Continuous exponential families may be employed to find continuous distributions with the same initial moments as the discrete distributions encountered in typical applications of classical equating. These continuous distributions provide distribution functions and quantile functions that may be employed in equating. To illustrate, an application…

The purpose of this study was to analyze opinions of selected school district stakeholders regarding potentially critical factors in school bond referendum success and failure in Kansas during the years 2004-2007. Of the 72 eligible school districts, one district was randomly selected from each of six groups formed through a stratified random…

We describe an easy-to-employ, hands-on demonstration using playing cards to illustrate the central limit theorem. This activity allows students to see how a collection of sample means drawn from a nonnormally distributed population will be normally distributed. Students who took part in the demonstration reported it to be helpful in understanding…

We propose a nonparametric (or distribution-free) procedure for testing the equality of several population variances (or scale parameters). The proposed test is a modification of Bakir's (1989, Commun. Statist., Simul-Comp., 18, 757-775) analysis of means by ranks (ANOMR) procedure for testing the equality of several population means. A proof is…

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…

While violation of the homogeneity of variance assumption has received considerable attention, violation of the assumption of normally distributed data has not received as much attention. As a result, researchers may have the mistaken impression that as long as the assumptions of independence of observations and homogeneity of variance are…

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

The meta-analysis of coefficient alpha across many studies is becoming more common in psychology by a methodology labeled reliability generalization. Existing reliability generalization studies have not used the sampling distribution of coefficient alpha for precision weighting and other common meta-analytic procedures. A framework is provided for…

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…

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)

This quantitative analysis of published results on the effect of coaching on Scholastic Aptitude Test scores differs from previous studies by separating out the within-study sampling error from the variation in coaching effectiveness. The authors conclude that the size of the positive effect seems too small to be practically important. (Author/SK)

Studied whether the theoretical sampling distribution of the U3 person-fit statistic is in agreement with the simulated sampling distribution under different item response theory models and varying item and test characteristics. Simulation results suggest that the use of standard normal deviates for the standardized version of the U3 statistic may…

Two-stage sampling procedures for comparing two population means when variances are heterogeneous have been developed by D. G. Chapman (1950) and B. K. Ghosh (1975). Both procedures assume sampling from populations that are normally distributed. The present study reports on the effect that sampling from non-normal distributions has on Type I error…

This paper illustrates an application of Efron's bootstrap to the repeated measures design. While this approach does not require parametric assumptions, it does utilize distributional information in the sample. By appropriately resampling from study data, the bootstrap may determine accurate sampling distributions for estimators, effects, or…