ANCOVA and MANOVA ANCOVA or MANOVA

A multivariate analysis of variance (MONOVA) is a statistical procedure for comparing a the population means of several groups and when two or more dependent variables exist ("StatSoft," 2011). One of the strengths of a MONOVA is that individual p-values are produced for each dependent variable. This enables a comparison of the levels of significance of the variables, and can show interactions among the dependent variables ("StatSoft," 2011). It is also possible to determine if changes to the independent variables will create significant effects on the dependent variables ("StatSoft," 2011).

If we consider the question about the influence of course delivery methods on the academic performance of students enrolled in statistics classes, we may find a MONOVA approach to be of assistance in our analysis. Recall that the three course delivery methods are: online, face-to-face, and hybrid. The course delivery methods are the independent variable and the statistical learning of the students is the dependent variable. Generally, when the topic of a research study is student learning -- not simply performance on a single assessment -- we are interested in pre-test and post-test scores. Adding a repeated measures component to the research design can clarify the extent of learning that students achieved. Another independent variable added to this analysis is college major, and number of mathematics courses taken previously. Moreover, a second dependent variable is tutoring requests during the course, and a third dependent variable is feelings about the course (distress or confidence) as rated by a Likert scale administered as an add-on to each test. Through this addition, the MANOVA can assist the analysis of the three types of course delivery with regard to effectiveness with students at various levels of competency. With these changes -- to a MANOVA approach and the addition of another independent variable (entry level of statistics knowledge) -- we are ready to articulate the research question and hypotheses.

RQ1: How are the various course delivery methods related to students' pre- and post- statistics skills?

The corresponding null and alternative hypotheses would be:

H0: there are no discernable differences in pre- and post- statistics scores for course delivery methods

H1: there are significant differences in pre- and post- statistics scores for course...

However, in this version of the research design, the SST will be administered to students on the first and last days of the courses, regardless of course delivery type.
Because several variables are used in this MONOVA analysis, and the analysis will report effects for each variable, it will be helpful to consider how the variables might interact or correlate with other variables. A MANOVA works well when the dependent variables are correlated to a certain degree, but if they are too highly correlated, they may be measuring the same construct.

A MANOVA has the same difficulties with regard to multiple post hoc comparisons as ANOVA. Essentially, MANCOVA is an extension of ANCOVR, but the dependent variables are adjusted for difference in covariates thereby reducing the error "noise."

Part 2:

Racism is pervasive in many societies and resists the efforts of people to eradicate it from the cultural practices and mindsets of many people in a population. Among the many negative outcomes of racism, one of the most important is the impact that perceived racism has on the very people against whom the racism is directed -- or the groups to which they belong. While it is natural to assume that the psychological and physiological outcomes of perceived prejudice have adverse effects on the perceivers, little research exists to demonstrate these relationships. Pieterse, et al. (2012) conducted…