# MANOVA

Multivariate Analysis of Variance (MANOVA) is an analytical technique that expands upon the principles of ANOVA to evaluate differences across multiple continuous dependent variables simultaneously. Unlike ANOVA, which focuses on discerning statistical differences in one continuous dependent variable influenced by an independent variable (or grouping variable), MANOVA considers several dependent variables at once. It integrates these variables into a single, composite variable through a weighted linear combination, allowing for a comprehensive analysis of how these dependent variables collectively vary with respect to the levels of 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 dependent variables would be the health metrics (blood pressure, cholesterol, heart rate), and the independent variable would be the type of drug administered (Drug X vs. Drug Y). 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.

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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 is explained by the independent variable. It is used as the effect size for the MANOVA model.

Post hoc test: If there is a significant difference between groups, then post hoc tests are performed to determine where the significant differences lie (i.e., which specific independent variable level significantly differs from another).

Multivariate F-statistics: The F- statistic is derived by essentially dividing the means sum of the square (SS) for the source variable by the source variable mean error (ME or MSE).

SPSS: Can be performed using the analysis menu, selecting the “GLM” option, and then choosing the “Multivariate” option from the GLM option.

Resources

Tabachnick, B. G. & Fidell, L. S. (2012). Using multivariate statistics (6th ed.).  Boston, MA: Pearson.

Related Pages:

Take the Course: MANOVA

Conduct and Interpret a One-Way MANOVA

ANOVA

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