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.

Mike says

Mr. Frost:

I took your data and loaded it into SPSS and performed a Hotelling’s T MANOVA on the data and indeed found multivariate significance in the three methods on the dependent variables. However, SPSS provides Post Hoc Default Analysis using T-Test with a Bonferroni correction and neither method comparisons came out to be not significant. I am wondering if you suggest the next step would be to perform a Discriminant Function Analysis to get to the root of the group differences.

Rachel P. says

Hello Jim,

What a fantastic resource you have here.

I am analyzing survey responses from each US state and have a much higher response rate from two of them. The issue I am running into is – these two states are leaders in this field and I want to see if they are statistically different than the others or if they change the collective of a little over 1,300 responses. I am isolating only the nine Likert-type 5-point questions. To compare these – would this work and would I have to do each question separately or would it work with one state vs. the others?

I appreciate any tips or links to articles – I am using SPSS v27 with very little experience.

With Gratitude –

Rachel

Jim Frost says

Hi Rachel,

This is a tricky problem for several reasons. I don’t have specific answer for you but can at least raise several issues and provide some information.

One difficult aspect is the fact that you’re using Likert scale data, which are ordinal data. Many analyst consider averages to be inappropriate for this type of data. However, there is some evidence that the regular parameteric tests are ok to use with them. For more information, read my post about analyzing Likert data. Note that the discussion is in context of using t-tests. I’m don’t whether the same details apply to ANOVA, which you’d need to use because you have more groups. But ANOVA is an extension of the t-test.

However, if you average several Likert items together (or add them), then you have stronger grounds for considering it to be a regular continuous variables. Something to consider.

Another point is that you’ll be comparing many groups. You’ll need to consider using a post hoc test to control the family-wise error rate. For more details on that, read my post about using post hoc tests with ANOVA. That will help you answer your questions about comparing states.

I hope that gives you enough information to get you started!

peter Ji says

I enjoyed your discussion about the usefulness of MANOVA in that it can assess patterns between multiple dependent variables. my question is this – is there any statistic result in the MANOVA output that directly indicates what is that pattern among the DV’s? To me, the output only tells you that there is a relationship among the DV’s. It doesn’t tell you what the nature of that relationship among the DV’s would be. Is the only way to detect a pattern is to plot out the DV’s and heuristically infer the pattern, as you demonstrated with your Excel plots? Thank you.

Jim Frost says

Hi Peter,

First, I wouldn’t underestimate the power of graphs to represent the results! Often, the patterns are clearly visible in the graphs and you just need to know whether they’re statistically significant.

You can also use Eigen values and Eigen vectors to help you understand MANOVA results. Use these values to determine how the IV means differ between the levels of the different model terms. Focus on the Eigen vectors that correspond to high Eigen values. They’ll point you towards the factor levels associated with the largest mean differences.

I don’t go into that here, but you can look those up for more information!

Ciara Taylor says

hi there

if i have 3 IV (depression, gender and ethnicity) and many DVs like (loneliness, internet use , social media followers etc) is a MANOVA best for this?

thanks

Ciara

Karan Mehta says

Hi Madelyn,

You can use python language or even Microsoft excel.

Please find the below link for python code example:

https://www.marsja.se/python-manova-made-easy-using-statsmodels/

And if you need any help you can mail me 🙂

[email protected]

I would be happy to help you and even those who have doubts in Data Science can contact me.

Moksh says

I recently discovered this website and damn, this is pure gold. Thank you!

Jim Frost says

You’re very welcome, Moksh! So glad it’s helpful!

Arturo J. Patungan Jr says

Hi Jim,

Thank you for your article. This help me a lot explaining MANOVA to my advisees on when and why they need to use MANOVA rather than the other alternatives.

Art

Lease says

This is excellent! Thank-you so much for the summarization of the differences between ANOVAs and MANOVAs. This was the most concise article I could find and will be helpful in my thesis defense!

Jim Frost says

You’re very welcome, Lease. I’m thrilled to hear it was so helpful! 🙂

Chloe says

Hi Madelyn,

I would suggest you to use jamovi, it is a free, open source software. It is ‘user friendly’ and you can find support for you analysis if needed, and it is intuitive to use.

Good luck fo you project !

Jim Frost says

Hi Chloe,

Thanks so much for the recommendation! I hadn’t heard of Jamovi before and I’ll look into it! Hopefully, it is helpful for Madelyn too!

Madelyn Davis says

Hi, I’m trying to run a MANOVA for a research project for my class (I’m a senior in high school). I’m wondering what software would be best for me. Ideally, it would be free and fairly simple to use as I am not the most versed in this kind of analysis. Any recommendations?

Thank you,

Madelyn

Andrea says

Hi Jim,

Thank you for your really informative post.

I encountered with the problematic in SPSS, that post hoc test is not being calculated as the IV has only two groups. (I have two sub-groups under the IV, and four correlated DVs to analyse).

I wonder if the results of the MANOVA can be still accepted (significant Pillai`s trace etc.)? How the lack of post hoc tests effect the results and overall is it an issue for MANOVA that its IV has only two sub-groups?

Hope my question makes sense.

Thank you very much

Andrea

Jim Frost says

Hi Andrea, if you’re just comparing two groups, then you there’s no need for post hoc tests. Post hoc tests are for cases where you have multiple comparisons. You need three or more groups. With two groups, you have only one comparison.

Grace Gibson says

Hi Jim,

I can’t figure out if my scenario is a MANova or another type of ANova (possibly 2 way).

I have test results for two separate groups of students – one from 2010 and another 2020. The same test was given to both groups, so I know fluid and crystallised intelligence. I’m now looking to test the Flynn effect and whether the effect applies to just one type of intelligence, or both.

I thought the two factors would be 2010 and 2020 and that the dependent variable was intelligence type.

But the more I read the more confused I get – do my two intelligence results mean I have multiple DV’s.

All the 2 way ANova videos I’ve seen are looking at two factors – gender and age I just have the year – 2010 ir 2020.

Thanks in advance,

Grace

Evrim Gökçe says

Hello,

I conducted a MANOVA for 2 independent variable (age (3 levels) / pysical activity level). Due to physical activity level was a continuous variable, I included it like if it’s a covariate. I’m confused about how to report the results.

I reported the main effect of age between the groups. But how can I report the interaction effect? Is it enough to say the interaction effect was significant or should we detail it? And if we should, how can we do it?

Thank you so much

Thomas says

Hi Jim,

Thank you so much for your help! I’ve done mixed ANOVA in SPSS, in which you can add the time point DVs into a ‘time’ IV — can’t find that when conducting MANOVA, so I’ll continue to investigate.

