to be identified, the model assumes a Markov process. These problems are evaluated with both real and Monte Carlo data. (SLD)

The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

This article presents an improved approximation formula for the problem of correcting correlation coefficients that arise from range-restricted distributions on either or both the independent and dependent variable. (BS)

Drawing a probability sample of homeless adults in Los Angeles' Skid Row resulted in a sampling design meeting statistical criteria. The design uses data from meal centers, bed counts, and outdoor congregations; and allows unbiased estimates of prevalence of mental disorders and assessment of service needs of the homeless. (TJH)

In large multipurpose surveys, it is common to select the sample systematically proportional to some measure of size (PPS) that is correlated with an important variable of interest. Assuming the frame is sorted in a useful deterministic manner, systematic sample methodologies provide an additional control on the sample allocation, beyond the…