# Statistical Advisor, How To Compare Means / Variances in Multiple Groups

Use one of the following:

GENERAL LINEAR MODELS (GLM): This chapter describes so-called analysis of variance (ANOVA). ANOVA is used, among other applications, for simultaneously comparing means in several groups. ANOVA assumes that the variables in the comparison are normally distributed within the groups, and that the variances are about the same in each group. GLM also contains several statistical tests for comparing the variances across groups. The ANOVA/MANOVA chapter will also describes ANOVA/MANOVA analyses.

GENERALIZED LINEAR MODELS (GLZ): This chapter describes analysis of variance (ANOVA) like designs, without assuming that the variables in the analysis follow the normal distribution, or that the effect of the categorical predictors is linear in nature. Also, the GLZ chapter refers to maximum likelihood methods instead of least squares estimation.

VARIANCE COMPONENTS AND MIXED MODEL ANOVA/ANCOVA. This chapter covers a comprehensive set of techniques for analyzing research designs with random effects, including the estimation of variance components for such effects. It is also well suited for analyzing large main effect designs (e.g., designs with over 200 levels per factor), designs with many factors where the higher order interactions are not of interest, and analyses involving case weights. There are several chapters that will describe Analysis of Variance for factorial or specialized designs. For a discussion of the statistical techniques that perform analysis of variance (ANOVA) and the types of designs for which they are best suited refer to the section on Methods for Analysis of Variance.

DISCRIMINANT FUNCTION ANALYSIS: This chapter describes analyses similar to ANOVA; specifically, it discusses how to identify the specific variables that show different means in different groups.

NONPARAMETRICS AND DISTRIBUTIONS: This chapter describes numerous so-called nonparametric tests for comparing groups. These test should be used if one is not sure of the distribution of the variables used in the comparison. For example, the data may actually consist of rankings rather than precise measurements.

GRAPHICAL ANALYTIC TECHNIQUES: This chapter refers to histograms, line graphs, scatterplots, etc. by groups.