Growth curve models are a useful tool for developmentalists because they can estimate an attribute's developmental function by providing a mathematical description of growth on an attribute over time. However, selection of a growth curve model appropriate for estimating individual developmental functions is problematic. The ideal model is the one…

Formulas for estimating the population measure of effect strength are based on the assumption that sample sizes are proportional to the sizes of their respective treatment populations. Because this assumption is frequently violated, a general method of estimating effect strength for the one-factor, fixed-effects design is presented. (Author/BW)

A methodology for determining the optimal number of observations to use in a measurement design when resource constraints are imposed is presented. Two- and three-facet designs are outlined. Parallel closed form formulae can easily be determined for other designs. (TJH)

The routine epsilon approximate test in repeated measures designs when the condition of circularity is unfulfilled uses an erroneous formula in the case of two or more groups. Because this may lead to underestimation of the deviation from circularity when the subject number is small, a correction is proposed. (Author/SLD)

In a complex sampling scheme it is desirable to select the primary sampling units (PSUs) without replacement to prevent duplications in the sample. Since the estimation of the sampling variances is more complicated when the PSUs are selected without replacement, L. Kish (1965) recommends that the variance be calculated using the formulas…

A general framework for conducting generalizability analyses is presented. Generalizability theory is extended to situations in which the objects of measurement are not persons but other factors, such as instructional objectives, stages of learning, and treatments. (Author/PN)

A generalized variance criterion is used for sequential sampling in the two-parameter item response theory model. Some principles are offered to enable the researcher to select the best sampling design for efficient estimation of item parameters. Topics include the choice of an optimality criterion, two-stage designs, and sequential designs. (SLD)

A study on sampling errors of variance components was conducted within the framework of generalizability theory by P. L. Smith (1978). The study used an intuitive approach for solving the problem of how to allocate the number of conditions to different facets in order to produce the most stable estimate of the universe score variance. Optimization…

Some approximate formulas are presented for standard errors of estimated regression coefficients in two-level designs. If the researcher can make a reasonable guess as to parameters occurring in the model, this approximation can be a guide to the choice of sample sizes at either level. (SLD)

Current omnibus procedures for the analysis of interaction effects in repeated measures designs which contain a grouping variable are known to be nonrobust to violations of multisample sphericity, particularly when group sizes are unequal. An alternative approach is to formulate a comprehensive set of contrasts on the data which probe the specific…

This report describes a statistically designed experiment that was carried out in an operational setting to determine the contributions of different sources of variation to the unreliability of scoring. The experiment made novel use of partially balanced incomplete block designs that facilitated the unbiased estimation of certain main effects…

The accuracy of trait estimates obtained from three vertical equating methods was examined. The procedures studied included two anchor test designs and a single-group design. Data from two content areas and two grade combinations were studied. A three-parameter logistic model was used to perform the equatings. The results obtained were used to…

A method is proposed for calculating the sample size needed to achieve acceptable statistical power with a given test. The minimally important difference significant (MIDS) criterion for sample size is explained and supported with recommendations for determining sample size. The MIDS criterion is computationally simple and easy to explain. (SLD)

An equating design in which two groups of examinees from slightly different populations are administered a different test form with a subset of common items is widely used. This paper presents standard errors and a simulation that verifies the equation for large samples for an equipercentile equating procedure for this design. (Author/BS)

Regression to the mean (RTM) is often misunderstood. It is demonstrated that artifactual RTM depends fundamentally on the magnitude of measurement error at pretest. Adjustment usually involves estimating the measurement error and determining consequences, but even without adjustment, effects of RTM can be ameliorated. (SLD)