ANOVA/MANOVA - Methods for Analysis of Variance

Statistica includes several methods of analysis for performing analysis of variance. Although many of the available statistics overlap in the different modules, each is best suited for particular applications.

General ANCOVA/MANCOVA. Use this module for analyzing full factorial designs, repeated measures designs, and multivariate designs (MANOVA), for evaluating planned and post-hoc comparisons, etc. This module allows you to perform probably 90% of all (univariate and multivariate) ANOVA/ANCOVA analyses that are typically encountered in actual research. The entire functionality of the ANCOVA/MANCOVA module is also available in the more general and powerful GLM module (see below). Therefore, users at all levels are encouraged to use the GLM module.

General Linear Model (GLM). This extremely comprehensive method of analysis offers a complete implementation of the general linear model, and includes the Sigma-restricted as well as the overparameterized approach. You can use this method of analysis to analyze all designs that can be handled by the ANCOVA/MANCOVA method of analysis (see above); in addition the GLM method of analysis will analyze incomplete designs, complex analysis of covariance designs, nested designs (balanced or unbalanced), mixed model ANOVA designs (with random effects), and huge balanced ANOVA designs (efficiently); GLM also offers numerous options for planned and post-hoc comparisons, custom hypotheses, custom error terms, detailed residual statistics, and a large number of auxiliary tests and results (e.g., model assumption tests, plots of weighted, unweighted, and least squares means, desirability profiler options, variance components, etc.).

General Regression Models (GRM). This method of analysis is very similar to GLM, and in addition will perform stepwise and best-subset model building (for continuous as well as categorical predictors). GRM is, in a sense, a superset of the Multiple Regression method of analysis; however, Multiple Regression has some unique features for dealing with different input data (e.g., pairwise deletion of missing data, matrix file input, etc.). Note that Statistica also includes Generalized Linear/Nonlinear Model (GLZ), a method of analysis for analyzing nonlinear relationships in ANOVA/ANCOVA-like designs (GLZ also offers stepwise and best-subset model building methods).

Mixed ANCOVA and Variance Components. Use this method of analysis to analyze factorial and hierarchically nested experimental designs with random effects (mixed model ANOVA), and to estimate variance components for random effects, or to analyze large main effect designs (e.g., with factors with over 100 levels) with or without random effects, or large designs with many factors, when you do not need to estimate all interactions. While all of these designs can also be analyzed via GLM, only the Mixed ANCOVA and Variance Components method of analysis will estimate variance components based on maximum likelihood methods.

Experimental Design (DOE). Use this method of analysis to generate and analyze standard experimental designs for industrial/manufacturing applications, including 2(k-p) and 3(k-p) designs, central composite and non-factorial designs, designs for mixtures, D and A optimal designs, and designs for arbitrarily constrained experimental regions. While all of these designs can also be analyzed via GLM, the DOE method of analysis is particularly convenient for analyzing standard designs (generated by the DOE method of analysis), i.e., analyzing such designs usually only requires little more than selecting the variables. However, for non-standard designs (any design not properly recognized by the DOE analysis facilities), use GLM.

Repeatability and Reproducibility Analysis (in Process Analysis). Use this option in the Process Analysis method of analysis when you want to analyze specialized designs for evaluating the reliability and precision of measurement systems; these designs usually include two or three random factors, and specialized statistics can be computed for evaluating the quality of a measurement system (typically in industrial/manufacturing applications).

Breakdown Tables (in Basic Statistics). Use this method of analysis for analyzing experiments with only one factor (and many levels), or with multiple factors, when a complete ANOVA table is not required; the Basic Statistics method of analysis also allows you to compute detailed descriptive statistics and graphical summaries for the data.