The three most commonly used statistics, the arithmetic mean, variance, and the product-moment correlation, are most unfortunate choices when data are not strictly Gaussian. A new measure of correlation and a measure of scale are proposed which are substantially more robust than their least squares counterparts. An illustration shows how increased robustness can be obtained through the use of equal regression weights without severe loss in accuracy. The paper also shows how incorporating knowledge about the theoretical structure of the regression coefficients into their estimation can aid substantially in increasing their robustness.

Orthogonal rotation of canonical variates is shown to preserve the major properties of the canonical solution and may increase its interpretability.

Interactive Scaling with Individual Subjects (ISIS) developed by Young & Cliff [1972], is a method involving interaction between subject and computer in real time to determine which judgments made by the subject are critical to the definition of a dimensional structure. The procedure is based on the mathematical fact that it is possible to define a space of R dimensions in terms of only the interpoint distances between all stimuli being scaled and a subset of (R +1) of these stimuli. For errorless judgments, any subset of (R + 1) stimuli is appropriate. However, fallible data require that the subset consist of stimuli that are maximally dissimilar, and the ISIS procedure is designed to obtain such an optimum subset (a “basis”).

This research evaluates a modified version of ISIS with respect to (a) a metric MDS analysis based on all possible pairs of the stimuli, and (b) a metric MDS analysis based on a subset of one-third of the possible pairs, or about the same number as that required by ISIS. Results show that the ISIS method achieves better fit than (b) at low error levels, and may also achieve better fit than (b) at higher error levels if the size of the basis is increased. The more stimuli in the basis the more indices of fit approach those of (a).

A new method of introducing error in MDS studies is used in the evaluation.

The kind of mastery score problem often encountered in educational and psychological testing may be roughly described as follows: given that a certain unit of instruction must be mastered by a subject, a test is administered at the end of this unit and, on the basis of the observed score or an estimate of the true score, a decision is made about the grant of the mastery status. If the subject is declared master of the unit, he will be allowed to proceed to the next unit of instruction. Otherwise, remedial work will be given. Given relevant consequences of misclassification, the problem is to determine an optimum decision rule.

A numerical procedure is outlined for obtaining an interval estimate of the regression of true score on observed score. Only the frequency distribution of observed scores is needed for this. The procedure assumes that the conditional distribution of observed scores for fixed true score is binomial. The procedure is applied to several sets of test data.

A large class of rank tests, which includes the familiar sign test and the Wilcoxon signed-ranks test, is described and discussed. This class of distribution-free tests provides a flexible basis for testing research hypotheses of various forms. Exact small sample and approximate large sample procedures are considered. Applications of these procedures are presented, including simple numerical examples.

By applying a general procedure for analyzing a correlation coefficient into components, the lens model equation is extended to a) analyze the effects of different types of variation and b) analyze the relations between judgmental systems that are not based on the same set of cues.

The utility of the jackknife for constructing confidence intervals and testing hypotheses about the disattenuated correlation is evaluated for small samples. Computer simulations were used to generate the empirical sampling distributions of jackknife statistics for two sample sizes (30, 60), five values of the disattenuated correlation coefficient (1.00, .90, .80, .50, .00) and three pairs of reliabilities (.90, .80; .80, .80; .90, .50). The theoretical and cumulative proportions of jackknife statistics were compared at selected points in the appropriate t-distributions. The results obtained support the claim that the jackknife can be used to construct sensible confidence intervals. However, the jackknife possesses limited utility for testing hypotheses about the disattenuated correlation coefficient.

A direct proof is given for the generalized Spearman-Brown formula for any real multiple of test length.