# How to perform this ANOVA?

I am interested to know if we have 3 dependent variables, and 2 independent variables, online and face to face, with 2 levels each, as in the example below. The sample size is 30 for each mode of study - 30 participants for online mode and 30 for face to face.

1. What type of ANOVA do we need to conduct?
2. Do we have to analyze each dependent variable at time? For instance, we first conduct an ANOVA for "graduation Time"; then another ANOVA for "Recall" and finally another ANOVA separately for "Job Skills"?
3. Will it be more complicated to conduct a MANOVA, instead of conducting separate ANOVAs?

Example: Mode of study (online (6 months, 12 months), face to face (6 months, 12 months)) has an influence on individual’s graduation time, recall of material, and job skills

Here is an external link to one of many resources that can help provide perspective on your question:

It sounds like you are looking for a MANOVA. The question of complicated is more of a relative one. If you look at the resource above, you will see that:

• A two-way ANOVA has two independent variables (which matches your case). That said, a two-way ANOVA still has only one dependent variable, which doesn't seem to fit the case that you described. Now, perhaps the two dependent variables are not actually dependent variables, and are levels. If one was able to recast them like this, then you might be able to fit things into a two-way ANOVA. That said, it doesn't sound like this is the best approach.

Based on this, we can then conclude that your case may better be cast as a MANOVA. A MANOVA fits the scenario when you have several independent variables and several dependent variables (which you described). If you have never done MANOVA before, and you happen to use R, then you might have a look at the excellent resources provided by QuickR covering MANOVA's.

As they show under the simple MANOVA example (which debunks the notion of complexity in my mind), if you have more than one "dependent (outcome) variable, you can test them simultaneously using a multivariate analysis of variance (MANOVA)."

In your case, we could let Y be a matrix whose columns are the dependent variables. Thus, with 3 dependent variables, and 2 indepedent, you might have the following R code:

Y <- cbind(y1,y2,y3)
fit <- manova(Y ~ A*B)
summary(fit, test="Pillai")


For information on testing, you can look online in a variety of places. The link shown at QuickR does provide a brief description.

• Thank you for the elaborated response. Actually, these are 3 dependent variables. I have never used R before. Will SPSS be more complex to conduct the MANOVA, as compared to R? Another question is that if I conduct an ANOVA 3 times, will that be more prone to Type I Error, in comparison to conducting a MANOVA? Many Thanks Apr 14, 2014 at 13:27