An approach for multiple factor analysis of dichotomized variables is presented. It is based on the distribution of the first and second order joint probabilities of the binary scored items. The estimator is based on the generalized least squares principle. Standard errors and a test of the fit of the model is given.

Suppose Pi(i) (i = 1, 2, ..., m, j = 1, 2, ..., n) give the locations of mn points in p-dimensional space. Collectively these may be regarded as m configurations, or scalings, each of n points in p-dimensions. The problem is investigated of translating, rotating, reflecting and scaling the m configurations to minimize the goodness-of-fit criterion Σi=1m Σi=1n Δ2(Pj(i)Gi), where Gi is the centroid of the m points Pi(i) (i = 1, 2, ..., m). The rotated positions of each configuration may be regarded as individual analyses with the centroid configuration representing a consensus, and this relationship with individual scaling analysis is discussed. A computational technique is given, the results of which can be summarized in analysis of variance form. The special case m = 2 corresponds to Classical Procrustes analysis but the choice of criterion that fits each configuration to the common centroid configuration avoids difficulties that arise when one set is fitted to the other, regarded as fixed.

This paper treats the problem of testing an ordered hypothesis based on the ranks of the data. The statistical procedures for the randomized block design with more than one observation per cell are derived. Multiple comparisons and estimation procedures are also included.

A Bayesian Model II approach to the estimation of proportions in m groups (discussed by Novick, Lewis, and Jackson) is extended to obtain posterior marginal distributions for the proportions. It is anticipated that these will be useful in applications (such as Individually Prescribed Instruction) where decisions are to be made separately for each proportion, rather than jointly for the set of proportions. In addition, the approach is extended to allow greater use of prior information than previously and the specification of this prior information is discussed.

A theory of discrimination which assumes that subjects compare psychological values evoked by a stimulus to a subjective referent is proposed. Momentary differences between psychological values for the stimulus and the referent are accumulated over time until one or the other of two response thresholds is first exceeded. The theory is analyzed as a random walk bounded between two absorbing barriers. A general solution to response conditioned expected response times is computed and the important role played by the moment generating function (mgf) for increments to the random walk is examined. From considerations of the mgf it is shown that unlike other random walk models [Stone, 1960; Laming, 1968] the present theory does not imply that response conditioned mean correct and error times must be equal. For two fixed stimuli and a fixed referent it is shown that by controlling values of response thresholds, subjects can produce Receiver Operating Characteristics similar or identical to those predicted by Signal Detection Theory, High Threshold Theory, or Low Threshold Theory.

Link and Heath [1975] have analysed a random walk model for two-choice reaction time on the assumption that the two probability density functions (p.d.f.s) of the step-size, each p.d.f. corresponding to one stimulus, are mirror reflections of each other; and they have demonstrated the critical role played by the symmetry of the moment generating function (m.g.f.) of the step size in the determination of whether or not error and correct reaction times are equal. It is shown here that, given reflection symmetry, m.g.f. symmetry is necessary and sufficient for the random walk model to be equivalent to a sequential probability ratio test.