Tuesday
Apr272010
ANOVA, MANOVA, and MANCOVA Question: What is the difference between ANOVA, MANOVA, and MANCOVA? (Eric, Lafayette, IN)
Jeremy Taylor | Tuesday, April 27, 2010 at 8:25PM The difference can definitely be confusing. There are differences on a few different levels. First, an ANOVA is different from both a MANOVA and MANCOVA because an ANOVA has only one dependent variable, while both a MANOVA and MANCOVA have multiple dependent variables. An ANOVA typically compares a continuous (a.k.a interval or scale variable) between multiple independent groups of responses (usually 3 or more groups).
By contrast, both a MANOVA and MANCOVA have multiple dependent variables, but there are differences between the two as well. The difference between a MANOVA and MANCOVA lies in the number of independent variables. A MANOVA, like an ANOVA, has only one independent variable (which is typically a categorical variable that represents independent groups) and compares multiple dependent variables between independent groups. A MANCOVA is a similar concept to MANOVA, except it allow for multiple independent variables (a.k.a. covariates).
In a MANCOVA, one is able to examine multiple dependent variables for differences between independent groups, while controlling for other variables that may also be related to the DV. These covariates may be either categorical or continuous. I hope this helps, Eric! Please keep the questions coming!
Reader Comments (58)
Hi,
Relevant to the above discussion, I have a query:
I'm interested in analysing a pre-post-control design with a follow-up. Both groups receive the same measures pre, post, and follow up. However, I find it quite confusing in my reviewing various other studies in terms of their methodology.
Basically, I want to know if the best method for my analysis is a MANCOVA, with the several pre-intervention measures as covariates (is there a limit to the number of covariates?) Also, assuming that gives me the change scores pre-post, I also predict change between post and follow-up. How do I handle this?
I am struggling to find a clear account. My DVs are all conceptually related (collectively they are part of a broader construct), so MANOVA is fine, and for change scores the pre-test covariates seem indicated, but then what do I do for the difference between post-test and follow-up?
Any clarity would be much appreciated!
Thanks!
Joe
Sorry for the delay in response, Joe. How many time points are you collecting/analyzing in all? If there is only the three (pre/post/follow-up), what is the approximate time between each and is it equal between each of them?
Hi, on the same point, one quick question: do the various DVs in a MANCOVA (or MANOVA) need to be independent of eachother?
Thank you
cheers
Roman
Hi Jeremy,
I only noticed your reply now. I didn't get the email notification, but did for Roman's comment.
I'm collecting data three times in a field study, and the pre-post measures are collected before and after 4 lessons in an educational context, so the data collection turned out to be not exact for all groups in terms of time, but is equal in terms of class sessions. Then the follow-up was due for 6mths, but that too looks to not be exact for all groups due to various field issues and cancellations, so the range will be 4-6mths.
If the question is too big and involved, perhaps you can recommend a book that deals with the above kind of design and analysis?
Thanks,
Joe
Hi,
I'm planning on a research study (Survey) to examine how different factors (patient's gender, diagnosis, clinician's gender) affect clinician's treatment decisions (dosage of treatment-once a day or once a week). We will send out questionnaire controlling independent variables (ex: 3 year old male vs 3 year old female) to group of people.
I'm guessing MANCOVA is the right tool to apply. Please clarify.
Thanks,
Ram
First of all, sorry for the delay in my reply, but I've been on my honeymoon for the past few weeks.
TO JOE: I would recommend the book "Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence" by Singer & Willett
Here is a link to the book on amazon: CLICK HERE
TO RAM: What is the nature of your dependent variable? Is it dichotomous (once a day vs. once a week)?
To Jeremy: Yes, the dependent variables are thee options (Once a week 30 min, Twice a week 30 min and Once a month 30 min).
Thanks in advance.
Ram
Ram: thanks for clarifying. If your deponent variable is categorical (as opposed to continuous/scale), which it sounds like yours is, then you will need to use a logistic regression. More specifically, you'll need to use a "multinomial logistic regression". Typically, MANCOVA is used for dependent variables that are continuous in nature. Also, MANCOVA is used when there is multiple dependent variables (DV), whereas ANCOVA is used when there is only on dependent variable.
For example, if I was analyzing student achievement and I had 5 different measures of this construct, I might use a MANCOVA to examine them. In your case, I believe you only have one DV (with 3 categories), so a univariate analysis would be appropriate (as opposed to multivariate). I hope that is helpful!
Hi
I need to analyze the data for a non randomized clinical trial (test and control) with measurements taken at 3 time points. So, far, I have been using repeated measures ANOVA for interim analysis. Now the data is complete and I need to run the complete analysis. What other tests could be very useful in this research? Any advises will be greatly appreciated.
Violet
I would like to know the group differences between performance on six neuropsychological measures between two patient populations. Should I do an ANOVA or a MANOVA.
thank you
Great question Cathy,
The answer depends on how you conceptualize the six different tests. If you conceptualize them as measures of a shared/related construct, then I think a MANOVA would make sense. If you conceptualize them a six completely independent constructs, then ANOVA makes more sense. I hope this is helpful!
If I wanted to see if there was a significant difference between x and y, I would use a t-test. But, what if I wanted to find the significant differences between several factors, so like I wanted to see if people did better in 3 classes if they had tutoring. I want to compare no tutoring math with tutoring math, no tutoring English with tutoring English, and no tutoring physics with tutoring physics. I want to find if there is a significant difference between each pair. Do I use a MANOVA for that?
Thanks.
Thanks for your question, Ashley! Do you have scores for each academic subject for each case (i.e. does each student have a score for every class)?
