. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. 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 consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues 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 illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.

The present review was designed to apply the Schmidt and Hunter meta-analysis procedures to the available literature on Fiedler's Contingency Theory of Leadership. In the present instance, this involved the quantification of the variance in correlations between leader style and performance that can be explained by sampling error. To the extent that the variance in these results across studies can be explained by sampling error, moderator variables, including situational favorability, would be unnecessary theoretical constructions. To the extent that the variance in study results cannot be explained by sampling error, the possibility of one or more moderators exists. Separate meta-analyses were conducted for those studies that led to the specification of the Contingency Theory and those conducted specifically to test the theory. Results suggested that the Contingency Theory was appropriately induced from the studies on which it was based. With regard to those studies conducted specifically to test the Contingency Theory, however, less supportive evidence resulted. Although the theory was supported for all octants except Octant II within the lab data set, only four of the eight octants produced supportive evidence within the field data set. In these instances, the evidence suggests that additional variables need to be specified to account more fully for the variance within those octants that cannot be explained by sampling error alone. Peters, Department of Administrative Sciences, Southern actenzed, on the basis of their scores on the

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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 r's and Fisher's z's, 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 r's and Fisher's z's showed no change over levels of rho( i) or p, but the intervals narrowed as N increased.

This study examined the relationship between selected class characteristics and student ratings of instructors. A large number of classes (N = 1247)and students (over 33,000) a t a large Midwestern University provided the data for this study. The results indicated that the class characteristics that had the strongest influence on the results of instructor ratings were the grades expected by students and the percentage of students in the class taking the course as an elective.