In analyzing exploratory repeated measures data with more than two measures, two competing tests must be administered simultaneously if one is to make an efficient and effective decision regarding the tenability of the null hypothesis of no differences among measurement means. Obviously, such a procedure is not without a cost vis-a-vis Type I…

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

A recurring problem in educational research is how to account for non-random selection that has restricted the range of the variables of interest in correlational analyses. Several expressions due to H. Pearson (1903) and presented in matrix notation by D. N. Lawley (1943-44) are commonly used in selection settings to adjust for samples chosen on…

This repeated measures factorial design study compared the results of two procedures for identifying multivariate outliers under varying conditions, the Mahalanobis distance and the Andrews-Pregibon statistic. Results were analyzed for the total number of outliers identified and number of false outliers identified. Simulated data were limited to…

Canonical correlation analysis is a powerful statistical method subsuming other parametric significance tests as special cases, and which can often best honor the complex reality to which most researchers wish to generalize. However, it has been suggested that the canonical correlation coefficient is positively biased. A Monte Carlo study…

This study investigated the distributional properties of the standardized residual that is commonly used in the Rasch model calibration program to develop various indices of item and person fit. The power of the standardized residual to detect measurement disturbances is also addressed. (TJH)

This study investigates parameter estimation under the simple linear regression model for situations in which the underlying assumptions of ordinary least squares estimation are untenable. Classical nonparametric estimation methods are directly compared against some robust estimation methods for conditions in which varying degrees of outliers are…

Traditionally, the errors-in-variables problem is concerned with the point estimation of the slope of the true scores regression line when the regressor is measured with error, and when no specification error is present. In this paper, the errors-in-variables problem is extended to include specification error. Least squares procedures provide a…

This paper examined the rank transformation approach to analysis of variance as a solution to the Behrens-Fisher problem. Using simulation methodology four parameters were manipulated for the two group design: (1) ratio of population variances; (2) distribution form; (3) sample size and (4) population mean difference. The results indicated that…

Item parameter estimation errors in test development are highlighted. The problem is illustrated with several simulated data sets, and a conservative solution is offered for addressing the problem in item response theory test development practice. Steps that reduce the problem of capitalizing on chance in item selections are suggested. (SLD)

Errors in item parameter estimates have a negative impact on the accuracy of item and test information functions. The estimation errors may be random, but because items with higher levels of discriminating power are more likely to be selected for a test, and these items are most apt to contain positive errors, the result is that item information…

Standard errors and bias of unidimensional and multidimensional ability estimates were compared in a factorial, simulation design with two item response theory (IRT) approaches, two levels of test correlation (0.42 and 0.63), two sample sizes (500 and 1,000), and a hierarchical test content structure. Bias and standard errors of subtest scores…

This study examined how four commonly used test equating procedures (linear, equipercentile, Rasch Model, and three-parameter) would respond to situations in which the properties or the two tests being equated were different. Data for two tests plus an external anchor test were generated from a three parameter model in which mean test differences…

With the help of widely available microcomputers, it is possible to demonstrate certain statistical phenomena which students of statistics are usually expected to take on faith. Two demonstrations are described. In the first demonstration, three common types of sampling (simple random, biased, and stratified-random) are used to compare statistics…

The use of stepwise regression has been criticized for both interpretive misunderstandings and statistical aberrations. A major statistical problem with stepwise regression and other procedures that involve multiple significance tests is the inflation of the Type I error rate. General approaches to control the family-wise error rate such as the…