In terms of the DV correlations, they’re mixed… But I’m scoring people at 2 timepoints on 3 DVs, and predicting big changes for the intervention group, so doesn’t it make sense that say…. T0 stress won’t correlate with T1 anxiety??

My correlations are:

Stress T0 – Stress T1: .548**

Stress T0 – Anxiety T0: .577**

Stress T0 – Anxiety T1: .127

Stress T0 – Depression T0: .325*

Stress T0 – Depression T1: .063

Anxiety T0 – Depression T0: .492**

Anxiety T0 – Depression T1: .173

Anxiety T1 – Depression T0: .141

Anxiety T1 – Depression T1: .558**

So the non-sig correlations are between T0 measure for one DV, and the T1 measures for the other DVs…

**Does this mean that MANOVA is no good???? Do they all have to correlate?**

Also, my Shapiro-Wilks is sig. for all but one DV, even with log transformed data and 3 x outliers removed… Though thankfully my Levene’s is non-sig.

**Does the SW failure mean I can’t continue with MANOVA, or can I just ‘proceed with caution’?**

Because I haven’t been able to include a repeated measures factor in my SPSS, my output hits a wall, so I’ve only done an ‘exploratory’ MANOVA just to see what output might happen with my logTr data and outliers removed etc..

So at this stage, I’m still feeling my way around. My supervisor said that 3 separate ANOVAs would inflate my results, but at this stage it’s a change I’m willing to take!

Thank you again, wish you were in my department!!

Thomas says

Hello,

I’m having a little trouble working out what to do and hoping you can help! I’m very new to stats, so please go easy on me!

My supervisor has told me I need to use a MANOVA rather than ANOVA, because I have 3 DVs, but I’ve been given no information on MANOVA or how to perform it in SPSS…. I’ve tried but I’m struggling. I can’t find any tutorials online that replicate my study, or are similar.

My study is an intervention:

Intervention Group versus control group

Both groups were tested on stress, anxiety and depression at 2 timepoints; pre- and post-intervention.

I have 3 DVs (stress, anxiety, depression), 1 between-subjects IV (group), 1 within-subjects IV (time).

I have some questions:

Is MANOVA the right analysis? Would it be called a mixed MANOVA?

In SPSS, I have 8 columns; P#, Group, stress T0, stress T1, anxiety T0, anxiety T1, depression T0, depression T1.

The problem I have here is that I don’t know how to create the time IV — because in all the tutorials I’ve found, there are no repeated measures…

That’s the only specific question I have, but generally do you know of any online tutorials that would walk me through this type of study, because I’m really lost and only have 3 weeks until dissertation submission.

Sadly, my supervisor has left it until now to tell me I shouldn’t be using ANOVA 🙁

Many thanks!!

Best wishes,

Tom

Jim Frost says

Hi Thomas,

I haven’t used repeated measures in MANOVA. However, I’d imagine it is similar to how you set up repeated measures models in ANOVA. I’ve written a post about repeated measures ANOVA that might be helpful. Unfortunately, it’s been a looooogn time since I’ve used SPSS and can’t provide guidance there.

If the three DVs are correlated, you do gain benefits by using MANOVA instead of ANOVA. If they’re not correlated, those benefits go away. Even if you do go with MANOVA, you can still fit the ANOVA models to help you understand what is happening. Those can some times be easier to interpret. Although you do lose some information as I show in this post. But, the ANOVA results can help fill in some details even when you use MANOVA.

I know that wasn’t super specific, but I hope it helps some!

Marcus says

Hi Jim,

thank you so much for this introduction. I was also wondering whether to perform 2 ANOVAs or a MANOVA.

I test 3 different sales tactics (IVs) in an online store and I observed the Conversion Rates and the Abandoned Shopping Carts.

I have two seperate sets of hypotheses for the DVs. (e.g. Sales Tactic 1 has higher Conversion Rate than Sales Tactic 2)

– Would you recommend to perform one ANOVA per DV? Or one MANOVA for all DVs?

What is the deciding criterium – is it the Correlations of DVs? Becuase i dont know whether they are correlated and if yes, it is probably not a positive correlation (does it still work?)

Thanks and best,

Marcus

Jim Frost says

Hi Marcus,

If you want to determine whether your DV means are equal vs not equal (Conversion rates vs Abandoned shopping carts) given the levels of your DV, then you’ll need to use MANOVA! You’d be seeing that relationship between those two DVs change based on the IVs. Look the scatterplot in this post to see the type of differences you’re assessing.

However, if all you need to know is whether the mean the individual DVs vary by the levels of the IVs and you’re not assessing the pattern of relationships between conversion rates and abandoned carts, then separate ANOVA models are ok. Although, if conversion rates and abandoned carts are related, you still gain some power benefits by performing MANOVA rather than ANOVA.

I hope that helps!

Kelly Papapavlou says

Τhank you very much Mr. Frost. So I presume the equality refers to all the DV means between the different data sets under comparison i.e. the combined DV (satisfaction + test scores) means for teaching method 1 are equal to the combined DV (satisfaction + test scores) means for teaching method 2 and method 3?

Jim Frost says

Hi Kelly,

It’s all one dataset but with multiple DVs. In the graph, if the results hadn’t been significant, the data points for the different methods would have all followed the same line instead of separate lines. However, because the results are significant, you can see that each method (IV) produces a different relationship between the DVs.

Kelly Papapavlou says

Thank you very much for this information. I am confused with setting the null hupothesis in the case of MANOVA i.e Ho; regarding the particular treatments, two or more groups do not differ in the mean response of two or more dependent variables?

Jim Frost says

Hi Kelly,

MANOVA interpretation can be less intuitive! MANOVA determines whether the multiple dependent variable (DV) means are different for the values of the independent variable (IV). Therefore:

H0: DV means are equal for the values of the IV.

HA: DV means are not equal for the values of the IV.

In the blog post, you can see an example of significant results (rejecting H0) in the Scatterplot of Test vs. Satisfaction. Each method (the IV) has mean test scores and satisfaction levels (the two DVs) that are significantly different. Read the interpretation below the graph for more details.

I hope that helps!

Kevin says

Hey Mr. Frost,

Great website. I hope this post is in the right place, but my question may be more broad. I am surveying teams with a questionnaire that test team characteristics (inputs and processes like clear roles, common purpose, trust,etc) and team cohesion. My goal is to see which of the team characteristics correlate with teams that are considered cohesive. What stats tests would I use with the data I get returned from the questionnaire to get results (I already know what I will use to aggregate individual responses to group-level)? Thanks for any help. I will try to find a post on the subject of my another question. I thought some sort of anova but not sure. Do I include normal distribution test? (Someone suggested anderson-darling)?

