A Fisher's Z transformation is developed for the corrected correlation for conditions when the criterion data are missing because of selection on the predictor and when the criterion was missing at random, not because of selection. The two Z transformations were evaluated in a computer simulation and found accurate. (SLD)

The topic of centers of similarity can be treated synthetically or analytically. While the synthetic method is more practiced, the analytic approach is more appropriate when the problem is given in an analytic geometry setting. In this article, two non-congruent squares ABCD and A'B'C'D' are given, where A(0,0), B(3,0), C(3,3), D(0,3) and A'(5,4),…

An interpretation of the transformation formulas for rotations in a plane in terms of the exponential function is given. Addition of two rotations is shown to correspond to the multiplication of the two corresponding matrices. (Author/LS)

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)

In this article, new arguments and empirical evidence are presented justifying the use of Standardized R - analysis (or equivalently Q - technique) in certain types of factor-analytic studies. The standardized R - analysis analyses the intercorrelations among respondents based on their "ipsative" scores, as opposed to the unstandardized…

Curves are considered to have the same shape when they are related by a similarity transformation of a certain kind. This paper extends earlier work on parallel curves to curves with the same shape. Some examples are given more or less explicitly. A generalization is used to show that the theory is ordinal and to show how the theory may be applied…

The research contained in this report is directed at the problem of assessing structures of knowledge in science. Toward this end graduate as well as undergraduate students were asked to make judgments of the perceived similarity of expressions that mark or label concepts in the subject matter of physics. An apriori model of the structure of…

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)

The good and bad points of Euclidean geometry and transformation geometry are briefly surveyed with emphasis on the teachability of Euclidean geometry and the mathematics of transformation geometry. (MN)

A multiple time series is defined as the sum of an autoregressive process on a line and independent Gaussian white noise or a hyperplane that goes through the origin and intersects the line at a single point. This process is a multiple autoregressive time series in which the regression matrices satisfy suitable conditions. For a related article…

The use of the arc-sine transformation in analysis of variance can lead to difficult inference situations and pose problems in interpretation. It can also produce tests of noticeably lower power when the null hypothesis is false, and is not recommended as a standard tool. Simulated illustrations are provided. (Author/GDC)

Illustrated is how students can be directed to move from a geometric to an algebraic mode of thought and back again in linear algebra, thereby deepening their understanding. Rotations and line reflections in the plane are used as the example. (MNS)