Wayne S. Zimmerman

A simple graphical method for orthogonal rotation of axes

A simple method of making orthogonal rotations by projecting coordinates from one plot to another is presented. An easily constructed apparatus for rapid and accurate work is described in detail. By the technique proposed 12 to 15 rotations of pairs of axes involving 20 test variables can be completed per hour by a practiced technician.

Factor analysis of the Army Air Forces Sheppard Field battery of experimental aptitude tests.

A factor analysis was made of 39 experimental printed aptitude tests and seven reference tests selected from the Army Air Forces Aircrew Classification Battery. Thirteen factors were extracted and two independent orthogonal rotational solutions were completed. Twelve factors were interpreted. Of these, seven were clearly identifiable with previously known factors: numerical, perceptual-speed, spatial-relations, visualization, visual-memory, paired-associates-memory, and length-estimation factors. A planning factor was not as clearly identifiable. A reasoning factor was probably a composite of two or more factors that failed to separate. A new factor possibly has to do with orientation with respect to the points of the compass. Two factors were doublets, each apparently specific to one kind of test. Better conceptions were gained of the spatial-relations and visualization factors and of the kinds of tests that measure them best. Efforts to improve measures of unique factors were not uniformly successful. The attempt to duplicate a psychomotor test rather directly by analogy in printed form failed almost completely.

An Investigation of the Nature of the Spatial-Relations and Visualization Factors in Two High School Samples

THE existence of at least two spatial abilities has been shown in several factorial analyses completed by workers in the psychological research units of the AAF (3) and in other analyses reported by Fruchter (i) and by the writers (10, i i, 18). However, in most of these studies samples consisting of adult males have been employed, and some degree of selection has been present. Thus, most samples have consisted of either college students, who in most instances had attained at least a specified minimum score on an aptitude test, or of aviation cadets, who

Hypotheses Concerning the Nature of the Spatial Factors

ature. The trouble really started with the series of factor analyses of Army Air Force tests (under the direct supervision of Dr. L. G. Humphreys) where it was demonstrated repeatedly that there were at least two and possibly three or more factors into which the variance of tests formerly appearing on a single factor could be split (13). The most persistent cleavage appeared to set apart one cluster of tests that involved a manipulative visual-imagery process, quite satisfactorily represented by the label &dquo;Visualization.&dquo; However, the description originally offered by Thurstone (29) for his Primary Mental Abilities Space factor (facility in visual and spatial imagery) seemed to fit this process also. This circumstance forced a reevaluation

The Influence of Item Complexity Upon the Factor Composition of a Spatial Visualization Test

IT has been difficult to construct non-overlapping or pure factor tests in the spatial-visualization domain. Some tests, designed as measures of the spatial relations factor but composed of very easy highly speeded items have correlated substantially with perceptual speed tests. Tests of spatial ability and of visualization have intercorrelated highly among themselves, while some more difficult tests designed to measure visualization have had unusually high correlations with reasoning tests ( I , chapters 7, 12, 16, and 19). On the basis of these findings i t was hypothesized that these four factors lay on a continuum and that each could be measured by a single kind of test simply by varying the item difficulty or complexity ( I , 510). Thus, as items increase in difficulty or complexity they should emphasize perceptual speed, spatial relations, visualization, and reasoning, in that order. Before this hypothesis had been advanced a different form of an AAF experimental test, Visualization of Maneuvers, was administered on three successive month-ends to unclassified aviation students, all of whom earlier in the month had taken the Aviation Cadet Classification Battery tests. Each of the three forms of the experimental test was made up of the same kind of item, but in the more complex forms the items presented additional maneuvers to be visualized, thus requiring more working time per item and yielding more errors per item. It appeared, therefore, that a good opportunity was afforded to evaluate the continuum hypothesis based on factor halyses of three forms. A fairly large group of students in one class, held over until the next month, had been administered two forms of the

A revised orthogonal rotational solution for Thurstone's original primary mental abilities test battery

By extension of the rotational process, meaningful orthogonally related positions were found for all of the thirteen centroid factors which Thurstone extracted from his original PMA intercorrelations. Most of the original primary ability factors were more sharply delineated and corresponded more closely to the Army Air Force factors that bear similar names (demonstrating greater invariance from analysis to analysis). While such different results obtained by two investigators applying the same methods on the same data may initiate some concern, the results strengthen rather than weaken the idea that more psychological meaningfulness and greater invariance will result if centroid axes are rotated, using the concepts of a simple structure and positive manifold.

An Investigation of Two Hypotheses Regarding The Nature of the Spatial-Rlations and Visualization Factors

PRIMARILY as a consequence of the factorial analyses of tests of intellectual abilities, the construct of a spatial and/or visual ability amenable to psychological measurement has received increasing attention in recent years. During the past twentyone years, at least a score of investigators have identified in their writings a space factor. In a pioneer study, Thurstone (16) included among his seven primary mental abilities a fac-

Implications of the Computer for Creativity

anecdote. A former student who received his graduate degree several years ago at a local university spoke recently to the professor who had served as his chairman. He asked this question, &dquo;If I were to submit the same dissertation problem and statistical design today, would it be acceptable?&dquo; The professor answered in the negative, as the questioner was sure he would. The change recognized by both the former student and the professor is the credit given for, or the weight assigned to, time spent in routine compilation and analysis of data, particularly numerical data. The student had spent literally hundreds of man-hours in copying numbers and in performing routine arithmetical and statistical manipulations. A graduate student attacking a similar statistical dissertation problem today may find it to be quite acceptable to assemble raw