Celine Laffineur says

Hi! Thank you for this helpful article. I am currently designing a study where I want to explore the effect of colour (IV = 4 colour conditions) on competence perception (1st DV) and voting intention (2nd DV). However, I don’t really understand if I conduct a within-participants MANOVA, does the ” within” condition only apply to IV or do the DV scores have to also come from all participants?

Thank you in advance,

Celine

Jon says

How would this differ from running an ANOVA with test score as DV, and the teaching method and satisfaction scores as IV’s with an interaction between the two?

Jim Frost says

Hi Jon,

With a regular ANOVA you have just one DV and multiple IVs (in your example). You can have an interaction between the IVs. For MANOVA, you’d have multiple DVs. You can also have multiple IVs and you can include the interaction term if needed. The main difference is the ability to include multiple DVs in the same model. If those DVs are correlated, you can gain the benefits that I describe in this post. The presence or absence of an interaction term is not a consideration in this context. Both of these analyses can handle interaction terms.

I hope that helps!

Amal George says

Greetings.

In my study I have 3DV and 3IDV. Is Manova suitable for this?

Jim Frost says

Hi Amal,

If your three dependent variables are correlated, then using MANOVA is a good idea. If the IVs are not correlated, use regular ANOVA and fit a separate model for each DV. Most of the benefits you get from MANOVA versus ANOVA occur when the DVs are correlated.

Phil says

Hi Jim,

Firstly, thank you for posting this. I am really needing your help/expertise:

I am working on a research study whereby I have collected quarterly SEC data for 10 companies which I plan to study for 2015-2019. All of these companies were affected by passage of new legislation which became effective 01/01/19, thus I have 16 quarters of data in the ‘before’ group and 4 quarters of data in the ‘after’ group. My research question is centered around “has passage of the new legislation caused a decrease in the 5 DVs in the study?

My plan is to use a one-way MANOVA (1 IV, 5 DVs) to compare the means of the before and after groups and test for stat significance. My stats prof says that because I’m using quarterly data, it represents ‘panel data’ and I may not be able to use a MANOVA. I was thinking that even though I have multiple quarters in the ‘before’ and ‘after’ groups, they’re all only really there to provide a more accurate mean for each DV in the ‘before’ and ‘after’ groups. I have searched high and low and can’t find an answer…..can you help???

Cheers,

Phil

Kyle says

Hi Mr. Frost,

Thank you for the concise article. If you were to cite a few references in support, what might they be? Bray & Maxwell, 1985? Tabachnick & Fidell, 2006?

Thanks again,

Kyle

ALVIN RAJ SANTHANADASS says

hi,

if the situation is, i have 1set of questionnaire on three domain afective, psychomotor and cognitive and im going to test to a male subject can i use manova? 3dv and 1 iv?

Jim Frost says

Hi Alvin,

If the the three DVs are correlated, then MANOVA can be a good method to use. However, if you’re assessing only one subject, be aware that you probably can’t generalize the results beyond that subject. It might be good for a pilot study.

Hakim says

Hi Jim,

I was thinking of running a two-way MANOVA for my project but when running the assumptions, I found that my DVs are multicolinear(90% correlation). References I have read so far recommend that I either average the two DVs or remove one DV from the analysis? Can you please advise me how to deal with it? Should I go ahead and run a MANOVA or run separate ANOVAs with the DVs?

I would really appreciate your expert advice.

Ajibola says

Hi Jim.

Thank you so much for the great work you’re doing. Your post has been so much helpful to me.

I need your assistance again to clarify a little confusion. I am trying to know the relationship between multiple IVs and DVs. My IVs (which are basically socioeconomic data) contain all possible measurement levels (interval, nominal, and ordinal data types) while my DVs are mainly categorical data types (nominal and ordinal).

I have done some reading online but not clear on the right statistical test to conduct; some seem to point at canonical correlation and others at factor analysis, but my little knowledge is pointing at MANOVA, even though no article I’ve read has explicitly considered the measurement levels of the variables.

Thank you so much, Jim.

Kay Lynn Stevens says

Hi Jim,

I am trying to use G*Power software to calculate an a priori sample size for a Hotelling’s T^2. How do I calculate the a priori effect size? Can I do this in SPSS? I have two independent groups of one categorical independent variable, and 3 continuous scale DVs.

Thank you for pointing me to the best resource!

Haradhan Saha says

Respected Sir,

Please I want a answer below mention question.

Using MANOVA rather than performing several one-way ANOVAs: a. Allows for a greater number of independent variables b. Ignores any correlation between dependent variables c. Increases the Type 1 error rate d. Decreases the Type 1 error rate

Jim Frost says

Hi Haradhan,

This is obviously a test question and I don’t like just giving people answers. Particularly when the article you’re posting this comment in provides you with the answer. So, I’ll give you a hint about where in this article you should read more carefully because the answer is there. Read the section titled “When MANOVA Provides Benefits.” Pay particular attention to the last bullet point! 😉

Daniela Cajiao says

Hi Jim,

I’ve been asked to think in a MANOVA for my data, related to tourists’ surveys. I am a little stuck though. Here it goes:

As independent variables I have tourists’ characteristics (age, country, gender, education levels) and trip characteristics (like experience of guides, itinerary and activities, educational opportunities, measured in an 11 point Likert Scale.

As dependent variables I have a series of responses on learning outcomes. Learning outcomes includes 3 variables: 1) knowledge (1-0 scale because is True/false), 2) attitudes, and 3) behavior intentions (measured in an 11 point Likert Scale). Each one of the dependent variables are formed of 7-8 different sub questions.

Besides that, in the middle, I have perceived learning (measured in an 11 point Likert Scale) that sometimes act as an independent variable and others as a dependent. My questions are:

1. Data does not meet normality assumptions. It is ok to rescale, transform and log?

2. I have PRE and POST responses, do you recommend me to use the change values in the data set to run MANOVA? –Rescaled, log and transform-?

3. Do you recommend me to group the responses of the sub questions to have 3 dependent variables instead of having a lot of sub questions within each dependent variable?

4. Do I have to use the perceived learning as a dependent variable? And is it ok to compare, let’s say: age X gender X trip characteristics with attitudes and perceived learning?

5. How do I know that the dependent variables are not correlated?

Thanks for any help.. and sorry for the long message 🙂

Daniela

Lucy says

Hello. Thank you for such helpful information on your website! Please may I ask; for my own research, I’ve run an intervention testing three DVs (e.g. depression, anxiety, resilience) at two time points (before/after) for two groups (Intervention and control). So, a 2*(2) design, but with 3 DVs that are correlated. I am hoping before intervention, no difference between groups across all three scales, but after the intervention, I would hope for significant changes for intervention group, across all three scales, compared with control and pre-test. Do you know if a MANOVA is appropriate, and if so, do you know how best to run this (for example, in SPSS) – examples seem to only include between-participants? Many thanks.

