This article considers optimal sample allocation between the treatment and control condition in multilevel designs when the costs per sampling unit vary due to treatment assignment. Optimal unequal allocation may reduce the cost from that of a balanced design without sacrificing any power. The optimum sample allocation ratio depends only on the…

Regardless of the related discipline, students in statistics courses invariably have difficulty understanding the connection between the numerical values calculated for end-of-the-chapter exercises and their usefulness in decision making. This disconnect is, in part, due to the lack of time and opportunity to actually design the experiments and…

This article presents a discussion of mixed methods (MM) sampling techniques. MM sampling involves combining well-established qualitative and quantitative techniques in creative ways to answer research questions posed by MM research designs. Several issues germane to MM sampling are presented including the differences between probability and…

Described herein are formulas and computational procedures for estimating the mean and second through fourth central moments of universe scores through multiple matrix sampling. Additionally, procedures are given for approximating the standard error associated with each estimate. All procedures are applicable when items are scored either…

Designs for sequential sampling procedures that adapt to cumulative information are discussed. A familiar illustration is the play-the-winner rule in which there are two treatments; after a random start, the same treatment is continued as long as each successive subject registers a success. When a failure occurs, the other treatment is used until…

Standard errors of pooled mean estimate in multiple matrix sampling were compared for two procedures. The data were from tests involving items with and without replacement. The two procedures involve the formulations of Madow and Lord, and Novick; the former permits sampling of item, with or without replacement, whereas the latter is to be used…

Researchers often use the analysis of variance to test hypotheses about the means, followed by a multiple comparison technique when the F-test is significant. The technique is this study was developed by Newman (1939) and Keuls (1952). A flaw in the rationale underlying this technique was evaluated to determine whether the flaw is sufficiently…

Behavioral scientists often wish to determine if a sample has been taken from a symmetric population. Similarly, classroom teachers are interested in symmetry if they wish to grade on a "curve." Previously, the sign test, the Wilcoxon test and the t-test have been used to test a hypothesis concerning the symmetry of a distribution of…

A model for multiple choice test-taking behavior is proposed which is different from those presently used for item sampling theory. A new theory is developed, which includes a new concept to facilitate comprehension of item sampling theory, a "number-known" score distribution. A major advantage of the model is that it accommodates data from…

Two potentially useful tests for homogeneity of variance--the jackknife test and the Box test--are described and compared. Recommendations for the use of these techniques and computational examples of each are provided. (Author/JKS)

Investigates implications for finite and known item populations for classical test theory, and the alpha coefficient among items in paper-and-pencil testing. (Author/AG)