Corrected item-test correlations

Previous papers on this subject derive the correlation between an item and the remainder of the test. This correlation is unsatisfactory because the reliability of the remainder varies inversely with the reliability of the item omitted. The present paper derives the correlation between an item and the total test, with that item replaced by a rationally equivalent item. The general formula is then modified, for dichotomus items, to give the corrected point-biserial, biserial, and Brogden biserial correlations. The results apply strictly only to factorially homogeneous tests: those in which the same trait or combination of traits is measured (apart from error) by every item.     

CTTITEM: SAS macro and SPSS syntax for classical item analysis

This article describes the functions of a SAS macro and an SPSS syntax that produce common statistics for conventional item analysis including Cronbach’s alpha, item difficulty index (p-value or item mean), and item discrimination indices (D-index, point biserial and biserial correlations for dichotomous items and item-total correlation for polytomous items). These programs represent an improvement over the existing SAS and SPSS item analysis routines in terms of completeness and user-friendliness. To promote routine evaluations of item qualities in instrument development of any scale, the programs are available at no charge for interested users. The program codes along with a brief user’s manual that contains instructions and examples are downloadable from suen.ed.psu.edu/~pwlei/plei.htm.     

Note on the computation of biserial correlations in item analysis

A rapid method is described for machine computation of biserial correlations in item analysis with several criteria. This method has been found to yield biserial correlations from punched IBM cards at the rate of about 41 per hour.     

Correction of item-total correlations in item analysis

The biserial correlation between an item and the total test of which the item is a part tends to be misleadingly high when used in item analysis, since the item is included in the total test. Two formulas with correction for this overlap are derived and compared with Zubin's and Guilford's formulas. One of the new coefficients is invariant to test length.     

Some relations between guttman's principal components of scale analysis and other psychometric theory

Guttman's principal components for the weighting system are the item scoring weights that maximize the generalized Kuder-Richardson reliability coefficient. The principal component for any item is effectively the same as the factor loading of the item divided by the item standard deviation, the factor loadings being obtained from an ordinary factor analysis of the item intercorrelation matrix.     

Characteristics of items in the Eysenck Personality Inventory which affect responses when students simulate

A large sample of students completed Form A of the Eysenck Personality Inventory, and four subgroups were later asked to simulate extraversion, introversion, neuroticism or stability. It was found that subjects could simulate these four personalities successfully. The changes in individual item responses were correlated with the items' factor loadings, validity, response bias, and detectability. The different scales and types of item were considered separately. In some cases the changes in item responses when simulating introversion and extraversion were related to the extraversion validities and factor loadings of the items. More often, however, the behaviour of items under simulation was correlated with aspects of the items that made them more like an item from another scale and thus lessened their susceptibility to a particular type of simulation.     

A note on the computation of biserialr in item validation

A method of computing biserial coefficients of correlation through the use of punch card tabulating equipment is presented. Each item is assigned a separate column and successes are punched 1. By arranging the cards on the criterion variable and obtaining progressive sums on several columns simultaneously, it is possible to obtain data for several correlations in one run of the cards through the machine.     

COMMENTS ON FACTORING DICHOTOMOUS SCORE MATRICES

The fact that the Holley-Guilford G index is a mean cross product between individuals has two implications. First, standard procedures are available for the estimation of R factor loadings. Second, the factor space contains a factor of means. This factor is not unique when item polarities are arbitrary. The factor structure in such cases is a result of both qualitative and quantitative interindividual similarity.     

Modelling non‐normal data: The relationship between the skew‐normal factor model and the quadratic factor model

Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew‐normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew‐normal factor are equivalent to those under a quadratic model up to third‐order moments. The reverse only holds if the quadratic loadings are equal to each other and within certain bounds. We illustrate that observed data which follow any skew‐normal factor model can be so well approximated with the quadratic factor model that the models are empirically indistinguishable, and that the reverse does not hold in general. The choice between the two models to account for deviations of normality is illustrated by an empirical example from clinical psychology.     

Factor analytic study of the Piers-Harris Children's Self-Concept Scale

A factor analysis of the Piers-Harris Self-Concept Scale was conducted with a biracial u sample of children over a wide age range. The Scale was completed by 348 10-17 year old students in a rural community. Seven factors of 10 had sufficient item loadings to be interpretable. Six matched those found in the manual and an additional factor was found relating to Aggression. Race, sex, and age relationships are also reported for these seven factors.     

A confirmatory factor analysis of the Bem Sex Role Inventory: Old questions,new answers

LISREL analyses of data from a sample of 671 adults (90% Caucasian, 10% Black) evaluated (a) item factor structure of the Bem Sex Role Inventory (BSRI), (b) second-order factor model for the item factors, and (c) structural equation models estimating age and gender differences in these factors. Seven first-order item factors were extracted and found to have equivalent factor loadings for males and females. Item factors were related to two second-order factors: Masculinity and Femininity. There were relatively small age and gender differences in the first- and second-order factors. There was a differential relationship between self-rated masculinity and femininity and the first-order BSRI item factors for males and females. Results suggest that the BSRI best assesses gender-related personality traits and represents only one component of the complex multidimensional construct of gender roles.We thank Herbert W. Marsh and an anonymous reviewer for valuable comments on previous drafts of this article.     