Victoria says

I’m trying to wrap my brain around this with the context of my research. The research question I am currently working on is: What is the impact of gender and the implementation of a freshman academy on academic achievement?

To answer this, I have eight years of student data (some pre-academy and some post-academy) that shows their cohort year, gender, GPA, and number of credits earned.

I’m a bit confused on what to use to answer my research question. Do I run a two-way ANOVA? Or since GPA seemingly also could impact credits earned, and vice-versa, should I look at a two-way MANOVA?

Thanks much,

A student with a brain about to explode!

Emma says

Hi Jim,

I am running two one-way MANOVAs for my final year project (and a further two-way with the data from both studies combined).

The first one-way was fine, but the second i’m not so confident about. The Pearson’s correlation came out at .808 when I tested for multicollinearity. I thought this was fine but I may have confused myself a little.

I know the DVs are meant to be correlated, but is this value too high? I have been trying to get some info but even in my textbook (Field, 2013) I can only find ‘acceptable ranges’ in relation to regression models. These ranges also vary between <5 and <10.

I am looking for some clarity in where my Pearson's value should fall between.

Thanks in advance,

Emma

Jim Frost says

Hi Emma,

Multicollinearity only refers to correlation between the independent variables and not the dependent variables. I don’t believe there is an upper limit to the correlation between DVs in MANOVA. You should be fine!

Eric Schmidt says

Hello Jim,

I need some help with a data analysis question. I am completing a research course and I am a bit stuck. I am sure the answer to this question will seem very obvious to you. Sadly, it has me a bit confused.

Here goes,

My research will examine stress levels and behavioural responses to unexpected positive stimuli and unexpected negative stimuli across different socio-economic circumstances.

Do I use MANOVA?

Variable include:

Socio-economic status

Stress levels

behavioural responses to (Surprise: Unexpected positive stimuli and Blindside: unexpected negative stimuli)

Think of a group of guys (differing SES) walking into a parking lot. they all discover parking tickets on their cars. They all react differently. I am trying to understand the factors that caused these different reactions. My hypothesis is that SES, Stress and excitability are contributing factors.

Can you help me out?

Actually, just writing this to you helped! LOL.

I look forward to hearing your reply.

Cheers,

Eric

Jim Frost says

Hi Eric,

Ha! If more people answered their own questions while typing it would make my job easier! 🙂

If your response variables are correlated, then it probably makes sense to use MANOVA. If they’re not correlated, using regular ANOVA (separate models for each DV) is probably fine. That’s the general rule of thumb. In your case, if responses to expected and unexpected stimuli are correlated (positive or negative), definitely consider MANOVA! Just look at the correlation between those variables to decide. I’m guessing yes, but I’m not in your field!

I hope that helps! Best of luck with your analysis!

Jeanie says

Hello Jim,

Thank you for this blog and a chance to ask questions, I am new to statistics, I have two questions for you.

I have one IV with two groups. Methods of contact: Telephone verses Secured Message

I want to see the affect on my two DVs: Response rate (number of responses from zero divided by number of attempts) and readmissions (number of days from zero to readmission).

First question: Would a MANOVA be a good choice or a two-tail hypothesis be a better choice?

Second question: Statistics wise, would I fair better if I separated my IVs (have two IVs) opposed to one IV with two groups?

Jeanie

Kay Lynn Stevens says

Thank you for your prompt reply! The test selector actually chose the Hotelling’s T^2, not the MANOVA.

Jim Frost says

Right, and Hotelling’s T^2 is the test statistic that MANOVA uses when you have two groups. So, it is in essence telling you to use MANOVA.

Kay Lynn Stevens says

Hi Jim,

Can you explain when to use a Hotelling’s T2 versus MANOVA? I am studying the impact of one dichotomous independent variable (defendant gender: male or female) on three correlated measures of juror decision making which are all continuous scale. I am sampling from jury-eligible individuals who live in one state. I used the statistical test selector function that Laerd Statistics offers, and it came up with the Hotelling’s T2, but it seems to me a MANOVA would do the trick.

Thank you!

Kay Lynn

Jim Frost says

Hi Kay,

Hotelling’s T^2 is a generalized form of the t-statistic that allows it to be used for multivariate tests. T-tests use the t-value to calculated the p-value for univariate tests. MANOVA uses Hotelling’s T^2 (and other test statistics) to calculate the p-value for multivariate tests like MANOVA. It looks like MANOVA uses Hotelling’s T2 when there are two groups, which makes sense because you’re assessing males and females.

So, that selector function is basically telling you to use MANOVA and it chose the test statistic for two groups.

Best of luck with your analysis!

Erin E says

Hi Jim,

What do you do if there is not enough of a relationship b/w the DVs? For example if the Pearson’s r is .168? Thank You!

Jim Frost says

Hi Erin,

If the correlation is very low, you can use regular ANOVA without losing any power. Just perform a separate ANOVA for each DV.

Lauren M says

Hi Jim,

I am running a MANOVA with one categorical IV and two continuous DVs. I was running the analysis and my Bartlett’s Test of Sphericity was not significant (p = 0.097) which I’ve never dealt with before. I’m not sure what to do next now that the factorial analysis cannot be done. I’ve heard getting more participants could help but I cannot do that due to time restrictions. I only have 52 participants. Are there other things I could do?

Nevein Mohammed says

Thank you

Nevein Mohammed says

Thank you for your reply. I think I should apply repeated measures MANOVA in this design, Can you help me in how to conduct this test in SPSS (steps). I have found many SPSS tutorials, but I got confused.

thank you

Jim Frost says

Hi, sorry, I don’t have SPSS.

Nevein Mohammed says

Hi Jim,

Also I have another question,

If I have a design of three groups (2 study and one control) and I want to see their effects on 7 DV (that are correlated). the DV are measured at 3 time intervals (pre, post and follow-up. in such case, you recommend me to use MANOVA ?

THANK YOU IN ADVANCE

Best

Jim Frost says

Hi Nevein, yes, that sounds like a good approach.

Nevein Mohammed says

Hi Jim,

Thank you for this informative post. I’m making a study with two IV (2 groups; study and control groups), and I have 3 DV that I measure at two time intervals (Pre and post). the IV are correlated. in this design, Would you recommend me to use MANOVA in analyzing my data or would you recommend a different approach ?

Aarti Dhanrajani says

Hi. Thanks for explaining the concept so well.

May i ask what should be done if there is multicollinearity in the DV?

Jim Frost says

Hi Aarti, multicollinearity among independent variables just means that they are correlated. For MANOVA, you actually want correlated *dependent* variables because that increases the power of the tests, as I discuss in the post.

