John T. Pohlmann

Parallel Analysis: a method for determining significant principal components

Numerous ecological studies use Principal Compo- nents Analysis (PCA) for exploratory analysis and data reduc- tion. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven con- sistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigen- values from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illus- trate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis

Use and Interpretation of Factor Analysis in The Journal of Educational Research: 1992-2002

The author reviewed the use and interpretation of factor analysis in articles published in The Journal of Educational Research articles from 1992 to 2002. He found all major forms of factor analysis among the 25 articles that he reviewed. Exploratory factor analysis was the most common application that he found. He noted only 3 applications of confirmatory factor analysis. In general, the author found that the analyses were performed appropriately and the results were presented informatively. In some studies, however, he found that the authors did not provide sufficient information about their analyses for readers to evaluate the results. The author provides a brief introduction to factor analysis history and models, along with an illustration of an exploratory factor analysis. He offers recommendations for the appropriate reporting and interpretation of a factor analysis.

Correlational Meta-Analysis: Independent and Nonindependent Cases

The purpose of this study was to determine the effect of the violation of the assumption of independence when combining correlation coefficients in a meta-analysis. In this Monte Carlo simulation the following four parameters were used with the values specified: N-the sample size within a study (20, 50, 100), p-the number of predictors (1, 2, 3, 5), rho(i)-the population intercorrelation among predictors (0, .3, .7), rho(p)-the population correlation between predictors and criterion (0, .3, .7). When cnly one predictor was used or when the intercorrelation among predictors equaled zero, the assumption of independence was not violated. The assumption of independence was violated when more than one predictor with an intercorrelation exceeding zero were used. Therefore, rho(i) the index of nonindependence was the main parameter of interest. For both rs and Fishers zs, the means, medians, and standard deviations showed no discernible change over levels of rho(i) or p, but the precision of estimation of the expected values improved as N increased. The 90%, 95%, and 99% confidence intervals for both rs and Fishers zs showed no change over levels of rho(i) or p, but the intervals narrowed as N increased.

A Factor Analysis of Raven's Advanced Progressive Matrices Freed of Difficulty Factors

The study presents a factor analysis of the 1962 revision of the Advanced Progressive Matrices (APM). The analysis was conducted such that substantive factor structure interpretations were freed of the effects of differences in item difficulty. The APM test was given to 237 examinees, 16–18 years old. The data were subjected to a Guttman scale analysis to determine whether the APM could be interpreted as a one factor instrument. Then the phi/phi max inter-item correlation matrix was factored. A principal components analysis, followed by a series of varimax rotations of the principal components, was performed. The Guttman coefficients of scalability were too small to support a one factor theory of the APM. The 2-factor solution provided the most interpretable factor structure. Factor I was composed of items in which the solution was obtained by adding or subtracting patterns. Factor II was composed of items in which the solution was based on the ability to perceive the progression of a pattern. Results are discussed in terms of representative cognitive tests and tasks believed to embody the logical operations responsible for successful performance on items loading on each factor. The possibility of forming subtests of items to enhance the predictive validity of the matrices also is discussed.

First and Second Language Reading Comprehension.

Random parallel reading comprehension tests in Japanese and English were administered to a sample of native Japanese students enrolled in intensive English instruction at three different levels of English language proficiency as assessed by an independent measure. Evidence for a threshold competence ceiling at which first language reading abilities transferred to second language reading abilities was found. At the highest proficiency level, those readers who scored high on the first language reading test also systematically scored high on the second language reading test. Pedagogical implications of the study are discussed.

A Factor Analysis of Direct and Indirect Measures of English as a Second Language Writing Ability

This paper reports the results of a study to determine whether an analysis of objective test measures and holistically scored composition data would support a single or a multifactor theory of writing assessment and to determine which category of measure-direct or indirect-was the more reliable. Four experimental objective tests of writing ability based on an information-processing approach were administered to one hundred foreign university students for whom English was not their native language. The subjects also wrote descriptive essays which were holistically graded. The results indicated that the holistic and objective assessments were relatively independent measures of writing ability, indicating support for a two-factor theory of ability assessment. The holistic assessment was found to be more reliable than the objective assessment.

Use of a Simulated MCAT to Predict Real MCAT Scores

A Mock MCA Twas developed and administered to 39 premedical students two weeks prior to the April 1977 administration of the New MCAT. Mock MCAT results were provided to these studentsfor each of the six areas of the actual MCA T. Twenty-seven examinees also took the real MCAT. Correlation coefficients between real and Mock MCA T scores were obtained and stepwise regression analysis was used to determine the extent to which the Mock MCA T could predict real MCA T scores. Correlations of .85, .76, .74, .81, .82, and .81 were obtained for biology, chemistry, physics, science problems, reading, and quantitative areas, respectively.