Multivariate group comparisons of variable systems: MANOVA and structural equation modeling.

Multivariate analysis of variance (MANOVA) and structural equation modeling (SEM) are compared as alternative approaches to the detection of multivariate mean differences in between-groups designs. MANOVA remains the most commonly implemented multivariate test of between-groups mean differences. When the set of outcome variables reflects a latent-variable system rather than an emergent-variable system, however, SEM provides an elegant alternative to MANOVA. Three generic types of latent-variable systems were considered. In the simplest case, SEM and MANOVA led to very similar substantive interpretations. In the 2 more complex variable systems, SEM provided parameter estimates and collateral information that was at least as informative as those provided by MANOVA. Researchers are encouraged to consider more carefully the nature of their variable systems before choosing too casually MANOVA over SEM. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

What to do with significant multivariate effects in multivariate analyses of variance.

Significant multivariate tests in the multivariate analysis of variance are often followed by analyses of the contributions of individual dependent variables to those significant effects. There has been little agreement, however, as to which specific analyses should be performed. The use of the 2 most common techniques, analysis of variance for each dependent variable and discriminant analysis, are discussed and then illustrated in a computer study. It is suggested that the purpose of the user should determine the technique chosen as the 2 methods are not alternative approaches to the same problem. Analysis of variance can be used for hypothesis testing of individual variables and is appropriate for research. The value of discriminant analysis is in prediction and classification, although it can indicate complex relationships between measures in hypothesis testing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multivariate analysis and the problem of Type I error.

Discusses the recommendation by M. R. Leary and E. M. Altmaier (see record 1981-02539-001) that MANOVA should be used with several dependent variables in order to control for overall Type I error rate. This paper calls attention to limitations and dangers in routine application of MANOVA, describes some alternative procedures, and laments the necessarily pervasive character of the problem of statistical error. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Reexamination of a plea for multivariate analyses.

Re-examines 2 issues raised in an article by M. R. Leary and E. M. Altmaier (see record 1981-02539-001) proposing MANOVA as a solution to the problem of inflated Type I error. Guidelines are discussed for choosing an overall MANOVA test statistic and post hoc tests that determine the dependent variable or variables responsible for any significant effects. It is concluded that guidelines based on recent comparisons of the various test statistics be used by researchers rather than advice found in basic textbooks. A discussion of the power of MANOVA concludes that although MANOVA may under some conditions reduce the chances of detecting significance, it is powerful for detecting legitimate experimental effects that are spread across more than one dependent variable. (37 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How the power of MANOVA can both increase and decrease as a function of the intercorrelations among the dependent variables.

This article directly addresses explicit contradictions in the literature regarding the relation between the power of multivariate analysis of variance (MANOVA) and the intercorrelations among the dependent variables. Artificial data sets, as well as analytical methods, revealed that (1) power increases as correlations between dependent variables with large consistent effect sizes (that are in the same direction) move from near 1.0 toward –2.0, (2) power increases as correlations become more positive or more negative between dependent variables that have very different effect sizes (i.e., one large and one negligible), and (3) power increases as correlations between dependent variables with negligible effect sizes shift from positive to negative (assuming that there are dependent variables with large effect sizes still in the design). Implications for the reliability of dependent variables and strategies for selecting these variables in MANOVA designs are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Between-subjects expectancy theory research: A statistical review of studies predicting effort and performance.

A large number of between-Ss expectancy theory studies have correlated measures of employee motivation (force) to perform with measures of effort and performance. The results of these studies vary considerably. A statistical review of the studies was conducted to determine the extent to which the variance explained (the dependent variable) was a function of various characteristics of the effort and performance and of the force-to-perform measures (the independent variables). There were 160 observations, derived from 32 studies. With the use of multiple regression analysis it was found that variance explained in these studies was greater when (a) self-report or quantitative measures of effort and performance were used rather than evaluations of these variables by someone other than the S; (b) 10–25 outcomes were included in the force measure rather than a greater or smaller number of outcomes; (c) outcome valence was numerically scaled with positive numbers only, and the scale values were described in terms of desirability rather than importance; and (d) the force measure contained either no assessment of expectancy or an assessment that confounded expectancy and instrumentality. These variables accounted for 42% of the variance in the results obtained in the studies reviewed. (31 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Enhancing a sense of agency through career planning.

