Multivariate ANOVA (MANOVA) extends the capabilities of analysis of variance (ANOVA) by assessing multiple dependent variables simultaneously. ANOVA statistically tests the differences between three or more group means. For example, if you have three different teaching methods and you want to evaluate the average scores for these groups, you can use ANOVA. However, ANOVA does have a drawback. It can assess only one dependent variable at a time. This limitation can be an enormous problem in certain circumstances because it can prevent you from detecting effects that actually exist.

MANOVA provides a solution for some studies. This statistical procedure tests multiple dependent variables at the same time. By doing so, MANOVA can offer several advantages over ANOVA.

In this post, I explain how MANOVA works, its benefits compared to ANOVA, and when to use it. I’ll also work through a MANOVA example to show you how to analyze the data and interpret the results.

## ANOVA Restrictions

Regular ANOVA tests can assess only one dependent variable at a time in your model. Even when you fit a general linear model with multiple independent variables, the model only considers one dependent variable. The problem is that these models can’t identify patterns in multiple dependent variables.

This restriction can be very problematic in certain cases where a typical ANOVA won’t be able to produce statistically significant results. Let’s compare ANOVA to MANOVA.

## Comparison of MANOVA to ANOVA Using an Example

MANOVA can detect patterns between multiple dependent variables. But, what does that mean exactly? It sounds complex, but graphs make it easy to understand. Let’s work through an example that compares ANOVA to MANOVA.

Suppose we are studying three different teaching methods for a course. This variable is our independent variable. We also have student satisfaction scores and test scores. These variables are our dependent variables. We want to determine whether the mean scores for satisfaction and tests differ between the three teaching methods. Here is the CSV file for the MANOVA_example.

The graphs below display the scores by teaching method. One chart shows the test scores and the other shows the satisfaction scores. These plots represent how one-way ANOVA tests the data—one dependent variable at a time.

Both of these graphs appear to show that there is no association between teaching method and either test scores or satisfaction scores. The groups seem to be approximately equal. Consequently, it’s no surprise that the one-way ANOVA P-values for both test and satisfaction scores are insignificant (0.923 and 0.254).

Case closed! The teaching method isn’t related to either satisfaction or test scores. Hold on. There’s more to this story!

## How MANOVA Assesses the Data

Let’s see what patterns we can find between the dependent variables and how they are related to teaching method. I’ll graph the test and satisfaction scores on the scatterplot and use teaching method as the grouping variable. This multivariate approach represents how MANOVA tests the data. These are the same data, but sometimes how you look at them makes all the difference.

The graph displays a positive correlation between Test scores and Satisfaction. As student satisfaction increases, test scores tend to increase as well. Moreover, for any given satisfaction score, teaching method 3 tends to have higher test scores than methods 1 and 2. In other words, students who are equally satisfied with the course tend to have higher scores with method 3. MANOVA can test this pattern statistically to help ensure that it’s not present by chance.

In your preferred statistical software, fit the MANOVA model so that Method is the independent variable and Satisfaction and Test are the dependent variables.

The MANOVA results are below.

Even though the one-way ANOVA results and graphs seem to indicate that there is nothing of interest, MANOVA produces statistically significant results—as signified by the minuscule P-values. We can conclude that there is an association between teaching method and the relationship between the dependent variables.

## When MANOVA Provides Benefits

Use multivariate ANOVA when your dependent variables are correlated. The correlation structure between the dependent variables provides additional information to the model which gives MANOVA the following enhanced capabilities:

**Greater statistical power**: When the dependent variables are correlated, MANOVA can identify effects that are smaller than those that regular ANOVA can find.**Assess patterns between multiple dependent variables**: The factors in the model can affect the relationship between dependent variables instead of influencing a single dependent variable. As the example in this post shows, ANOVA tests with a single dependent variable can fail completely to detect these patterns.**Limits the joint error rate**: When you perform a series of ANOVA tests because you have multiple dependent variables, the joint probability of rejecting a true null hypothesis increases with each additional test. Instead, if you perform one MANOVA test, the error rate equals the significance level.

feafeafeaf says

DVs aren’t supposed to be correlated

Jim Frost says

Hi, you’re thinking about

independentvariables. When independent variables are correlated it is known as multicollinearity, and it can be a problem. I’ve written a post about multicollinearity in case you are interested.Most analyses aren’t designed to handle multiple

dependentvariables. However, MANOVA is not only designed for that but there are benefits when they are correlated.Sophia says

Hi Jim,

Thanks for writing this very informative post! I am in my final year of Applied Psychology and am currently in the process of completing my final year project. My study is investigating whether a difference exists among the eating patterns and behaviours of college students of the different years (i.e. 1st-4th year college students). My independent variable would be college year and my dependent variables are: (i) eating patterns, (ii) emotional eating and (iii) attitudes towards healthy eating. Would you recommend me to use a MANOVA in analyzing my data or would you recommend a different approach to analyses? I am confused on what approach to use!

