In this paper, the notion of Markov move from algebraic statistics is used to analyze the weighted kappa indices in rater agreement problems. In particular, the problem of the maximum kappa and its dependence on the choice of the weighting schemes are discussed. The Markov moves are also used in a simulated annealing algorithm to actually find the configuration of maximum agreement.

The author arrives at a simple rule for ascertaining when a matrix of correlations, with communalities reducing it to minimum rank, cannot be analyzed into factors such that every column of loadings has at least as many zeros as the number of common factors, as required by Thurstone. A more exact but arithmetically tedious rule is also deduced from Ridley Thompson's boundary conditions, and a correction is made to the latter.

An algorithm, using a short cut due to Feldman and Klingler, for the Fisher-Yates exact test is presented: the algorithm is quick, simple and accurate.

Van Breukelen offers a promising method for modeling both response speed and response accuracy. However, the underlying conception of both dependent measures is somewhat flawed, leading the author to conclude that the approach possesses limitations that, under revised assumptions, may not hold. The central misconception, and a set of related misconceptions, is addressed, and it is suggested that this approach holds a good deal of promise for application in the perceptual and cognitive sciences.

Applications of structural equation modeling (SEM) may encounter issues like inadmissible parameter estimates, nonconvergence, or unsatisfactory model fit. We propose a new factor rotation method that reparameterizes the factor correlation matrix in exploratory factor analysis (EFA) such that factors can be either exogenous or endogenous. The proposed method is an oblique rotation method for EFA, but it allows directional structural paths among factors. We thus referred it to as FSP (factor structural paths) rotation. In particular, we can use FSP rotation to “translate” an SEM model to incorporate theoretical expectations on both factor loadings and structural parameters. We illustrate FSP rotation with an empirical example and explore its statistical properties with simulated data. The results include that (1) EFA with FSP rotation tends to fit data better and encounters fewer Heywood cases than SEM does when there are cross-loadings and many small nonzero loadings, (2) FSP rotated parameter estimates are satisfactory for small models, and (3) FSP rotated parameter estimates are more satisfactory for large models when the structural parameter matrices are sparse.

The problem in multiple correlation work of nonsense results attributable to linear dependence of variables, which has been discussed by Ragnar Frisch in relation to economic data, is presented from the standpoint of its significance in psychological research. It is shown that a symmetric correlation determinant with unity in the diagonal cells can vanish only when there is a first-order or partial correlation of unity between one pair of the variables. On the basis of this result, it is argued that the problem should be expected to cause less difficulty in the field of psychology than in economics and that psychologists should be able to avoid the pitfall by bringing to bear their knowledge of the variables with which they are working.

When several criteria are available, it is ordinarily necessary (1) to select one of them as the criterion, (2) to use several and thus arrive at several different sets of weights, or (3) to combine them into a single measure. A formula is derived for the determination of a unique set of weights. The use of these weights will produce the highest possible average coefficient of correlation between the various criteria and two (or more) weighted independent variables. If desired, the criteria may be assigned any predetermined weights. The weights then derived for the independent variables are such that the weighted average of the correlation coefficients between the various criteria and the independent variable composite will be a maximum. In the use of these formulas, no assumptions are necessary regarding the interrelationships existing among the criteria and it is not necessary to compute the intercorrelations among the criteria. A numerical example is included.

Results of an experiment to obtain data on the consistency of the items of two forms of an Activity Preference Blank are presented. Both Form I and Form II, which was a revised edition of Form I, were administered twice, so consistency data are available for both forms. A sub-item is said to be consistent if a high proportion of men marked it the same way, M for preferred Most and L for preferred Least, on both administrations of the test. The data of the experiment were investigated to see what happens to the consistency of sub-items when the items are changed in context, when the number of sub-items in an item is reduced, and when the time-interval between the administration and the re-administration of the test is increased. The author also gives data on the consistency of the responses made to particular combinations of sub-items and data on item consistency when all sub-item combinations are taken into consideration.

When a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable, the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the independent variable. In typical cases, this increased misclassification rate due to sampling is remarkably small relative to other increases in expected measures of prediction accuracy due to samplings that are typically encountered in statistical analysis.

This issue is particularly striking if a polytomous variable predicts a polytomous variable, for the excess misclassification rate due to estimation approaches 0 at an exponential rate as n increases. Even with a continuous real predictor and with simple nonparametric methods, it is typically not difficult to achieve an excess misclassification rate on the order of n−1. Although reduced excess error is normally desirable, it may reasonably be argued that, in the case of classification, the reduction in bias is related to a more fundamental lack of sensitivity of misclassification error to the quality of the prediction. This lack of sensitivity is not an issue if criteria based on probability prediction such as logarithmic penalty or least squares are employed, but the latter measures typically involve more substantial issues of bias. With polytomous predictors, excess expected errors due to sampling are typically of order n−1. For a continuous real predictor, the increase in expected error is typically of order n−2/3.

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for differential equation modeling usually consider data that are atypical of many psychological applications. Using embedded and observed data matrices, a statistical approach to differential equation modeling is presented. This approach appears robust to many characteristics common to psychological time series.

Two types of matching designs, static and dynamic, are differentiated. While all matching designs are logically the same in terms of the probability model which determines chance level of performance, an attempt is made to demonstrate that there is an interaction between the tactics, strategies, and actual knowledge of S and the type of design used which will, in turn, lead to different results even when S's knowledge is held constant. It is suggested that analogous situations may exist within the framework of the traditional psychometric model.

The theoretical probability of misclassification in a mastery test is exactly computed using the raw score probability distribution (in the Rasch model) as a function of the examinee’s latent ability. The resulting misclassification probability curve, together with the latent ability distribution in the group of examinees, completely determines the expected rate of classification errors. It is shown that several distinct ability thresholds, playing different roles in connection to classification reliability, can be associated to a test with a single cut score. In particular, it is possible to define (and compute) two relevant ability intervals, which encapsulate the functioning of a mastery test (about and far from the cut score, respectively); the dependence of these intervals on the item difficulty spectrum is investigated. Extension to the 2PL model is also discussed, with emphasis on the effects of weighted scoring.

A model is proposed to predict the performance on a compound stimulus as a function of the performance on the component stimuli in a two-choice situation. Data from a learning task are used to evaluate the model.

Most indexes of item validity and difficulty vary systematically with changes in the mean and variance of the group. Formulas are presented showing how certain item parameters will vary with these alterations in group mean and variance. Item parameters are also suggested which should remain invariant under such changes. These parameters are developed under two different assumptions: first, the assumption that the total distribution of the item ability variable is normal, and, second, that the distribution of the item ability variable for each array of the explicit selection variable is normal.