Tested the effectiveness of a program for parents to help their adolescent sons and daughters develop a greater sense of agency regarding a career. In a pretest–posttest control group design involving 39 families in the experimental group and 25 families in a wait-listed control group, a multivariate analysis of variance (MANOVA) with repeated measures was used to test improvement on 6 variables concerned with career and a sense of agency. The MANOVA yielded a significant effect for groups over time. ANOVA with repeated measures showed that 4 of 6 univariate tests were also significant. Through career planning with a parent, adolescents in Grade 12 showed a greater career certainty, less indecision, more career salience, and stronger ego identity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Parents as agents of career development.

This study tested the effectiveness of a program for parents to help their adolescent children in career planning. In a pretest–posttest control group design involving 20 families in the experimental group and 20 families as a wait-listed control group, a multivariate analysis of variance (MANOVA) was used to test improvement on five variables concerned with parent–child relations and career development. The MANOVA yielded a significant effect for groups over time. Using an analysis of variance (ANOVA) with repeated measures, four of five univariate tests were also significant. In addition, all parents and six adolescents were interviewed after the program to gain a qualitative assessment of program effectiveness. Interview data tended to support the varied degrees of improvement that the adolescents showed on the quantitative measures. It was concluded that parents can function effectively in fostering the career development of their children, when provided with a structured program that they can follow. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Another look at ANCOVA versus blocking.

Compared methods of incorporating a concomitant variable into an experimental design. A 3?×?3 conceptual framework for these methods was developed, with one dimension representing 3 methods of assignment to treatment groups and the other dimension representing 3 methods of data analysis. Monte Carlo procedures were used to investigate the relative statistical power and apparent imprecision of the 9 methods. Results show that the recommendation of most experimental design texts to consider the correlation between the dependent and concomitant variables in choosing the best technique for utilizing a concomitant variable is incorrect. Instead, the 2 factors that should be considered are whether scores on the concomitant variable are available for all Ss prior to assigning any Ss to treatment conditions and whether the relationship of the dependent and concomitant variables is linear. (32 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A new tabulation of statistical procedures used in APA journals.

Tabulated articles in the American Psychological Association journals from 1964 to 1972 to show the types of statistical procedures used. Analysis of variance (ANOVA) consistently increased in frequency of use and by 1972, 71% of all articles using statistical inference used ANOVA. Although simple 1-way ANOVA was sometimes used, 88% of the ANOVA articles employed repeated measures or factorial designs. It is recommended that these techniques as well as simple 1-way ANOVA be taught in introductory statistics courses for psychology students. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Using a repeated measures ANOVA to analyze the data from a pretest-posttest design: A potentially confusing task.

The pretest-posttest control group design (or an extension of it) is a highly prestigious experimental design. A popular analytic strategy involves subjecting the data provided by this design to a repeated measures analysis of variance (ANOVA). Unfortunately, the statistical results yielded by this type of analysis can easily be misinterpreted, since the score model underlying the analysis is not correct. Examples from recently published articles are used to demonstrate that this statistical procedure has led to (a) incorrect statements regarding treatment effects, (b) completely redundant reanalyses of the same data, and (c) problems with respect to post hoc investigations. 2 alternative strategies-gain scores and covariance-are discussed and compared. (19 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Response variable hypotheses in the multivariate analysis of variance.

Es using multivariate analysis of variance (MANOVA) usually want to analyze effects separately for each response variable after rejecting a null hypothesis of multivariate dispersion. From the standpoint of the multivariate general linear model, 4 measures of importance for response variables are discussed: univariate F statistic for each response, standardized canonical coefficient for each response, contribution to the MANOVA test criterion by each response, and simultaneous confidence intervals on estimates of treatment effects on each response. Artificial data are presented to illustrate problems in using these measures. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Variability across sources of performance ratings: Further evidence.

33 1st-yr graduate students (aged 21–55 yrs) completed a simulated counseling interview. Self-, peer, and supervisor ratings were obtained for the simulated interviews using 7 measures of counseling performance. A multiple analysis of variance (MANOVA) indicated statistically significant differences among self-, peer, and supervisor ratings. Analyses also showed significant differences on 4 of the 7 dependent measures. Implications for training are discussed. (23 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A power primer.

One possible reason for the continued neglect of statistical power analysis in research in the behavioral sciences is the inaccessibility of or difficulty with the standard material. A convenient, although not comprehensive, presentation of required sample sizes is provided. Effect-size indexes and conventional values for these are given for operationally defined small, medium, and large effects. The sample sizes necessary for .80 power to detect effects at these levels are tabled for 8 standard statistical tests: (1) the difference between independent means, (2) the significance of a product–moment correlation, (3) the difference between independent rs, (4) the sign test, (5) the difference between independent proportions, (6) chi-square tests for goodness of fit and contingency tables, (7) 1-way analysis of variance (ANOVA), and (8) the significance of a multiple or multiple partial correlation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bivariate median splits and spurious statistical significance.