Best,

Sophia

Jim Frost says

Hi Sophia,

If the dependent variables are correlated, then you gain benefits by using MANOVA rather than ANOVA. However, if they are not correlated, ANOVA might be just fine. I’m not an expert in that field, but it seems like your dependent variables might be correlated.

I hope this helps. Best of luck with your analysis!

Aba Merci says

Hi Jim,

Could please explain why computing a variance of several numbers is like analyzing their differences

Jim Frost says

Hi Aba,

To calculate the variance (which is the square of the standard deviation), you take the difference between each individual value and the mean, square those differences, add all of those squared differences together, and then divide by the number of observations. If you want the standard deviation, which is easier to interpret, you need to take the square root of that.

So, you’re really analyzing the differences between the individual observations and the mean. A larger variance (or standard deviation) indicates that the differences between the individual data points and the mean tends to be larger (the data points tend to fall further from the mean–they’re more dispersed). Smaller values of the variance/standard deviation indicate that the differences are smaller. The data points are clustered more tightly around the mean. That’s how differences come into play with the variance and standard deviation!

I hope this helps!

Joe Smith says

Dumb question: What test or tests does one run in SPSS to find out if the dependent variables are related, to “gain the benefits of MANOVA” as you say. Thank you sir!

Joe Smith says

correlated rather

Jim Frost says

Hi Joe, of course there is no such thing as a dumb question! All you need to determine is if they are correlated. So a simple Pearson’s correlation. Or, you can even use regression analysis. Nothing fancy! As long as there is some sort of relationship between the dependent variables, MANOVA is beneficial.

Tan says

Hi Jim,

I have a few questions:

IV = independent variable

DV = dependent variable

1. Suppose I conducted 2 x 2 x 2 factorial design using Manova. My hypotheses cover the direct effect, two-way interaction, and three-way interaction.

I found that based on the direct effect, IV1, IV2, IV3 are significantly related to DV1 and IV1 is the most important factor. Furthermore, interaction effect of X2 and X3 also significantly related to DV1.

When writing the discussion part in paper, I provide that reasons why IV1, IV2, IV3 are significantly related to DV1, then do I need to explain IV1 is the most important factor? If not, why?

Finally, I discuss the interaction effect.

2. I understand that SPSS will run Manova and then run Anova automatically. The reason is that if the program run Anova in several times, the type I error will increase. Am I correct?

Thank you very much

Gemma says

Hi there,

So what would be the difference between a 2-way ANOVA and a MANOVA? When would you use them and why? Is one more powerful?

Thanks so much!

Jim Frost says

Hi Gemma,

There are several differences. For one thing, 2-way ANOVA can handle two independent variables (IV) and only one dependent variable (DV). MANOVA can handle 1 or more IVs and 1 or more DVs. The real key advantage of MANOVA is how it handles multiple DVs at the same time. This provides MANOVA with more power when those DVs are correlated.

Use MANOVA when you have multiple DVs that are correlated. As this post shows, it can detect multivariate patterns in the DVs that ANOVA is simply unable to detect at all. Plus, it is more powerful when those DVs are correlated.

When you have only one DV, use some form of regular ANOVA, which includes 2-way ANOVA.

I hope this helps!

Esther says

Hi Jim! Thank you for your informative article, the concepts are so much clearer to me now.

However, I have a question.What if I have 4 independent variable but only 1 dependent variable? Would ANOVA be able to process that? Or should I employ MANOVA?

Jim Frost says

Hi Esther, It makes me happy to hear that my blogs have helped clarify things for you!

MANOVA requires multiple dependent variables. It is particularly useful when those dependent variables are correlated.

When you have only one dependent variable, you have to use an ANOVA procedure. With some ANOVA procedures, such as General Linear Model, you can have multiple independent variables.

I hope this helps!