Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. This article describes a framework for robust estimation and testing that uses trimmed means with an approximate degrees of…

The problem of selecting (from several bionomial populations) the one with the highest probability is discussed in this brief article. Several approximate solutions are offered and the solution is extended to bivariate correlation. (Author/JKS)

In many situations in education and psychology it is desired to select from k binomial populations the one having the largest probability of success. This paper describes a two-stage procedure for accomplishing this goal. (Author/CTM)

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

When comparing k normal populations an investigator might want to know the probability that the population with the largest population mean will have the largest sample mean. This paper describes and illustrates methods of approximating this probability when the variances are unknown and possibly unequal. (Author/BW)

A formal framework is presented for determining which of the distractors of multiple-choice test items has a small probability of being chosen by a typical examinee. The framework is based on a procedure similar to an indifference zone formulation of a ranking and election problem. (Author/BW)

The classical estimate of a binomial probability function is to estimate its mean in the usual manner and to substitute the results in the appropriate expression. Two alternative estimation procedures are described and examined. Emphasis is given to the single administration estimate of the mastery test reliability. (Author/CTM)

When comparing examinees to a control group or person, the examiner usually does not know the probability of correct classification based on the number of items used and the number of people tested. Using ranking and selection techniques, a framework is described for deriving a lower bound on this probability. (Author/JKS)

Several Bayesian approaches to the simultaneous estimation of the means of k binomial populations are discussed. This has particular applicability to criterion-referenced or mastery testing. (Author/JKS)

Two stage multiple-comparison procedures give an exact solution to problems of power and Type I errors, but require equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes. (Author/BW)

The problem of determining which of several populations has the largest mean is considered. The procedure described by Dudewicz and Dalal is extended to the case of unequal sample sizes. (JKS)

Wilcox has described three probability models which characterize a single test item in terms of a population of examinees (ED 156 718). This note indicates indicates that similar models can be derived which characterize a single examinee in terms of an item domain. A numerical illustration is given. (Author/JKS)

A mastery test is frequently described as follows: an examinee responds to n dichotomously scored test items. Depending upon the examinee's observed (number correct) score, a mastery decision is made and the examinee is advanced to the next level of instruction. Otherwise, a nonmastery decision is made and the examinee is given remedial work. This…

Three separate papers are included in this report. The first describes a two-stage procedure for choosing from among several instructional programs the one which maximizes the probability of passing the test. The second gives the exact sample sizes required to determine whether a squared multiple correlation coefficient is above or below a known…

A problem of considerable importance in certain educational settings is determining how many items to include on a mastery test. Applying ranking and selection procedures, a solution is given which includes as a special case all existing single-stage, non-Bayesian solutions based on a strong true-score model. (Author/JKS)