An equation was derived to determine the relationship between the pooled within-subgroup r (correlation coefficient) and the r obtained from the total group data. It was, thus, possible to assess the amount of distortion introduced by pooling heterogeneous subgroups. As a basis for deciding whether to pool two subgroups in order to calculate a…

Rooted binary trees with weighted nodes are structures encountered in many areas, such as coding theory, searching and sorting, information storage and retrieval. The path length is a meaningful quantity which gives indications about the expected time of a search or the length of a code, for example. In this paper, two sharp bounds for the total…

The teacher's guide for the second unit of this SMSG series covers the two chapters in Unit 2 of the student text on algorithms and flow charts and on problem formulation. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed,…

A set of mathematical consistencies that forms conditions of inequality in a theorem is summarized, and a strategy for its application with real data is presented. The theorem and strategy are suggested for immediate use by the practitioner seeking cause-effect relationships in a system of variables to cut down guess work and time in analysis and…

In this report four models are formulated which forecast the enrollment and financial needs of students in higher education. The four models are: the undergraduate enrollment model, postbaccalaureate enrollment model, undergraduate student aid model, and postbaccalaureate student aid model. In addition to computing total financial needs, these…

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…