Self-efficacy and mathematics anxiety have been identified as predictors of mathematics achievement. In the present study, secondary analyses on matrix summaries available from prior published studies were utilized to investigate the contribution that self-efficacy and mathematics anxiety made in mathematics performance. Commonality analyses were…

Correlation matrices and standard deviations are the building blocks of many of the commonly conducted analyses in published research, and AERA and APA reporting standards recommend their inclusion when reporting research results. The authors argue that the inclusion of correlation/covariance matrices, standard deviations, and means can enhance…

An overview of several statistics useful in interpreting variates constructed by using canonical correlation analysis is presented. A computer program which calculates coefficients not typically provided by computer packages is discussed. An illustrative example of the output is provided. (Author/JKS)

Conventional canonical methods distinguish between the two variable sets being analyzed, but the methods do not attempt to optimize the variance from a given variable set that will be contained in the final solution. In this respect canonical methods are said the be "symmetric." This paper proposes two non-symmetric, canonical-like…

Virtually all parametric statistical procedures have been shown to be special cases of canonical correlation analysis, which is a useful research methodology particularly when augmented by the calculation of canonical structure, index, and invariance coefficients. A logic for conducting stepwise canonical correlation analysis based upon evaluation…

The calculation of second-order results in the validity assessment of measures and some useful interpretation aids are presented. First-order and second-order results give different and informative pictures of data dynamics. Several aspects of good practice in interpretation of second-order results are presented using data from 487 subjects…

In the present study Monte Carlo methods were employed to evaluate the degree to which canonical function and structure coefficients may be differentially sensitive to sampling error. Sampling error influences were investigated across variations in variable and sample (n) sizes, and across variations in average within-set correlation sizes and in…

The author contends that model misspecification can occur even after researchers have selected the generally most appropriate class of methods, or general linear model techniques. It is suggested specifically that canonical correlation analysis may provide more meaningful results, as compared with regression, particularly if analysis is augmented…

Virtually all parametric statistical procedures have been shown to be special cases of canonical correlation analysis. This article proposes a logic for conducting stepwise canonical correlation analyses, based upon evaluation of canonical communality coefficients. The procedure is a direct analogue of stepwise multiple regression. (Author/RD)

Canonical correlation analysis is a powerful statistical method subsuming other parametric significance tests as special cases, and which can often best honor the complex reality to which most researchers wish to generalize. However, it has been suggested that the canonical correlation coefficient is positively biased. A Monte Carlo study…

Canonical correlation analysis is a sophisticated multivariate technique that subsumes all parametric methods (the "t"-test, analysis of variance, analysis of covariance, multivariate analysis of variance, multivariate analysis of covariance, and discriminant analysis) as special cases. This bibliography lists 83 applications of…

Hypothetical data sets are used to demonstrate how canonical correlation methods subsume other commonly utilized parametric methods. Analysis of variance, analysis of covariance, multiple analysis of variance, and multiple analysis of covariance are heavily used by educational researchers. It is concluded that researchers would do well to consider…

Effect sizes have been increasingly emphasized in research as more researchers have recognized that: (1) all parametric analyses (t-tests, analyses of variance, etc.) are correlational; (2) effect sizes have played an important role in meta-analytic work; and (3) statistical significance testing is limited in its capacity to inform scientific…