Analysis of variance (ANOVA) was invented in the 1920s to partition variance of a single dependent variable into uncorrelated parts. Having uncorrelated parts makes the computations involved in ANOVA incredibly easier. This was important before computers were invented, when calculations were all done by hand, and also were done repeatedly to check…

Analysis of variance (ANOVA) is a frequently used statistical procedure in education and the social sciences. Very often the use of ANOVA involves situations with unequal cell sizes. When confronted with data to analyze from an unbalanced design, the researcher should select very carefully from the method or option in the statistical package being…

Analyses of data are presented to illustrate the advantages of using a priori or planned comparisons rather than omnibus analysis of variance (ANOVA) tests followed by post hoc or posteriori testing. The two types of planned comparisons considered are planned orthogonal non-trend coding contrasts and orthogonal polynomial or trend contrast coding.…

The validity conditions for univariate repeated measures designs are described. Attention is focused on the sphericity (equality of variance) requirement. It is recommended that separate rather than pooled error term procedures be routinely used to test a priori hypotheses. (Author/JKS)

H. Levene (1960) proposed a heuristic test for heteroscedasticity in the case of a balanced two-way layout, based on analysis of variance of absolute residuals. Conditions under which design imbalance affects the test's characteristics are identified, and a simple correction involving leverage is proposed. (SLD)

Research in the behavioral and health sciences frequently involves the application of one-factor analysis of variance models. The goal may be to compare several independent groups of subjects on a quantitative dependent variable or to compare measurements made on a single group of subjects on different occasions or under different conditions. In…

Factorial analyses differ from nonfactorial analyses in that in the former all possible hypotheses (all possible main effects and interaction effects) are tested regardless of their substantive interest to the researcher and their interpretability, while in the latter, only substantive and interpretable hypotheses are tested. This paper shows the…

Three analyses of pretest and posttest data are considered: (1) posttest only designs; (2) two-way repeated measures of analysis of variance (ANOVA); and (3) one-way analysis of covariance (ANCOVA). Conditions that ensure legitimacy of inferences about the equality of treatment effects on the latent variable theta are discussed. (SLD)

Simulations demonstrate the effects of correlated errors on the person-by-occasion design in which the confounding effect of equal time intervals results in correlated error terms in the linear model. Two specific error correlation structures were examined. Conditions under which underestimation and overestimation occur are discussed. (SLD)

Basic principles underlying statistical power are examined; and issues pertaining to effect size, sample size, error variance, and significance level are highlighted via the use of specific hypothetical examples. Analysis of variance (ANOVA) and related methods remain popular, although other procedures sometimes have more statistical power against…

This article reviews some of the less well-known hypothesis tests for variance, how they are employed, and how the results may be interpreted. Tests include testing for a single variance and the T-test for correlated variances. (CT)

By employing a concomitant variable, block designs and analysis of covariance (ANCOVA) can be used to improve the power of traditional analysis of variance (ANOVA) by reducing error. If subjects are randomly assigned to treatments without considering the concomitant variable, an experiment uses a post-hoc approach. Otherwise, an a priori approach…

The use of analysis of variance was examined under the assumption that the treatment had been randomly assigned to students, when in fact, the class had been the unit. Data support the idea that if one can randomly assign treatments to intact classes, consideration should certainly be given to doing so. (Author/GK)

The value of variance is emphasized, and the element of design, frequently not adequately understood, is clarified to underscore the importance of variance to the researcher. Two analytic methods, analysis of variance (ANOVA) and multiple regression, are discussed in terms of how each uses/applies variance. Advantages and major difficulties with…

This article focuses on steps in conducting empirical-analytic research and the problems of controlling for or estimating three sources of error: the amount of measurement error, research design error, and the amount of statistical or sampling error. (Author/CT)