Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity…

Large-scale experiments that involve nested structures may assign treatment conditions either to subgroups such as classrooms or to individuals such as students within subgroups. Key aspects of the design of such experiments include knowledge of the variance structure in higher levels and the sample sizes necessary to reach sufficient power to…

Field experiments with nested structures assign entire groups such as schools to treatment and control conditions. Key aspects of such cluster randomized experiments include knowledge of the intraclass correlation structure and the sample sizes necessary to achieve adequate power to detect the treatment effect. The units at each level of the…

This study examined the percentage of task-sampling variability in performance assessment via a meta-analysis. In total, 50 studies containing 130 independent data sets were analyzed. Overall results indicate that the percentage of variance for (a) differential difficulty of task was roughly 12% and (b) examinee's differential performance of the…

Bechhofer's procedure for selecting the population with the largest mean from among several populations with known variances is discussed as it applies to the problem of selecting the bivariate normal population with the largest correlation coefficient. Tables of appropriate sample sizes are provided and an example is discussed. (Author/JKS)

The nature of the approximate chi-square test for hypotheses concerning multinomial probabilities is reviewed. Also, a BASIC computer program for calculating the sample size necessary to control for both Type I and Type II errors in chi-square tests for hypotheses concerning multinomial probabilities is described.

Examined Type I error rates and power for four tests for treatment control studies in which a larger treatment mean may be accompanied by a larger treatment variance and examined these aspects of the independent samples "t" test and the Welch test. Evaluated each test and suggested conditions for the use of each approach. (SLD)

Some sampling characteristics of three estimators of the intraclass correlation were investigated under a variety of conditions within the context of a one-way analysis of variance. The results promote caution in the use of all three estimators. The three estimators differed very little in their bias or in their standard errors. (Author/JKS)

A concise table is presented based on a general measure of magnitude of effect which allows direct determinations of statistical power over a practical range of values and alpha levels. The table also facilitates the setting of the research sample size needed to provide a given degree of power. (Author/CM)