Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

The gold standard for identifying more effective pedagogical approaches is to perform an experiment. Unfortunately, frequently a hypothesized alternate way of teaching does not yield an improved effect. Given the expense and logistics of each experiment, and the enormous space of potential ways to improve teaching, it would be highly preferable if…

Exploratory factor analysis involves five key decisions. The second decision, how many factors to retain, is the focus of the current paper. Extracting too many or too few factors often leads to devastating effects on study results. The advantages and disadvantages of the most effective and/or most utilized strategies to determine the number of…

Investigated empirically through post mortem item-examinee sampling were the relative merits of two alternative procedures for allocating items to subtests in multiple matrix sampling and the feasibility of using the jackknife in approximating standard errors of estimate. The results indicate clearly that a partially balanced incomplete block…

The effect of stratified sampling of items on the estimation of test score distribution parameters by multiple matrix sampling was studied. Item difficulty and/or interitem correlations were the bases of stratification. Various item iniverses were created by computer simulation and sampled according to several plans. The results indicate that…

A single conceptual and theoretical framework for sampling any configuration of data from one or more population matrices is presented, integrating past designs and discussing implications for more general designs. The theory is based upon a generalization of the generalized symmetric mean approach for single matrix samples. (Author/CTM)

The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)

Distributional characteristics of the measure of sampling adequacy (MSA) were investigated in sample correlation matrices generated from multivariate normal populations with covariance matrix equal to the identity. Systematic variation of sample size and number of variables resulted in minimal fluctuation of the overall MSA from .50. (Author/RC)

Problems of sampling error and accumulated rounding error in canonical variate analysis are discussed. A new technique is presented which appears to be superior to canonical variate analysis when the ratio of variables to sampling units is greater than one to ten. Examples are presented. (Author/JKS)

An alternative derivation of Tryon's basic formula for the coefficient of domain validity or the coefficient of generalizability developed by Cronbach, Rajaratnam, and Glaser is provided. This derivation, which is also the generalized Kuder-Richardson coefficient, requires a relatively minimal number of assumptions compared with that in previously…

Empirical evidence is presented related to the effects of using a stratified sampling of items in multiple matrix sampling on the accuracy of estimates of the population mean. Data were obtained from a sample of 600 high school students for a 36-item mathematics test and a 40-item vocabulary test, both subtests of the Iowa Tests of Educational…

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…

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…