Bailey W says

Hi Jim,

This post has been extremely helpful in understanding what data analysis i need for my thesis, however, can you help clarify if im on the right track for using MANOVA. I have three IV’s (persisters, remitters, and controls) and three DV’s (Tests – Flanker, Stroop, Parent Report) with data being assessed at 8 years old and then 18 years old, would MANOVA suit this sort of analysis?

Regards,

Bailey

Jim Frost says

Hi Bailey,

Yes, if the DVs are correlated, then MANOVA is a good choice. If they’re not correlated, just use regular ANOVA.

Jay says

Hi Jim,

I’m experiencing a similar quandary, however, my IV is continuous (Autism quotient score). I’m assuming from your response that it does not matter that there is only one IV. And MANOVA is a perfectly acceptable tool in these scenarios.

Thanks for your continued assistance.

Best,

Jay

Vree says

Hi Jim , I have a question.

I am currently conducting a final year thesis study with 1 independent variable (Gender) and 3 dependent variables (Perceived stress, anxiety and loneliness), titled Gender differences in Perceived stress, anxiety and Loneliness among International Undergraduates during the Covid-19 pandemic. I am trying to find if there are gender differences on the 3 variables. Can I run a one way independent anova 3 times for this study or a Manova?

I am genuinely confused as what to run because I only want to see the differences of gender.

Thank you in advance!

Vree

Jim Frost says

Hi Vree,

The answer is you can do it either way. Often times it’s just simpler to understand regular ANOVA results. You can try one-way ANOVA first with three separate models to see what results you get. However, if that doesn’t work *and* those three DVs are correlated, you can try using MANOVA. MANOVA does have some benefits as I point out in this article but it can be harder to interpret. So, if your ANOVA results for separate models seem to miss something you expect to be there, try MANOVA.

I hope that helps!

Alice says

Yes, I read your article about two-way ANOVA just now and it definitely cleared my confusion. Thank you so much for all your help. I really appreciate it.

Jim Frost says

You’re very welcome, Alice!

Alice says

Thank you so much for your help. Just one more question again. I came across a lot of Youtube tutorials employing Univariate analysis in SPSS to see the interaction effect of the IV’s on the DV when they have two IVs and one DV, like in my case. Will it be correct if I do the same?

Jim Frost says

Hi Alice,

If you’re performing ANOVA you’re not performing univariate analysis. Univariate analysis is the simplest type of analyses because you have just one variable. The simplest form of ANOVA requires TWO variables. One-way ANOVA requires one IV and one DV.

Additionally, if you’re talking about interaction effects, you’ll need a minimum of three variables. 1 DV and 2 IVs. An interaction involves at least two IVs. So, if you’re performing univariate analysis or one-way ANOVA, you cannot consider interaction effects. Typically, you’d be using at least two-way ANOVA or multiple regression.

I believe you’re talking about ANOVA because you’re posting in the comment section of an ANOVA post. So, I’ll refer you to my article about two-way ANOVA. In it, I talk about interaction effects amongst other topics. I also have an additional article about interaction effects you might want to read. However, read the two-way ANOVA post first because it covers the number and types of variables you need.

Wagner Fontes says

Hi Jim,

Thank you for this post. You did a great job in explaining the concepts.

If I may ask, I have one question:

If I had a thousand of dependent variables, How could I be able to interpret and draw groups of correlation among them using MANOVA?

A real-world example for that would be the quantification of a thousand proteins from cells in three different conditions (control, treatment 1, treatment 2). Currently I’m using ANOVA to analyze each one, but I’m pretty sure many of them are correlated, involved in connected cell-signaling pathways.

Thank you for your time!

Jim Frost says

Hi Wagner,

Wow, so a thousand dependent variables. That would be quite the knot to untangle! The same principles would apply but the results would be vastly more complex because you’re talking about multivariate relationships between a thousand DVs plus whatever IVs you have. I think it would require a custom solution to be honest that incorporates subject-area knowledge.

Radhika says

Hi,

Thank you for the informative and easily understandable post.

Can you please suggest a statistical measure for my data; I have three independent variable and eight dependent variables. The DVs are not correlated, for ex. DV1 mean 1.5 and DV5 mean 350.

Thank you very much

Alice Kenye says

Hi Jim,

Firstly, thank you so much for this useful blog. You are a blessing to many of us who are struggling with statistics.

Please give me some advice on the following question.

I have two independent variables and one dependent variable and I also want to see whether there is an interaction effect of those two IVs on the DV. Would it be better to employ MANOVA instead of using ANOVA?

Jim Frost says

Hi Alice,

You should use ANOVA because you have only one dependent variable. Because you have two IVs (presumably categorical), you should use two-way ANOVA. Click the link to see where I show examples of two-way ANOVA.

LadyMae says

Wow! Thank you so much for this, Jim. I’m currently working on my final year thesis and I’ve been confused as to whether to use ANOVA or MANOVA. It’s a lot clearer now. Thanks again!

Kehinde Ogunbiyi says

Hi, I am currently conducting a study on the effects of student type (domestic or international) on levels of trait emotional intelligence, mindfulness, emotional distress and perceived stress. I used a MANOVA analysis which found non-significant differences in three of the variables but not one. I would like to analyse the variable with the difference, Would I need to run a post-hoc (which apparently isn’t possible because there are less than three categories) or can I simply say the mean differences as it appears in the estimated marginal means?

Oksana says

Thank you very much!) This information helps a lot!

Oksana says

Dear Jim,

First of all, I hope you are safe in these worrying times of disease.

I want to thank you for your wonderful posts on statistics. They make things much clearer!

And if I may I also wanted to ask a question: you say that to apply MANOVA, dependent variables should be correlated, but I wonder if the sign of correlation matters? I mean should all the DVs be positively correlated, or they could be both positively and negatively correlated? For example, I have 5 DVs, and there are both positive and negative correlations between them, is it still possible to apply MANOVA in this case?

Thank you very much.

Kind regards,

Oksana

Jim Frost says

Hi Oksana,

No, the correlation sign doesn’t matter. All that matters is that the correlations among the DVs exists because it provides more information for the model to assess. It’s ok, and even good, to use MANOVA in the situation you describe with a mix of positive and negative correlations.

Ajab tareen says

Thanks Jim for your to the point reply, sure my dependent variable are correlated so i used MANOVA, Now i have both significant as well as non-significant result for DV, but stuck how to identify which one is significant among the five cultivars for a particular dependent variable.

Ajab tareen says

Hello Jim, Feeling pretty good to see your posts regarding statistics. I am going to analyze my research data. I had taken 5 different apple cultivars and determined TPC, TFC, mineral contents etc. Now which type anova would be good to analyze the data.