Hi, I am doing pre, post and follow up (at 2 months) on a program intervention (IV). I have six DV's but want to control for one of them before I make conclusions on the effect of the program on the other five DVs. Eg. I want to make sure the other five DV's dont improve just because patient's depression improved, and then want to see if improvements are sustained, What do you suggest for analysis?
Thanks
Hey Kim,
Based on the information that you provided, I think a growth curve model might be a good option for you. In a growth curve model, you can estimate the effect of intercept and slope separately, while also regressing the intercept and/or slope of any variable on the intercept or slope of any other variable.
In your case, you might regress the slope of your "other five" DVs on the slope of your control DV (e.g. depression), and then see if the slopes of the remaining five (when the slope of depression is controlled) are equal between the intervention groups, by testing a nested model where slopes are constrained to be equal between the intervention and control groups. I hope this is helpful!
Hey Jeremy,
I found your advice very helpful. Still I have some questions left to be solved. I am using a MANCOVA in order to test the influence of 4 different groups on the evaluation of a product (three DVs).
I need to include covariates. Therefore I have already confirmed the homogeneity of the regression slopes. Now that I conducted the MANCOVA, it was stated that although the Box-M Test was not significant, the Levene-Test for the dependent variables was significant in one case. How do I proceed? Do you have any advice?
And one question concerning ANCOVA: What can I do, if the Levene-Test is significant? Is there any other method to test the mean difference between groups, in case I use covariates?
Additionally, I would like to find out if there is a difference in those 4 groups over time. At the first measurement I ask for the evaluation of the product without any treatment. Before the second and the third measurement of the evaluation I introduce further information. Which method is the best to be used?
I hope I could give you enough details to answer my questions. If not, please do not hesitate to ask me.
Thank you very much in advance,
Eva
First of all, thank you for the wonderful questions, Eva. However, I must warn in advance, that the depth and breadth of the issues you've asked about may be challenging to fully address in a forum setting. With that said, I'll give it a shot:
With respect to the significance of the Levene-test, there are several things to consider here:
1. how large is your sample?
2. how severe is the violation of the equal variance assumption?
A significant Levene-test indicates that the variability in the dependent variable is unequal among the different groups in your analysis. what steps you take next are dependent on these two questions, as well as other factors. In some instances, you may not need to take any additional steps (especially since your box – M test was not significant).
With respect to how to evaluate differences in your groups over time, do I understand correctly that the four groups you have are different treatments? If so, I would probably still advise using a growth model, examining the equality of growth (slopes) overtime among your groups.
I hope some of this is helpful, and feel free to follow-up with additional answers to my questions, and I'll try to offer additional assistance if it is needed.
Thanks.
Jeremy
I use 10 different groups all of them having a different treatment. My sample consists of 450 people so that in every group I have 39-49 respondents.
Although I told you last time that I was using a MANCOVA, I had to adjust my method to an ANCOVA because my dependent variables do not all express the same. The Levene-test is still significant in some cases. In the meantime I've read that I might still use the data but accept a significance at the 0.01-level instead of 0.05. What do you think about it?
Thank you for your answer so far.
Eva
Hey Eva,
Thanks for the additional info. I'd be concerned about the number of groups, relative to your sample size to be honest. That may vary well be a large factor in your significant levene-test actually, as it is more vulnerable to being significant when the N of each group is lower. As sample sizes get smaller, a small number of outlier scores can have a large impact on the variance.
What other covariates are in your model (besides the treatment grouping variable)?
I have different covariates depending on the dv I'm analyzing. In one case it's only one covariate, in others I include 6 different ones. This is another complex factor. I've tested them on the homogeneity of their regression slopes and their influence on the dv.
You could also see if any of the other covariates are associated in a linear way with the heterogeneity of your error, by plotting the predictors against the residual in scatter plots. That could tell you if transforming one of those predictors might help (or the outcomes)... I hope that helps and let me know if you have other specific questions!
Is MANCOVA a suitable analysis tool to use for the following analysis,
What I am doing is analyising and trying to improve a resource evaluation tool. To do this I have broken down the tool into multiples descrete sections, each having a mark awarded out of 10, I average these out once conducted to get an average score out of 10. I also have an out of 10 mark ordained by mass survey, which I am taking to be the 'right' answer.
What I want to do, is to try out different numbers of these descrete sections, and see if it is possible to use less of them and still arrive somehwere close to the 'right answer'.
After I have done this, I want to be able to compare these results for multiple resources (10), so that I can find out the best combination of descrete sections (allowing me to get close to the 'right' answer) on average for around 10 resources
Somebody suggested doing a MANCOVA analysis, but statistics is not my strong point!
Fantastic! Could you please just go ahead and write a textbook that makes it this simple! This was the perfect answer I was looking for NOW as I am in the middle of completing a thesis and it's all becoming meshed together after hours and hours of work! Thank you!!!!!
I want to compare 2 patient groups (Depressed vs. nondepressed) on 7 or so neuropsychological measures that are correlated significantly with one another (but all correlations are very small r < .10). I would like to control for 3 continuous variables (age, SES, pubertal development). I think that MANCOVA may be the best approach. Does this sound right? Related to this, I need to do a power analysis and am wondering how to go about it. Are there references on this you would recommend? Thank you!
hi
if you have "7 or so neuropsychological measures that are correlated significantly with one another " , I recommend you to read "analysis of longitudinal data: by "peter diggle " to account for the structure of correlations between your dependent variables . to realize which of the models "marginal model, random effect model, transition model" fits your data better.