MANOVA
MANOVA extends ANOVA to assess differences across multiple continuous dependent variables. Unlike ANOVA, which examines one continuous dependent variable, MANOVA considers multiple dependent variables simultaneously. It combines these variables into a composite through a weighted linear combination, analyzing their collective variation with the independent variable. Essentially, MANOVA investigates whether the grouping variable explains significant variations in the combined dependent variables.
Healthcare Example: In a healthcare setting, researchers might use MANOVA to examine the effectiveness of two different drugs (X and Y) across multiple health outcomes in patients with a particular disease. For instance, they could look at how Drug X and Drug Y impact blood pressure, cholesterol levels, and heart rate in patients with hypertension. The health metrics (blood pressure, cholesterol, heart rate) serve as the dependent variables, while the type of drug administered (Drug X vs. Drug Y) acts as the independent variable. MANOVA would help determine if there’s a statistically significant difference in the combined health outcomes between patients treated with Drug X and those treated with Drug Y.
Social Science Example: In the field of education, a social scientist might employ MANOVA to investigate how various educational interventions impact student performance across multiple assessments. For example, the study could compare the effects of traditional teaching methods versus technology-enhanced learning on students’ math scores, reading comprehension, and science knowledge. Here, the dependent variables are the scores on the different subject assessments, and the independent variable is the teaching method. MANOVA would reveal whether the teaching approach has a significant overall impact on student achievement across the subjects studied.
By applying MANOVA in these scenarios, researchers can gain insights into how different factors or treatments influence multiple outcomes simultaneously, offering a richer, more nuanced understanding of their effects compared to analyzing each dependent variable in isolation.
Assumptions:
Independent Random Sampling: MANOVA assumes that the observations are independent of one another, there is not any pattern for the selection of the sample, and that the sample is completely random.
Level and Measurement of the Variables: MANOVA assumes that the independent variables are categorical and the dependent variables are continuous or scale variables.
Absence of multicollinearity: The dependent variables cannot be too correlated to each other. Tabachnick & Fidell (2012) suggest that no correlation should be above r = .90.
Normality: Multivariate normality is present in the data.
Homogeneity of Variance: Variance between groups is equal.
Key concepts and terms:
Levene’s Test of Equality of Variance: Used to examine whether or not the variance between independent variable groups are equal; also known as homogeneity of variance Non-significant values of Levene’s test indicate equal variance between groups.
Box’s M Test: Used to know the equality of covariance between the groups. This is the equivalent of a multivariate homogeneity of variance. Usually, significance for this test is determined at α = .001 because this test is considered highly sensitive.
Partial eta square: Partial eta square (η2) shows how much variance the independent variable explains and serves as the effect size for the MANOVA model.
Post hoc test: If a significant difference exists between groups, post hoc tests identify where the differences lie (i.e., which specific independent variable level differs from another).
Multivariate F-statistics: The F-statistic derives by dividing the sum of squares (SS) for the source variable by the mean error (ME or MSE) of the source variable.
Tabachnick, B. G. & Fidell, L. S. (2012). Using multivariate statistics (6th ed.). Boston, MA: Pearson.
Related Pages:
Take the Course: MANOVA