Jim Frost says

Hi Ajab,

I’m glad you like my posts!

It sounds like you can either use one-way ANOVA or MANOVA. It appears that you have one factor: apple cultivar. This factor forms the five groups. If your dependent/response variables are correlated, then I’d consider using MANOVA for the reasons I mention in this post. If they’re not correlated, consider performing one-way ANOVA multiple times for each of the DVs. While performing multiple tests can increase the family-wise error rate, it’ll be easier to interpret.

Sumit Mishra says

Can we use individual ANOVA rather than MANOVA since MANOVA is a considerably more complex design than ANOVA and therefore there can be some ambiguity about which independent variable affects which dependent variable. The dependent variables should be largely uncorrelated for MANOVA. If the dependent variables are highly correlated, there is little advantage in including more than one in the test given the resultant loss in degrees of freedom. Under these circumstances, use of a single ANOVA test would be preferable (French et al., 2008)

http://online.sfsu.edu/efc/classes/biol710/manova/MANOVAnewest.pdf

Do you agree?

Jim Frost says

Hi Sumit,

I agree that MANOVA models are more complex and interpreting the results can be more difficult. However, some cases really require it. I show one such case in this blog post where if you don’t use MANOVA, you completely miss the findings! I’d say try using ANOVA and see what you get. However, if you have multiple correlated DVs, there are some occasions where you might really need to use it. And, I disagree with what you right about using MANOVA for uncorrelated DVs. If your DVs are uncorrelated, you have less reason to use MANOVA. If they are correlated, you have more reason. Again, this post indicates one such scenario!

David Sanderson says

Jim,

I have a question on how far can we expand the independent and defendant amount. In my case I have 5 different offices types (independent variables) and a scores for 32 different categories (dependent variables). Can a MANOVA test distinguish if there is any significant differences between the office types and how would the data be interpreted?

Thanks David

Danielle says

Hi Jim,

I’m in the toxicology field and my project involves assessing the effects of 5 different compounds, with various concentrations of each, in wild type and mutant animals. I think in this case I would have 3 independent variables, right? Compound, concentration and animal strain. However, if I’m making all these comparisons, I’m losing power. So what I don’t understand is why a result would be statistically significant in a scenario were I would have, for example, only one compound, one concentration and one strain, but if I have multiple of each, this same result wouldn’t be statistically significant? Hopefully I made myself clear! Thank you for your website, you make statistics much more fun!!

100womenloudoncounty says

Hi Jim,

My study includes one independent variable with 3 levels (participation in one of 3 networks) and 3 dependent variables which are likely to be correlated (teacher expectations, teacher self-efficacy, and teacher collective efficacy). I want to determine which networks result in higher scores of these factors. I am having trouble wording my questions though and thinking about what information the MANOVA will tell me. I originally worded it as.. Is there a relationship between network membership and scores of teacher expectations, self-efficacy, and collective efficacy? But, to me this implies more of a correlation, which is not possible because it is not two pieces of ordinal data. Should I word it as differences instead? And is it possible for example that more than one network will show a statistically significant relationship to a DV or multiple DVs? Should I have a research question which addresses the possible correlation of my DVs?

I don’t know if that makes any sense. I know what I’m trying to investigate, but I’m not sure how to word the questions and I also wonder how specific I should make my hypotheses. For example, I suspect one network will be statistically higher in teacher expectations and possibly collective efficacy. But, I also see the potential for another one to be statistically higher in collective efficacy in regard to another.

Is it possible to stick with the relationship question and then have a hypothesis that predicts a relationship between more than one IV and the same DV?

Desiree Tse says

Hi Jim,

Thanks for the informative post. I am wondering if only Roy’s largest root is significant out of the 4 MANOVA tests, would you still take the result as significant?

And how to interpret a quadratic interaction between my within and between subject variables?

I am testing my participants’ memory on emotional faces, which have been categorized into negative, neutral and positive faces for data analysis. They are also the within subject DVs, while I got 2 clinical populations and 3 treatment conditions as my between subject variables.

If MANOVA doesn’t work, what other tests would you recommend? I am interested in the interaction between the between subject variables.

Thanks,

Desiree

Michaela says

Hi Jim,

thank you for an informative post! I am currently designing a grant proposal and have always struggled with stats so I was wondering if you could please help me out. I want to be looking at the differences of autistic and neurotypical adults’ performance on reading facial and body language expressions – there will therefore be two populations (autistics vs. non-autistic) and 3 conditions (one where only faces are shown (2 types of emotions will be displayed)), one where only bodies are shown (again, 2 types of emotions will be displayed), one where faces and bodies are both shown (either displaying congruent or incongruent emotions)). All participants will be completing all the conditions.

Previous papers that have looked into this used repeated measures ANOVA, however what I want to do is have all participants complete a couple additional questionnaires that will be looking into a condition that is often associated with autism (alexithymia) – it is therefore very possible that my populations will look something like neurotypical adults with low score for alexithymia, neurotypical adults with high score for alexithymia vs. autistic patients with low score for alexithymia, and autistic patients with high score for alexithymia. The presumption is that autistic patients with high score for alexithymia will perform worst, while neurotypical adults with low alexithymia score will perform best.

The aim of the project is to determine to what extend do autism and alexithymia contribute to the impairment of expression recognition (individually and combined) – is it still okay to use ANOVA or would MANOVA be better? Or am I meant to be running a regression analysis? Any post-hoc tests that should be considered?

Thank you very much for your help!

Best,

Michelle.

Laura says

Dear Jim, thank you very much, your reply was very helpful!

I have now performed the MANOVA analyses and have found that one of my group variables, variable A, (described in my first post) best discriminates between brain measures (the outcome measures), and would like to follow up on this with a post-hoc test. Variable A consists of group 1, 2, 3 and 4 and I would now like to know if one of these groups is driving this effect. Could you please tell me if this is possible to test and what would be the best way to do this? I have read online that ANOVA is sometimes used to follow up, but I am not very interested to see which groups are associated with brain measures, I just want to know which groups differ across all brain measures.

Thank you so much in advance!

Best,

Laura

Jim Frost says

Hi Laura,

It sounds like you need to perform a post-hoc test to determine which groups are significantly different from the others for variable A. Post hoc tests a common follow up for both MANOVA and ANOVA. MANOVA and ANOVA tell you that there is a significant effect while the post hoc tests help you map out the nature of those effects–which groups are significantly different from the others.

I hope this helps!

Jessica says

Hi Jim,

Thank you for a useful and informative post.

I was wondering if you could help me with a question.

