Many bandpass signals can be sampled at rates lower than the Nyquist rate, allowing significant practical advantages. Illustrating this phenomenon after discussing (and proving) Shannon's sampling theorem provides a valuable opportunity for an instructor to reinforce the principle that innovation is possible when students strive to have a complete…

Modeling the population in survey sampling problems continues to be controversial. An important reason is that the likelihood principle makes it somewhat necessary to model the population. Estimating the population total in two-stage survey sampling is considered, making use of a "superpopulation" model. The problem is then really one of…

An Edgeworth approximation for accurate significance probabilities for the Wilcoxon two-sample test is substantially simplified. A method is developed that allows quick calculations of very accurate probabilities. Exact formulas are given for most of the remaining cases, and tables are presented comparing the new simplification to likely…

An approximate statistical test is derived for the hypothesis that the intraclass reliability coefficients associated with two measurement procedures are equal. Control of Type 1 error is investigated by comparing empirical sampling distributions of the test statistic with its derived theoretical distribution. A numerical illustration is…

Statistical significance is often misinterpreted to mean replicability or generalizability of results, although a statistically significant difference does not equal a reliable difference. Sample splitting procedures may be a more accurate way of estimating research result generalizability. This type of cross-validation involves randomly dividing…

L-scaling is introduced as a technique for determining the weights in weighted averages or scaled scores for T joint observations on K variables. The technique is so named because of its formal resemblance to the Leontief matrix of mathematical economics. L-scaling is compared to several widely-used procedures for data reduction, and the…

Some recent methods are presented for analyzing categorical data from complex surveys involving clustering familiar in educational research. Methods that provide first-order corrections to standard multinomial-based chi-square tests by taking into account survey design effects are highlighted. Design-based calculation techniques guarantee that the…

Whether it is possible to develop a classification function that identifies the underlying range restriction from sample information alone was investigated in a simulation. Results indicate that such a function is possible. The procedure was found to be relatively accurate, robust, and powerful. (SLD)

The empirical Bayes modeling approach--latent ability random sampling in the item response theory (IRT) context--to the IRT modeling of psychological tests is described. Under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test.…

The asymptotic sampling distributions (means and variances) are presented for the signed and unsigned estimates for the Rasch model, two-parameter model, and the three-parameter model with fixed lower asymptotes. Applications for item-bias research are discussed. (SLD)

A Monte Carlo simulation explored how to optimize power in the extreme groups strategy when sampling from nonnormal distributions. Results show that the optimum percent for the extreme group selection was approximately the same for all population shapes, except the extremely platykurtic (uniform) distribution. (SLD)

Use of linear combinations of Fisher's "z" transformations as a combined test for the common correlation parameter based on "k" independent sample correlations has been previously studied. This article considers additional "z" additive properties and methods of combining independent studies when planning the number of…

A distribution theory is derived for a G. V. Glass-type (1976) estimator of effect size from studies involving paired comparisons. The possibility of combining effect sizes from studies involving a mixture of related and unrelated samples is also explored. Resulting estimates are illustrated using data from previous psychiatric research. (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…

Recently, C. E. McCulloch (1987) suggested a modification of the Morgan-Pitman test for comparing the variances of two dependent groups. This paper demonstrates that there are situations where the procedure is not robust. A subsample approach, similar to the Box-Scheffe test, and the Sandvik-Olsson procedure are also assessed. (TJH)