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Chapter 6 provides a description of one-way and two-way Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) statistical procedures. The chapter includes a presentation on the basic statistics that inform one-way ANOVA (i.e., the mean and the variance), components of the ANOVA summary table, estimation procedures, required assumptions, planned and post-hoc comparisons, and examples of the use of one-way ANOVA in social work research. Building on this, the next section provides an explanation of two-way ANOVA, including main and interaction effects, estimation procedures, required assumptions, and multiple comparisons as well as a description of examples of the use of two-way ANOVA in social work research. ANCOVA is covered in the third section, including basic statistics (i.e., adjusted mean and partitioned variance), the important role of the covariate, required assumptions as a consequence of including a covariate in the model, and ANCOVA examples from social work research. The final section provides step-by-step instructions for running one-way ANOVA in SPSS, using data from the National Education Longitudinal Study of 1988.

This chapter begins with an introduction to multivariate procedures, which allow social workers and other human services researchers to analyze multidimensional social problems and interventions in ways that minimize oversimplification. Examples of multivariate statistical procedures to predict and describe relationships include multivariate multiple regression (MMR), multivariate analysis of variance (MANOVA), and multivariate analysis of covariance (MANCOVA). Structural equation modeling (SEM) may be used for data simplification and reduction, description, and prediction. The discussion then turns to the rationale for multivariate analysis followed by a description of the organization and contents of this book.

The chapter sets out the aims of the book, the approach, what is covered in the book and what is not. The book starts by introducing several different variations of the basic linear model analysis (analysis of variance, linear regression, analysis of covariance, etc). Then two extensions are introduced: generalized linear models (for data with non-normal distributions) and mixed-effects models (for data with multiple levels and a hierarchical structure). The book ends by combining these two extensions into generalized linear mixed-effects models. To allow a learning-by-doing approach the R code necessary to perform the basic analysis is embedded in the text along with the key output from R.

ANCOVA of designed experiments combines one categorical and one continuous explanatory variable. Panel plots are usually the best way to graphically display ANCOVA designs with a separate linear regression within each level of the factor. The ANCOVA can test for effects of both variables and interactions between them. The chapter focuses on ANCOVA of designed experiments. Detailed analysis is given of subset of the variables from an experimental study of the effects of low-level atmospheric pollutants and drought on agricultural yields.

This chapter builds on the previous chapter by elaborating from theories of causal knowledge presented earlier to practical considerations for the design, execution, and analysis of randomized experiments and randomized controlled trials in music education research. The straightforward statistical analysis of the two-group experimental designs is explained through the t test. The analysis of variance technique is explained for the analysis of experimental and quasi-experimental data involving more than two groups. The chapter closes with a discussion of the analysis of data arising from experiments where additional data, beyond group membership and the score on an outcome measure, is known about the participants (i.e., analysis of covariance).

This chapter summarizes similarities and differences between multivariate analysis of variance (MANOVA), multivariate analysis of covariance (MANCOVA), multivariate multiple regression (MMR), and structural equation modeling (SEM). It offers suggestions to guide their differential use. It also compares and contrasts MANOVA and MANCOVA versus MMR, MANOVA and MANCOVA versus SEM, and MMR versus SEM.

ANCOVA of designed experiments combines one categorical and one continuous explanatory variable. Panel plots are usually the best way to graphically display ANCOVA designs, with a separate linear regression within each level of the factor. ANCOVA can test for effects of both variables and interactions between them. The chapter focuses on ANCOVA of designed experiments. A detailed analysis is given of a subset of the variables from an experimental study of the effects of low-level atmospheric pollutants and drought on agricultural yields.