I am conducting a study looking into the effectiveness of a post-therapy relapse-prevention intervention in maintaining treatment grains after therapy. Questionnaires measuring treatment gains quantitatively (e.g. mood) are taken at three time points: pre-therapy (T1), on completion of the therapy (T2) and 2 months after the therapy (T3).

I am comparing a control group completing therapy but without relapse-intervention with a group who receive the relapse-prevention intervention between T2 and T3. In order to test the effectiveness of the intervention, I want to see if the IV (intervention group or control group) predicts the DV (change in outcomes between T2 and T3).However, the DVs are correlated AND I will need to account for the change in outcomes from T1 to T2 (a covariate) and so I thought an MANCOVA would be appropriate.

So I have 2 IVs and 4 DVs.

However I have a much smaller sample size that I had first intended (n=15 per group – total n=30). so my question is is this too small a sample size to conduct a MANCOVA with? If so, what would be a better option?

I hope this makes sense.

Many thanks in advance!

Jessica

Jae says

Hi Jim,

I’m doing a study with 1 IV and 3 DVs. In theory, my 3 DVs should be at least weakly correlated, although my results do not show this. 2 of them are very strongly correlated (r is very close to +1), while the third is not correlated at all with either of them. Can I still use a MANOVA? or should I do 3 separate ANOVAs instead? If I were to do the ANOVAs separately, is there a way in which I reduce the Type I error?

Thank you in advance.

Jim Frost says

Hi Jae,

It still sounds like MANOVA would be helpful given the correlations. Although, you probably should investigate why the correlations are so high between a pair and non-existent with the third variable when that doesn’t match your theory. It almost sounds like two variables practically measure the same thing and third isn’t related at all. It’s not necessarily wrong, but worth investigating because they don’t match your expectations. You should check to be sure that you’re measuring what you think you’re measuring, and that there were no measurement/data entry errors.

Best of luck with your analysis!

steph says

HI, thanks for your kindly help. I have a doubt.

I have a IV with 2 groups (control/experimental), and one DV (sensory processing). However, the DV has 4 main scales. The way in which I measured was through a questionnaire that doesn’t have a single scores, but 4 scores per each scale. So, is it appropriate using a MANOVA with my DV plus 4 IV??

Jim Frost says

Hi Steph,

If those four scales are correlated to some extent, then it sounds like you’d get some real benefits out of MANOVA. If they’re not correlated, you can just run separate ANOVA analyses for each scale. Actually, because there are just two groups, you can use t-tests if they’re not correlated. But, yes, if the four scales are correlated, definitely consider MANOVA! MANOVA provides benefits when the DVs are correlated.

Litsa says

Hi Jim,

Thanks so much for the post! I have a question. Can we use MANOVA when we have more than one independent variables? I have a design in which I am testing 4 dependent variables and I have 4 independent variables also. I have used lmer in R so far for each of the 4 dependent variables looking at the influence of the independent variables. Do you think I should use MANOVA? My dependent variables are correlated.

Jim Frost says

Hi Litsa,

Yes, it sounds like MANOVA is a good possible analysis to try with your dataset. You can use more than one independent variable. And, it provides the most benefits when the dependent variables are correlated.

Best of luck with your analysis!

Sylvia says

Hi Jim – your blog post and the follow-up questions and your replies are very helpful and much appreciated. Would you please advise on the following questions – is MANOVA most appropriate here and what should the sample size be per group? We have 3 groups who will be measured once pre-operatively and 4 times post-operatively. There are 13 measurements, which can be grouped as patient-reported outcomes (5 measures; means) and clinical outcomes (8 measures, means). We want to compare pre- and post-op differences by group and also compare post-operative measures between groups. We expect there to be some correlations among the measures in both the patient-reported outcomes and the clinical outcomes. We also have 10 measures of patient characteristics (e.g., age, gender, BMI, etc.; 4 means, 6 categorical) that we want to compare by group. I hope I’ve provided enough information for you to advise on this. Thanks!

Ifedayo Adu says

Hello Jim,

Good day Jim. I find your articles on statistics quite interesting. However, I need you to help me with a statistical issue. Please may I know why a researcher would decide not to introduce a moderating variable in a model. Thanks for your anticipated assistance.

From,

Adu Emmanuel.

Jim Frost says

Hi Adu,

Moderation effects are included in models as interaction effects. Read my post about interaction effects for more information.

The only legitimate reasons that I can think of for why analysts would not include an interaction effect in the model are either because the effect is not statistically significant or because theory very strongly suggests that the interaction effect is not appropriate for the model.

If interaction effects are significant and appropriate for the subject area, you risk extreme interpretation problems by not including them in the analysis. You can read about that in the post I link to!

Meysam says

Hi Jim,

Thank you for this helpful information about MANOVA,

I have a question, In one of the study I have done for my PhD, I have two independent variables, each categorical with two levels, and I measured 3 dependent variables which are correlated. I also have a covariate.

Q1: First of all the data significantly violated the assumption of homogeneity of covariance (p<.00000), considering this can I use the Mancova test (my sample size in each of four groups is about 95, in total 380)?

Q2: When I do a separate ANCOVAs on each dependent variable I have significant result for both IVs, however, when I use MANCOVA the effect of one of my IV becomes non-significant, which test should I report in my thesis?

Thank you

Minie Bulay says

hello Jim, I find your blog very useful especially for those struggling in this realm of statistics, like me. I just want to ask, the way of framing questions in MANOVA, like when my IVs are Sex and Study Habits, and the DVs are the Learning gains, GPA and NAT scores? how will I state if MANOVA applies for this?

Jim Frost says

Hi Minie,

If your DVs are correlated, then MANOVA becomes a more powerful analysis because it can use the correlation between the DVs to increase the statistical power. It can also detect multivariate effects that ANOVA can’t, which I demonstrate in the blog post. If your DVs are not correlated, then MANOVA doesn’t really provide additional benefits compared to ANOVA.

I hope this helps!

laura says

Hi Jim,

Thank you for this very informative post! I hope you could give me some advice regarding the following issue:

I am trying to examine which of two group variables best map to underlying brain measures. I have two independent (group) variables (say A and B) and around 30 dependent variables. I would like to examine whether group variable A (group 1,2 or 3) or B (group i,ii,iii) best discriminate groups based on these brain measures. I was thinking of running MANOVA twice, once with variable A and once with variable B, but is there a way to test whether these results are signficantly different so we can conclude for instance that group variable A best maps to underlying brain measures?

Thanks very much in advance!

Best,

Laura

Jim Frost says

Hi Laura,

It makes me happy to hear that you found the post to be helpful!

MANOVA will help you out if those 30 dependent variables are correlated amongst themselves. With so many dependent variables, you will have to be aware of sample size concerns. I’ve written about how to ensure that your linear model has a sufficiently large sample size based on the independent variables and other terms in the model. I don’t know how the number of dependent variables factors in, but it’s something to keep in mind.