Despite pleas from methodologists, researchers often continue to dichotomize continuous predictor variables. The primary argument against this practice has been that it underestimates the strength of relationships and reduces statistical power. Although this argument is correct for relationships involving a single predictor, a different problem can arise when multiple predictors are involved. Specifically, dichotomizing 2 continuous independent variables can lead to false statistical significance. As a result, the typical justification for using a median split as long as results continue to be statistically significant is invalid, because such results may in fact be spurious. Thus, researchers who dichotomize multiple continuous predictor variables not only may lose power to detect true predictor–criterion relationships in some situations but also may dramatically increase the probability of Type I errors in other situations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A critical analysis of the Hardiness Scale's validity and utility.

Prior research has suggested that hardiness buffers the effects of stressful life events. This prior research also contains several shortcomings, including (a) little evidence that hardiness does in fact have a buffering effect; (b) the failure of a previous factor analysis of the hardiness subscales to reproduce the three dimensions of hardiness; (c) the measurement of hardiness with negative indicators that may tap general maladjustment; and (d) the frequent use of inappropriate statistical techniques. We conducted this study to address these shortcomings. First, although we were able to replicate the main effects for hardiness found in previous retrospective studies when the data were analyzed by an analysis of variance (ANOVA) we found no buffering effects. Second, a factor analysis of the hardiness subscales revealed two factors. The loadings of subscales on these factors were not consistent with the conceptualization of hardiness. Third, we found statistically significant correlations (p?     

Canonical correlation analysis: A general parametric significance-testing system.

Suggests that significance tests for 9 of the most common statistical procedures (simple correlation, t test for independent samples, multiple regression analysis, 1-way ANOVA, factorial ANOVA, analysis of covariance, t test for correlated samples, discriminant analysis, and chi-square test of independence) can all be treated as special cases of the test of the null hypothesis in canonical correlation analysis for 2 sets of variables. (15 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Dependent variable reliability and the power of significance tests.

Assuming that the linear models for classical test theory and ANOVA hold simultaneously for some dependent variable, it is shown that 2 contradictory statements concerning the relationship between reliability and statistical power are both correct. J. E. Overall and J. A. Woodward (see PA, Vol 53:8623, 57:7284) showed that when the reliability of a difference or change score is zero, the power of a statistical test of a hypothesis of no change can be at a maximum. J. L. Fleiss (see record 1977-07259-001) found the opposite result (i.e., that the power of a statistical test of no pre–post change is at a maximum when the reliability of the difference or gain scores is equal to one). The role of the reliability of the dependent variable in statistical evaluations of controlled experiments is examined. It is argued that the conditions that yield high reliability coefficients are not necessarily optimal for significance testing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Interviewer perceptions of applicant qualifications: A multivariate field study of demographic characteristics and nonverbal cues.

Eight interviewers' perceptions of 517 applicants (mean age 16.7 yrs) for seasonal employment at a large amusement park were studied by obtaining their ratings of personal style variables, body movements, speech characteristics, and a final judgment on overall qualifications. Analysis of nonverbal clues showed the relative importance of speech characteristics (articulation, proper pauses) and unimportance of personal appearance variables (cleanliness, clothing) when these variables were simultaneously considered. MANOVA and MANCOVA showed a relationship between the race and sex of the applicant, sex of the interviewer, and nonverbal cues. A unique variance for these demographic variables was demonstrated even after education background data and nonverbal cues were controlled. It is concluded that communication skills are primary influences on judgment of qualifications when considered simultaneously with other nonverbal cues and that demographic differences are systematically related to these nonverbal cues and judgments of qualifications. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Validity generalization in the context of situational models.

A primary objective of validity generalization (VG) analysis is to decompose the between-situation variance in validities into (1) variance attributable to between-situation differences in statistical artifacts and (2) variance attributable to between-situation differences in (unidentified) situational moderators. This process is based on the assumption that the effects of statistical artifacts on validities are independent of the effects of situational moderators on validities. The present article seeks to question the independence assumption by theoretically integrating situational variables into the VG estimation process. It is shown that the independence assumption may be untenable because at least 1 artifact (criterion reliability) is a function of, rather than independent of, the situational variables that moderate validities. An alternative approach to VG analysis is recommended. This approach rests heavily on proactive research designs in which potential situational moderators are included in the generalizability analysis. (PsycINFO Database Record (c) 2010 APA, all rights reserved)