This paper is concerned with methods for analyzing quantitative, non-categorical profile data, e.g., a battery of tests given to individuals in one or more groups. It is assumed that the variables have a multinormal distribution with an arbitrary variance-covariance matrix. Approximate procedures based on classical analysis of variance are presented, including an adjustment to the degrees of freedom resulting in conservative F tests. These can be applied to the case where the variance-covariance matrices differ from group to group. In addition, exact generalized multivariate analysis methods are discussed. Examples are given illustrating both techniques.

Domain sampling principles permit formulation of a general method of multidimensional analysis. Cluster and factor analysis methods are special cases stemming from decisions made at different stages of the general method, especially in defining an independent dimension. Key cluster analyses define a dimension as a selection of s variables drawn from the full n set. Centroid, principal axes, and maximum likelihood analyses define it by the n variables (raw or residual, weighted or unweighted); bifactor and second-order analysis, by both types of selection; square root analysis, by one variable. Key cluster methods can be designed to test hypotheses.

The usual least squares estimate of the transitional probability matrix of a finite Markov process is given for the case in which, for each point in time, only the proportions of the sample in each state are known. The purpose of this paper is to give another estimate of this matrix and to investigate the properties of this estimate. It is shown that this estimate is consistent and asymptotically more efficient than the previously considered estimate in a sense defined in this paper.

The Estes model for spontaneous recovery and regression is modified by relaxing the assumption that within-experiment stimulus fluctuation can be treated as negligible in the general case. The augmented model allows description of stimulus fluctuation both between and within experimental periods. Application of the model to mock experimental situations illustrates some of its properties.

This paper presents a model of individual choice behavior for application to experimental situations in which a subject is required to compare utility intervals (differences in subjective value). This model is contrasted with a weaker model, which is also derived. Both models generate ordered metric scales, but differ in predictive power. An experiment on the utility of grades, which provides a test and comparison of the models, is presented.

A modification of the Gram-Schmidt process yields an easily constructed orthogonal transformation matrix which may be used to rotate a centroid, principal axis, or maximum likelihood factor matrix in a manner such that one of the new axes has predetermined direction. The procedure is illustrated by rotating a centroid factor matrix into an abbreviated bifactor matrix, the general factor being defined as the centroid of a specified subgroup of reasoning tests.

The K-R (21) formula can be derived without recourse to the undesirable assumption that the test items are all indistinguishable.

Two nomographs are presented for estimating item validity indices identical in value to those obtained from Flanagan 's table and to those obtained from Davis' chart. Experience has shown that the use of the nomographs results in the saving of a significant amount of time with no loss in accuracy. The nomographs also provide a method of quick conversion between the familiar coefficients and the Davis indices, which are less familiar but which offer greater flexibility.