As for determining which categorical variable is better, you can try including both in the model at the same time. This approach can give you some valuable head-to-head comparison information. You might also want to read my post about identifying the best independent variable. I write about this in the context of regression models, but it’ll give you some good ideas to consider and other things that you should disregard.

I hope this helps!

Pamela Marcum says

Wow, thanks Jim for taking the time to write such a wonderfully detailed and helpful reply, and for providing links to your other posts for much-needed background reading. Can’t express enough how appreciative I am of your willingness to share such hard-earned knowledge with others!

Sarah says

Hi Jim, Thank you for this blog. Do you by chance have a reference for you last section “When MANOVA Provides Benefits”?

Jim Frost says

Hi Sarah, I don’t have a specific reference but these are commonly understood benefits of MANOVA. I’d imagine that any textbook that covers this analysis will confirm them.

Pamela Marcum says

Hi Jim,

First of all, thanks so much for this extremely informative and comprehensive blog. I’m thinking that MANOVA might be exactly the tool that I need for a problem that I am currently grappling with, but an additional “twist” in my data might actually invalidate the use of MANOVA. So here goes (I am an astronomer): I have a plot of gas mass normalized by luminosity (y axis) versus luminosity (x axis) for a large control sample of galaxies. This plot is a nonlinear relation in which dimmer galaxies generally have higher normalized gas masses. Overlayed on this plot is a (smaller) sample of galaxies that is the focus of my research. If I squint and look sideways at the plot, I think that my sample trends towards having somewhat larger normalized gas mass as compared to the control objects with similar luminosity.

I’d like quantify the statistical significance of any gas mass enhancement in the small/study sample. Here’s the problem: the smaller set of data mostly bunches up at the low-luminosity end and as a result does not cover the full range of X values (luminosity) represented by the control sample and therefore does a poor job of sampling that relationship. Because the smaller set of data are at the low-luminosity end, they are expected to have higher normalized gas mass (that’s what the relationship defined by the control sample shows), so the fact that the study sample objects are generally gas-rich is not what is surprising. What WOULD be interesting is if those galaxies have MORE gas mass than what would be predicted by the relationship for their given luminosity.

My concern is that the smaller sample being so heavily skewed towards one end of the X-axis and not “adequately” sampling along the same range of X values as the control sample will invalidate any MANOVA application (?) On the other hand, there is nothing about the example you provide above that would have excluded the possibility that “satisfaction” would have been skewed to one of the extremes for one of the exam methods. In that example, however, the sample sizes being compared are equal (or nearly so), unlike my situation.

If MANOVA is definitely not the tool for my situation, would a better approach be to just truncate the control set so that the same x values are covered between both samples, and then apply a 1-dimensional test to the Y-axis parameter ? (A steeply-rising “knee” in the gas mass to luminosity relationship in the mid-range of the x-axis would be mostly clipped out if a truncation to the control sample was performed. Losing the information of this underlying relationship in any statistical comparisons between these 2 data sets could be an undesirable consequence?). Thanks for any advice you might have, particularly with regards to the robustness of the MANOVA test to such a situation in which one sample is seriously skewed towards one end of the x-axis relative to the other, and has significantly fewer data points than the other.

Jim Frost says

Hi Pamela,

First, I just want to let you know that I LOVE astronomy. I totally don’t have any official education in it but I love to absorb as much of it as possible! In a parallel universe I’m an astronomer or maybe a physicist!

I think what you need to do is actually fit a regression model and include an sample indicator variable and an interaction term. The gas mass normalized by luminosity would be your dependent variable and luminosity would be an independent variable. You’d also need to include an indicator variable that identifies whether the data are from the control sample or your sample (you’d need to put all the data in one data sheet). Then include a two-way interaction term (luminosity*sample indicator). You should also include the indicator variable as a main effect/independent variable. Collectively the indicator variable and interaction term will tell you whether the relationship between the independent and dependent variable is different between your sample and the control sample. The main effect for the indicator variable will tell you if the relationship is shifted up or down on the X-Y scatterplot. The interaction effect tells you whether the slope is different. Use the p-values for these terms to determine whether each one is statistically significant.

I *think* that is what you need to do based on your description. I’ve written a couple of posts that describe this process that you should read:

Comparing Regression Lines

Understanding Interaction Effects

There is one possible complication that I can see with your scenario. You mentioned that it is a nonlinear relationship. The way forward depends on whether that is nonlinear in the common meaning of the word (i.e., the line isn’t straight) or in the exact statistical sense. The process I describe above works for linear models. But linear models can fit curves using a variety of methods. However, if it’s truly nonlinear in the statistical sense of the word, you’ll need to use an entirely different and unfortunately much more complex methodology. I’ve written two posts that should help you answer that question. The first defines the differences between linear and nonlinear in the world of statistics. The second walks you through the different ways of fitting curves using an example dataset.

The Difference Between Linear and Nonlinear Regression

Curve Fitting Using Linear and Nonlinear Regression

Hopefully a linear model will fit because that’s a lot more straightforward to work with! Oh, and about your sample being skewed towards one end of the range, I don’t think that’s a problem. You should be able to determine whether the same relationship applies to both samples or not. One issue I see is if the two samples don’t overlap. In that case, if the relationship is different, it might be hard to determine whether the difference is due to whatever the defining characteristic of your sample is or just because you’re in a different range of the data. Sometimes the relationship can change for the same type of data as you move along the range of data.

At any rate, I hope this helps!

Jim Frost says

Hi again, one more thought in addition to my previous reply. Given that there is curvature in your data, it probably is a problem that your data just covers a portion of the range. You won’t be able to use the same model because if it’s just a portion it won’t have the same curvature most likely. You might need to truncate the control sample data to fit the same range of data that your sample covers. I’m not sure how many data points the sample data has in that range or if there might be other subject related concerns for that approach. But, it would let you compare the models for the same range of data and if the curvature was different within that range, it would be meaningful. Whereas if you compared your range to the full range, the difference wouldn’t be meaningful.

Omotayo says

Thanks for your kind response.

Omotayo says

Hi Jim, I need more clarifications, your comment on this subject seems to be tending towards my needs. However, my question is, between ANOVA and Manova, which of them is suitable for an hypothesis stating that, there is no deference between male and female in terms of impact of Staff development policies, practices on job performance. Thanks for your response in anticipation.

Jim Frost says

Hi Omotayo,

If gender is your independent variable and staff development policies and practices on job performance are your dependent variables, and those two DVs are continuous variables that are correlated, I’d recommend MANOVA.

Jim

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!

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!

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

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.

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!

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!

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.