The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Type I error rates were estimated for three tests that compare means by using data from two independent samples: the independent samples t test, Welch's approximate degrees of freedom test, and James's second order test. Type I error rates were estimated for skewed distributions, equal and unequal variances, equal and unequal sample sizes, and a…

A simulation study compared the performance of the Mann-Whitney "U" test, Student's "t" test, and the alternate (separate variance) "t" test for two mutually independent random samples from normal distributions, with both one-tailed and two-tailed alternatives. Type I error probabilities were computed with equal and…

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…

Using computer simulated data, the Type I error rate and statistical power were empirically estimated for several pairwise multiple comparison strategies for situations where population variances differ. Focus was on comparing modified Bonferroni procedures with Dunnett's solutions, and determining whether or not J. P. Shaffer's suggestion of…

A modification of the TUCKALS3 algorithm is proposed that handles three-way arrays of order I x J x K for any I. The reduced work space needed for storing data and increased execution speed make the modified algorithm very suitable for use on personal computers. (SLD)

When one wants to set data reliability standards for a class of scientific inquiries or when one needs to compare and select among many different kinds of data with reliabilities that are crucial to a particular research undertaking, then one needs a single reliability coefficient that is adaptable to all or most situations. Work toward this goal…

The jackknife statistic is discussed as a viable invariance procedure. Data from a study of leadership illustrates the use of the jackknife in determining the stability of canonical function coefficients following canonical correlation analysis. The jackknife procedure entails arbitrarily omitting one observation or a subset of observations at a…

The one-sided problem of comparing treatments with a standard on the basis of data available in the context of a one-way analysis of variance is examined, and the methodology of S. Chakraborti and J. D. Gibbons (1991) is extended to the case of unequal sample sizes. (SLD)

E.J. Bedrick recently derived the asymptotic distribution of the modified sample biserial correlation estimator of F.M. Lord and studied its efficacy for bivariate normal populations. A more detailed examination of the properties of Lord's estimator is provided, and the small sample bias and variance are studied. (SLD)

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)

This Monte Carlo simulation studied the relative power of 8 tests for sphericity in randomized block designs where sample size was small (10, 15, 20, and 30) and population covariance matrices of dimension-to-sample size ratio approached 1.0. The locally best invariant test demonstrated substantial power to detect departures from sphericity. (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…

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…

The mean and variance of the statistic psi-star, which is useful for measuring agreement between two raters and allows for tests of significance in the case of large samples, are considered. Results may also be applied for the "G" index of J. W. Holley and J. P. Guilford (1964). (SLD)