In most research projects the relationships among more than two variables are assessed at the same time. When there are more than two independent variables but only a single dependent variable, multiple regression is the most appropriate data analysis procedure. The independent variables in a multiple regression can be entered simultaneously, hierarchically, or by using a stepwise approach. The factorial Analysis of Variance is really a type of regression analysis in which the independent variables are nominal. When there is more than one independent variable and the dependent measure is nominal, loglinearanalysis, rather than ANOVA, is the appropriate statistical test.
One difficulty in ANOVA designs that have more than two conditions is that the F values do not always provide information about which groups are significantly different from each other. A number of means comparison procedures, including contrast analysis, the Fisher LSD test, the Scheffé test, and the
Tukey HSD test, can be used to help make this determination.
In cases where more than one dependent measure has been assessed, multivariate statistics may be used to analyze the relationships among the variables and to reduce their complexity. Examples of multivariate procedures include exploratory factor analysis, MANOVA, and canonical correlation. When a theoretical relationship among the variables is specified ahead of time, structural equation modeling can be used to test whether the observed data fit the expected pattern of relationships.
One of the important aspects of research is learning how to use the complex array of available statistical procedures to analyze the data that have been collected. There is no substitute for experience in learning to do so.