Age and gender invariance of self‐concept factor structure: An investigation of a newly developed Chinese self‐concept instrument

A new instrument, the Chinese Adolescent Self‐Esteem Scales (CASES), was developed to measure the self‐concepts of the young people in Hong Kong in seven aspects: social, academic, appearance, moral, family, physical/sport, and general self‐esteem. LISREL procedures were utilized to test the extent of factorial invariance for age and gender based on the responses to CASES of 551 Hong Kong adolescents. It was found that CASES possesses the necessary invariance properties for between‐group measurement in terms of the number and pattern of the underlying factors, item factor loadings, and inter‐factor relations, but not in terms of item uniqueness. Implications of these findings are discussed in terms of the use of CASES and of empirical support for the equivalence of self‐concept factor structure for age and gender groups for both Western and non‐Western adolescents.     

A New Explanation and Proof of the Paradoxical Scoring Results in Multidimensional Item Response Models

In multidimensional item response models, paradoxical scoring effects can arise, wherein correct answers are penalized and incorrect answers are rewarded. For the most prominent class of IRT models, the class of linearly compensatory models, a general derivation of paradoxical scoring effects based on the geometry of item discrimination vectors is given, which furthermore corrects an error in an established theorem on paradoxical results. This approach highlights the very counterintuitive way in which item discrimination parameters (and also factor loadings) have to be interpreted in terms of their influence on the latent ability estimate. It is proven that, despite the error in the original proof, the key result concerning the existence of paradoxical effects remains true—although the actual relation to the item parameters is shown to be a more complicated function than previous results suggested. The new proof enables further insights into the actual mathematical causation of the paradox and generalizes the findings within the class of linearly compensatory models.     

The difficulty of a test and its factor composition

A factor analysis of the ten sub-tests of the Seashore test of pitch discrimination revealed that more than one ability is involved. One factor, which accounted for the greater share of the variances, had loadings that decreased systematically with increasing difficulty. A second factor had strongest loadings among the more difficult items, particularly those with frequency differences of 2 to 5 cycles per second. A third had strongest loadings at differences of 5 to 12 cycles per second. No explanation for the three factors is apparent, but the hypothesis is accepted that they represent distinct abilities. In tests so homogeneous as to content and form, where a single common factor might well have been expected, the appearance of additional common factors emphasizes the importance of considering the difficulty level of test items, both in the attempt to interpret new factors and in the practice of testing. The same kind of item may measure different abilities according as it is easy or difficult for the individuals to whom it is applied.     

Psychometric evaluation of the outcome based performance measures

The Outcome Based Performance Measures are widely used to evaluate and accredit organizations providing services to persons with disabilities. This study evaluated the interrater reliability, levels of difficulty for items, and factor groupings of this measure with 448 Nevadans with mental retardation. Results supported the measure's reliability and most of the items' levels of difficulty. Factor analysis yielded seven factors with item loadings that varied moderately from prior reports, tending to coincide with the original measure's logically-based groupings. Revisions to the measure are suggested.     

Instrumental and expressive representations of aggression: One scale or two?

The Expagg questionnaire was developed to measure a subject's view of their own aggression as a relatively instrumental or relatively expressive act. Two issues have been raised pertaining to the dimensional structure of the questionnaire: the use of principal components analysis on dichotomous responses and the possibility that instrumental and expressive representations might be independent dimensions rather than opposite ends of a single continuum. In study 1, dichotomous Expagg data from 405 subjects were subjected to microfact, principal components, and factor analysis. Each produced a first general factor, and the correlations between the item loadings were in excess of r = .99. In study 2, a 40‐item Likert scale version of Expagg was given to 295 subjects. Principal components analysis, paired item correlations, and subscale correlations suggested partial independence of instrumental and expressive items. Two new 8‐item scales measuring instrumental and expressive representations were constructed that maximise their independence. Potential uses of these revised scales are discussed. Aggr. Behav. 25:435–444, 1999. © 1999 Wiley‐Liss, Inc.     

THE EFFECT OF PERFORMANCE TIME AND RETESTING UPON THE FACTOR STRUCTURE OF INTELLIGENCE TESTS

Changes in the factor structure of intelligence tests between early and later stages of performance and between testing and retesting were studied. In addition to factor analyses, correlations between the test scores of various time periods and the final factor scores were computed. The principal findings were the powerful influence of the verbal ability in the initial stages of most tests, the gradual 'purification' of the factors, and the occurrence of a shift of the highest factor loadings of some tests from one factor to another, particularly in tests with increasing item difficulty.     

Spanish adaptation of the scale of psychological empowerment in the workplace

The objective of this study is to adapt and translate into Spanish Spreitzer's Psychological Empowerment Scale (1995a). A process of translation and reverse-translation was applied to the scale's items, whose psychometric properties were then examined using a sample of 272 professional nurses at public hospitals in the province of Seville. The data were subjected to confirmatory factor analysis. The significance of the factor loadings demonstrated the need to create a new model eliminating one item. The 11-item model was shown to possess adequate construct validity and internal consistency. The results confirm the original, four-factor structure obtained by Spreitzer, with the exception of item 10, and support the utilization of the Spanish version of this scale in the workplace. Future research should more extensively investigate its construct validity, and test the nomological network of the operationalized construct within the field of psychological well-being and in the context of the workplace.