Factor pattern of test items and tests as a function of the correlation coefficient: Content,difficulty, and constant error factors

A dilemma was created for factor analysts by Ferguson (Psychometrika, 1941,6, 323–329) when he demonstrated that test items or sub-tests of varying difficulty will yield a correlation matrix of rank greater than 1, even though the material from which the items or sub-tests are drawn is homogeneous, although homogeneity of such material had been defined operationally by factor analysts as having a correlation matrix of rank 1. This dilemma has been resolved as a case of ambiguity, which lay in (1) failure to specify whether homogeneity was to apply to content, difficulty, or both, and (2) failure to state explicitly the kind of correlation to be used in obtaining the matrix. It is demonstrated that (1) if the material but (2) if content is homogeneous but difficulty is not, the homogeneity of the content can be demonstrated only by using the tetrachoric correlation coefficient in deriving the matrix; and that the use of the phi-coefficient (Pearsonianr) will disclose only the nonhomogeneity of the difficulty and lead to a series ofconstant error factors as contrasted withcontent factors. Since varying difficulty of items (and possibly of sub-tests) is desirable as well as practically unavoidable, it is recommended that all factor analysis problems be carried out with tetrachoric correlations. While no one would want to obtain the constant error factors by factor analysis (difficulty being more easily obtained by counting passes), their importance for test construction is pointed out.     

The concept of test and item reliability in relation to factor pattern

It is shown that approaches other than the internal consistency method of estimating test reliability are either less satisfactory or lead to the same general results. The commonly attendant assumption of a single factor throughout the test items is challenged, however. The consideration of a test made up ofK sub-tests each composed of a different orthogonal factor disclosed that the assumption of a single factor produced an erroneous estimate of reliability with a ratio of (n–K)/(n–1) to the correct estimate. Special difficulties arising from this error in application of current techniques to short tests or to test batteries are discussed. Application of this same multi-factor concept to item-analysis discloses similar difficulties in that field. The item-test coefficient approaches 1/K as an upper limit rather than 1.00 and approaches 1/n as a lower limit rather than .00. This latter finding accounts for an over-estimation error in the Kuder-Richardson formula (8). A new method of isolating sub-tests based upon the item-test coefficient is proposed and tentatively outlined. Either this new method or a complete factor analysis is regarded as the only proper approach to the problem of test reliability, and the item-sub-est coefficient is similarly recommended as the proper approach for item analysis.     

Test anxiety and reaction time for matching decisions

Subjects selected by test-anxiety level were presented pairs of words and asked to make judgments of physical identity, acoustic matching, or taxonomic category membership. Experiment 1 varied type of judgment between subjects; in Experiments 2 and 3, each subject made all three decisions. There was no consistent support for the hypothesis that, relative to low-anxiety subjects, high-anxiety subjects would show a more pronounced decrement in reaction times for semantic decisions than for nonsemantic decisions.     

Test selection with integral gross score weights

A new method of test selection, which attempts to combine the merits of the ToopsL-Method with those of the Wherry-Doolittle Method, is presented. It results in integral (unit if desired) positive and/or negative (optional) weights. This flexibility makes the method applicable to all kinds of material and for both selecting items for tests and tests for batteries. An explicit solution of one test construction problem is presented. Necessary changes in method for the solution of five other types of test construction problem are presented. A few cautions are provided for potential users.     

The relation of multiserial eta to other measures of correlation

Ordinary product-moment correlation and regression methods are frequently not immediately applicable to qualitative data, whereas multiserialr, point-multiserialr, and multiserial eta can be easily applied. The multiserialr is rejected for prediction since it tells us only what the correlationmight be if certain assumptionswere true and if wecould measure what isnot now measured. The point-multiserialr and multiserial eta are identical when the number of categories is two but differ when it is three or greater. The multiserial eta is identical with the product-momentr when categories are assigned scale values equal to their means on the continuous variable. With three or more categories, the point-multiserialr, whichassumes linearity withequal step intervals, is always lower than the multiserial eta, whichforces linearity by adoption ofunequal step intervals based upon difference in criterion attainment. While the multiserial eta expends one degree of freedom with the weighting of each category, this is known and correctable, whereas the vague partial loss of degrees of freedom due to the ordering of categories in the point-multiserial is not correctable.Personnel Research Section, A.G.O.     

Clergy Who Experience Trauma as a Result of Forced Termination

Forced termination of clergy is a demeaning and psychologically distressing experience. Clergy who experience a forced termination are subjected to mobbing (psychological harassment) and other activities meant to publicly or privately demean a minister in such a way that they resign their ministry position. In a purposive convenience sample of 55 ministers who had been forcibly terminated, participants scored above the known cut-off score for post-traumatic stress disorder (PTSD) and scored high on a measure of burnout and generalized anxiety disorder (GAD). Forced termination has been anecdotally connected to PTSD and GAD, this project sought to empirically link PTSD and GAD to the forced termination of clergy. This study raises concern for the long-term mental health effects of ministers who have been forcibly terminated and provides implications for future clinical study on this group of clergy. Findings in this research indicate there may be a process to forced termination, which could be developed into a theory on forced termination of clergy.     

A new iterative method for correcting erroneous communality estimates in factor analysis

A new method for correcting erroneous communality estimates is applicable to any completed orthogonal factor solution. It seeks, by direct correction of factor loadings, to make the residuals conform to the chance error criteria of zero mean and zero skewness for each row separately. Two numerical examples, with one and two factors, respectively, are presented. The method can be used as a short cut for Dwyer's extension in adding variables to a matrix. It can also be used as a short cut in cross-validation factor studies. Successful use on problems with many variables and numerous factors is claimed. Factors can be made oblique,after correction, if desired.     

CPQ personality factors of upper elementary gifted students

The results of administering the Children's Personality Questionnaire (CPQ) to gifted students in the fourth, fifth, and sixth grades indicated that they had personality profiles similar to the norm group. Gifted males were more controlled, socially precise, self-disciplined, and compulsive than females, described as more casual and careless of social rules. Also, gifted females were more assertive and independent than males who had scores suggesting a more obedient, mild, or conforming personality. In comparing personality factors across grades, fourth graders had profiles significantly different from sixth graders.