John Schmid

The development of hierarchical factor solutions

Although simple structure has proved to be a valuable principle for rotation of axes in factor analysis, an oblique factor solution often tends to confound the resulting interpretation. A model is presented here which transforms the oblique factor solution so as to preserve simple structure and, in addition, to provide orthogonal reference axes. Furthermore, this model makes explicit the hierarchical ordering of factors above the first-order domain.

Some Modifications of the Multiple-Choice Item:

concept so that the student has an articulated and meaningtul task to perform. Generally a test writer can refine or improve an item by incorporating better ideas into the item or by changing the diction in the statement of the ideas. In doing this he may exercise considerable ingenuity in the development of keys and directions in order that higher mental processes rather than mere memoriter learnings may be tested. For example, the key-true, probably true, insufficient data, probably false, false-may require a rather high level of judgment. In some cases the complaint has been registered, with reason, that understanding of the directions is more difficult than working the test items. Such variations and refinements, however, have produced genuinely better items and have extended the scope of the educational outcomes measurable by such items; nevertheless, such items have basic limitations which make it desirable to extend our exploration of item types. Multiple-choice items may be divided roughly into two classes: first, those in which the stem states a problem which involves recall of an answer or one which involves a reasoning process which, correctly employed, leads directly to the an-

The Effect of Writing Frequency upon Essay-Type Writing Proficiency at the College Level

FACULTY OF American colleges continually raise questions about methods for improving the written expression of college students. At Michigan State College, considerable evidence in the form of corres pondence, term papers, book reports, and other essay type composit ion indicated that students had not acquired the proficiency in the writ ing skills expected of them. This study was initiated as one of several to provide further information on the problem. Required training in writing skills by Michigan State College studen ts consists of one three -hour course in communication skills for three quarters. Not more than one-third of that time is devoted to written expression ? or the equivalent of one quarters work. It may be that this amount of training is not sufficient to produce the desired improv ement in all students deficient in writing abilities. That more writing experiences are at least a partial answer to this problem, is supported by the experience at Purdue University where the amount of writing in a composition class was doubled. (The normal amount was about equ al to the amount done by Michigan State College students during the three quarters of their course. ) Doubling the amount of writing done

Some Factors in Job Satisfaction: A Comparison of Three Methods of Analysis

MOTIVATION has generally proved to be harder to assess than knowledge and aptitude. Yet evidence is accruing that motivational factors are important in job performance, so that measures of motivation are needed. One way of assessing job motivation is to find out how well satisfied a man is with his job. This study reports on the Job Satisfaction Inventory, which is a pencil and paper test designed to measure Air Force mechanics’ expressed degree of satisfaction with their work. The problem for analysis is how generalized such satisfaction (or dissatisfaction) may be. For example, if a mechanic is satisfied

Further Application of the Principles of Direct Rotation in Factor Analysis

Essentially, factor analysis presents a statistical method of summarizing a matrix of intercorrelations in such a way as to describe each of the variables in terms of a limited num ber of assumed factors. An important end product of the analysis, therefore, is a set of linear equations describing each of the variables in terms of the assumed factors. This set of equations, which may be regarded as multiple regression equations, will be called a factor pattern, following Holzinger. 1 The analysis of a correlation matrix, with communalities in the diagonals, may be made in terms of either correlated or uncorrelated common factors. The latter solution is called an orthogonal one, and is illustrated by such well-known types of solution as the bi-factor, the centroid, and the principal-factor solution. A solution in terms of correlated common factors is called an ob lique solution. It is this type of solution that Thurstone emphasizes in his recent text. 2 The procedure for computing an oblique sol ution that has been followed most commonly is that of first calculating an orthogonal solution, such as the centroid, and then rotating this in itial orthogonal solution to the desired oblique solution. In such a procedure the calculation of the initial orthogonal solution serves prim arily as a method of estimating the number of common factors, or minimum rank of the given correlation matrix, R, and of determining the communalities. Any initial solution that yields the same number of common factors and the same communalities would serve equally well as this intermediate stage in developing the de sired oblique solution. It, therefore, is evident that the initial orthogonal solution might be re placed by an initial oblique solution in this pro cedure. This opens the possibility of combin ing certain earlier developments in factor meth od to yield a modified procedure for arriving at the desired oblique solution. Holzinger has shown explicitly that the de sired oblique solution with m common factors may be calculated quite simply if the variables whose correlations make up the matrix can be grouped into exactly m distinct clusters. 3 This method is essentially one of sectioning the cor relation matrix into groups of variables of ap proximate unit rank, and then passing axes through these groups, or clusters. The com putation provides for determining the correla tion of each variable with each of these axes (the structure matrix, S) and the intercorrela tions, , of the axes or factors. 4 As Holzinger shows, the oblique pattern, P, is given by:

Relating Factor Traits of Elementary, Secondary, and College Teachers

Factor analytic studies of teacher characteristics at the elementary, secondary, and college educational levels were restudied by relating the factors with a numerical-analytic methodology. The professional and personal characteristics found at all levels were an in formed systematic presenter of the course curricular materials and a sympathetic and fair-minded individual toward the learner.

A comparison of two procedures for calculating discriminant function coefficients

Alternative procedures for calculating discriminant function coefficients have been illustrated in reported research. One method proceeds from data which has been expressed in deviation score units, whereas the other method implies that the data has been expressed in standard units. It is shown algebraically that both procedures yield identical discriminant function coefficients, and therefore, the method involving less mathematical manipulation and computation is preferable.Alternative procedures for calculating discriminant function coefficients have been illustrated in reported research. One method proceeds from data which has been expressed in deviation score units, whereas the other method implies that the data has been expressed in standard units. It is shown algebraically that both procedures yield identical discriminant function coefficients, and therefore, the method involving less mathematical manipulation and computation is preferable.

Reduction of Error by Matching Subjects in the Two-Group Experimental Design.

McNemar’s discussion of error reduction in a mixed two-group design fails to provide an algebraic presentation of this error reduction. This manuscript presents not only the algebraic development of the error term but shows that under certain conditions mixing may increase experimental error.