1 DESCRIPTION OF THE TOPICINTRODUCTION Let us refresh our basic knowledge in ANOVA before we delve into MANOVA. ANOVA ANOVA stands for Analysis of Variance. ANOVA is a family of multivariate statistical technique for helping to infer whether there are real differences between the means of three or more groups or variables in a population, based on sample data. Analysis of variance must have a dependent variable that is metric (measured using an interval or ratio scale) and one or more independent variables that are all categorical (non-metric). Categorical independent variables are also called factors. One way ANOVA One-way analysis of variance involves only one categorical variable, or a single factor. In one-way analysis of variance, a treatment is the same as a factor level. N way ANOVA In research, one is often concerned with the effect of more than one factor simultaneously.If two or more factors are involved, the analysis is termed n-way analysis of variance. ANCOVA When examining the differences in the mean values of the dependent variable related to the effect of the controlled independent variables, it is often necessary to take into account the influence of uncontrolled (usually metric) independent variables. If the set of independent variables consists of both categorical and metric variables, then the technique is Analysis of Covariance (ANCOVA). In this case, the categorical independent Items Description of TopicCourse Data Analysis for Social Science Teachers Topic MANOVA

2 variables are still referred to as factors, whereas the metric-independent variables are referred to as Covariates. MANOVA Developed as a theoretical construct by Samual S. Wilks in 1932 (Biometrika). It is an extension of univariate ANOVA procedures to situations in which there are two or more related dependent variables (ANOVA analyses only a single DV at a time). DVs should be correlated (but not overly so; otherwise they should be combined) or conceptually related. The MANOVA procedure identifies (inferentially) whether: Different levels of the IVs have a significant effect on a linear combination of each of the DVs There are interactions between the IVs and a linear combination of the DVs. There are significant univariate effects for each of the DVs separately. Types The main types of ANOVA are listed below. They are all part of the general linear model. ANOVA models Definitions t-testsComparison of means between two groups; if independent groups, then independent samples t-test. If not independent, then paired samples t-test. If comparing one group against a fixed value, then a one-sample t-test. One-way ANOVAComparison of means of three or more independent groups. One-way repeated measures ANOVAComparison of means of three or more within-subject variables.