Mental Illness and Perceived Racism in Black Americans

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 delivery methods

RQ2: How are the various course delivery methods related to students' perceptions of stress or confidence?

The corresponding null and alternative hypotheses would be:

H0: there are no discernable differences in course delivery methods and students' perceptions of stress or confidence

H1: there are significant differences in the relation of SST scores to perceptions of stress or confidence

RQ3: How are students' SST scores related to their college majors?

The corresponding null and alternative hypotheses would be:

H0: there are no discernable differences in SST scores and college majors

H1: there are significant differences in SST scores and college majors

As before, the dependent variable reflects learning of statistical skills and may be measured as a quantitative, interval variable through a structural skills test (SST), which is a 100-item test rating the test scores of students on a scale of 1 to 100. 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 a meta-analysis review of 66 studies (which means that the sample size was 18,140) conducted during the period from January 1996 to April 2011 in an effort to better understand the relation between racism and mental health in Black Americans.

The research question and the research hypotheses are listed below:

R1: What is the magnitude of the relation between perceived racism and mental health among Black Americans.

H0: no relation exists between perceived racism and mental health among Black Americans

H1: a relation does exists between perceived racism and mental health among Black Americans

The search generated 138 empirical studies which were further scrutinized for inclusion criteria and sufficient statistical information to productively determine effect sizes. The researchers conducted a search of the literature using the following inclusion criteria: The studies needed to have a specific analysis of indicators of mental health and perceived racism. The studies also needed to focus on subjects who were Black Americans living in the United States. Moreover, the studies had to have been dissertations or published in peer-reviewed journals between the years of 1996 and 2011. A coding protocol and coder training manual were developed; university students were trained to code the dissertation articles and dissertations, and inter-rater reliability of 90% was achieved.

Five moderator variables were identified: Racism scale type was a measure of the frequency of perceived prejudicial events and the associated level of stress. Measurement precision was the reported reliability estimate on the racism scale. Sample type indicated whether the subjects were from the community, colleges, or combined. Publication type indicated whether the study was from a dissertation or an article from a peer-reviewed journal. Outcome type indicated the effect size for mental health clusters: anxiety or depression; psychiatric symptoms; life satisfaction or self-esteem; and general distress.

Effect sizes were measured by the Pearson product-moment correlation in order to indicate positive correlations between perceived racism and mental distress. Using a random effects model, the effects from the studies were aggregated for overall effect size and weighted contributions of each study. The researches checked for publication bias by using a funnel plot, which is an artifact of published works tending to contain larger samples and significant effect sizes.