ABSTRACT
In this chapter we discuss the selection and application of appropriate statistical methods to answer complex research questions. When referring to complex research questions, we are discussing analyses that have more than one independent variable and sometimes more than one dependent variable. Although many different statistical analyses could be included in this category, we discuss the most common analyses in some detail, providing examples where appropriate. We focus on three analyses in particular: (1) the two-factor between-groups analysis of variance; (2) the mixed analysis of variance with reference to the analysis of designs that includes a pretest and posttest; and (3) multiple regression. We also touch on other analyses such as analysis of covariance, two-factor withinsubjects analysis of variance (ANOVA), linear or bivariate regression, discriminant analysis, and logistic regression. All of these complex difference and associational statistics have a dependent variable that should be approximately normally distributed or, for discriminant analysis and logistic regression, dichotomous. There are no common complex nonparametric inferential statistics for ordinal dependent variables. Data transformations or other statistical adjustments are necessary when the assumptions of these complex statistics are markedly violated.
