Summary: Introduction to MANOVA, its purpose, and how it differs from ANOVA.
Learning Objectives:
Understand the concept of MANOVA and its advantages over univariate ANOVA.
Learn how MANOVA simultaneously analyzes multiple dependent variables.
Recognize situations where MANOVA is appropriate and how to interpret its results.
MANOVA (Multivariate Analysis of Variance) is a statistical technique that is similar to ANOVA but involves two or more response variables (Huberty & Olejnik, 2006:7) Like ANOVA, MANOVA can be conducted as a one-way or two-way analysis.
In a MANOVA, the purpose is to determine if the independent variable(s) affect the response variable(s), similar to other tests and experiments. For example, if the goal is to investigate if different textbooks have an impact on students' scores in math and science, where improvements in math and science are the two dependent variables, a MANOVA would be appropriate.
While ANOVA provides a single f-value for analysis of one dependent variable, MANOVA produces a multivariate F value to assess multiple dependent variables. MANOVA tests the combined effect of the dependent variables by creating new artificial dependent variables that maximize the differences between groups. These new dependent variables are linear combinations of the original measured dependent variables.
Assumptions for the MANOVA analysis are having independent observations, multivariate normality homogeneity of variance and/or covariance matrices. If groups have nearly equal size, MANOVA is robost for violations of normality and homogeneity (Leech etal, 2013: 162).
Example 1: Assessing the Effect of Exercise on Multiple Health Parameters
Suppose you are conducting a study to investigate the effect of exercise on multiple health parameters in a group of individuals. You randomly assign 50 participants to two groups: Group 1 undergoes an exercise program for 12 weeks, while Group 2 serves as a control and does not participate in any exercise program. At the end of the 12-week period, you measure several health parameters, including blood pressure, cholesterol levels, and body fat percentage.
To analyze the data using MANOVA, you would organize the health parameters into a multivariate outcome variable. In this case, the outcome variable would include blood pressure, cholesterol levels, and body fat percentage. MANOVA allows you to determine whether there is a significant difference in the combined multivariate outcome between the exercise group and the control group. If the p-value is below a predetermined significance level (e.g., 0.05), you can conclude that there is a significant difference in the overall health parameters, suggesting that exercise has an effect on multiple health variables simultaneously.
Example 2: Evaluating the Impact of Different Advertising Channels on Consumer Behavior
Let's say you work for a marketing agency and you want to assess the impact of different advertising channels (TV, radio, and online) on consumer behavior. You randomly select 100 participants and expose them to advertisements through one of the three channels. After exposure, you measure multiple consumer behavior variables, such as brand preference, purchase intention, and recall.
To analyze the data using MANOVA, you would create a multivariate outcome variable that includes the consumer behavior variables (brand preference, purchase intention, and recall). MANOVA allows you to determine whether there is a significant difference in the combined multivariate outcome across the different advertising channels. If the p-value is below a predetermined significance level (e.g., 0.05), you can conclude that there is a significant difference in consumer behavior among the advertising channels, indicating that the choice of advertising medium has an impact on multiple consumer variables simultaneously.
In both examples, MANOVA allows you to analyze the relationship between multiple dependent variables and one or more independent variables. It helps you understand whether there are significant differences among groups when considering multiple outcome variables simultaneously, providing a more comprehensive understanding of the relationship between the variables of interest.
