It is argued that many investigators utilize the Tucker and Messick (1963) Model with no intention of looking for individual differences or, after utilizing the model, draw improper inferences. An example is given illustrating the difficulties which result from improper use of the model. Several proper methods are outlined. (Author)

A new basic algorithm is discussed that may be used to do factor analysis by any of these three methods: (1) unweighted least squares, (2) generalized least squares, or (3) maximum likelihood. (CK)

The stepped-up reliability coefficient does not have the same standard error as an ordinary correlation coefficient. Fisher's Z -transformation should not be applied to it. Appropriate procedures are suggested. (Author)

A theory that there is a correspondence between Piagetian conservation operations and groups of symmetry transformations, and that these symmetry transformations may be used in explaining human problem solving behaviors, is developed in this paper. Current research in artificial intelligence is briefly reviewed, then details of the symmetry…

Given multiple independent measures of an underlying true factor and information on group membership, it is possible to compute a set of observed group means for each measure. Given at least three tests, these sets of means may be used to compute the reliability of the means for each test. The procedure for estimating true scores from the…

The contention that interpretation of a student's performance on a criterion referenced test should be independent of the performance of his classmates is challenged. The Mastery Learning Test Model, which was developed for analyzing criterion referenced test data, is described. An estimate of the proportion of students in an instructional group…

Training programs for data processing personnel are plagued by the rapid turnover of the technology involved. An attempt was made to provide a self-paced training plan for a large, data processing staff. Factor analyses of questionnaires about the skills and tasks involved divided the population into specialization groups. Within the…

Bounds for the tails of Dirichlet integrals are established by showing that each integral as a function of the limits is a Schur function. In particular, it is shown how these bounds apply to the simultaneous analysis of variance test and to the multinomial distribution. (Author)

Results of a comparative study of F and Q tests, in a randomized block design with one replication per cell, are presented. In addition to these two procedures, a multivariate test was also considered. The model and test statistics, data generation and parameter selection, results, summary and conclusions are presented. Ten tables contain the…

The mathematical derivation of the statistics used for inference in some linear models assumes that values of the independent variables are pre-selected such that these variables can be treated as fixed rather than random variables. This assumption is often disregarded when these models are utilized in research. This study is an investigation of…

There are at least two situations in which the behavioral scientist wishes to transform uniformly distributed data into normally distributed data: (1) In studies of sampling distributions where uniformly distributed pseudo-random numbers are generated by a computer but normally distributed numbers are desired; and (2) In measurement applications…

Computational formulae for the following three tests of significance, useful in the interrupted time series design, are given: (1) a "t" test (Mood, 1950) for the significance of the first post-change observation from a value predicted by a linear fit of the pre-change observations; (2) an "F" test (Walker and Lev, 1953) of the…

In a pilot study of college students' understanding of mathematical induction, the author asked 2,320 students and 152 faculty members to determine whether eight statements were true or false. The difficulty of the statements was analyzed for subgroups of the population. (SD)

Presents two models for statistically analyzing occupational mobility. The models show how the destination distribution is shifted for each shift of one or more steps on the scale of occupational origins. (Author/AV)

The controversy surrounding regression methods for unbalanced factorial designs is addressed. The statistical hypotheses being tested under the various methods, as well as salient issues in the use of these methods, are discussed. The use of statistical computer packages is also discussed. (Author/JKS)