# Repeated measures ANOVA within and between factors

I have conducted repeated measures ANOVA, with 2 factors: One within factor (time, pre-post intervention) and one between factor (treatment, two groups). I have measured different dependent variables. I find in all the cases an effect of the within factor, an effect of the between factor, and only in some cases an interaction between both. I want to know how to interpret these results.

• What does the interaction mean?
• Is the significance of the factor treatment (between) sufficient to be able to say that one group is superior to other one, that one treatment is better?

EDIT: The measures I took in three moments are: time spent using technologies, frecuency of use, abuse.. The significant interaction is for within factor (moment) X between factor (group), but it's only significant for the time spent using technologies. What means the sugnificance of between factor? Why it's important the intetaction? Thanks

The measures I took in three moments are: time spent using technologies, frecuency of use, abuse.. The significant interaction is for within factor (moment) X between factor (group), but it's only significant for the time spent using technologies. What means the sugnificance of between factor? Why it's important the intetaction? Thanks

• I think you need to be more specific about the problem. What is the model? What factors were significant and which ones weren't? Commented Aug 31, 2012 at 20:06
• If you have both pre vs. post & treatment1 vs. treatment2, & they were significant but the interaction wasn't, then you may have had a failure of randomization. You want your pre-treatment observations to be equivalent & only your post-treatment observations to differ. Ie, you want your interaction to be significant, but your main effects not to be. Also, if you have >1 DV, you should probably be doing MANOVA. Commented Aug 31, 2012 at 22:46
• Then, the most important result is the interaction? The allocation to the different conditions was random. Thanks Commented Sep 1, 2012 at 9:29
• This is a program of prevention of technological addictions. One of the conditions or groups is the traditional program and the other contains additional control techniques. The total sample comprised 1160 students. I have three measures: pre, post and follow-up. Commented Sep 1, 2012 at 9:41
• The dependent variables are several: the frequency of use, time of use, the degree of dependence ... There are no differences between the previous groups, homogeneous groups. I've done ANOVA and MANOVA. For example, I find an effect of between and within factor when I take pre-post dates. And only appears a significant interaction (time X group) for the time of use. My doubt is what means each one of the effects. I don't know if I can say that by having a significant factor between, there is a treatment that produces a superior improvement. I don't understand the meaning of the interaction Commented Sep 1, 2012 at 9:42

I assume time of use refers to an addiction (such as use of a drug). Also when you say dependent variables i think youprobably mean the predictors (usually called independent variables). Time of use interacting with treatment group could mean that the effect of the intervention can be stronger/weaker depending on how recently the subject was using the drug for example.

• The measures I took in three moments are: time spent using technologies, frecuency of use, abuse.. The significant interaction is for within factor (moment) X between factor (group), but it's only significant for the time spent using technologies. What means the sugnificance of between factor? Why it's important the intetaction? Thanks Commented Sep 2, 2012 at 10:44
• I think the meaning is exactly what I said. At the three different times the time spent using the technologies changes significantly. But it doesn't for the other variables (abuse and frequency of use). That is all there is to interpret. Regarding the importance of the interaction, it is important because it says that time spent using technologies will not have the same effect at different times. Commented Sep 2, 2012 at 11:06
• Thanks. And how can I know if one of the programs is better? Then, what means the significance of between groups factor? Commented Sep 2, 2012 at 11:21

What does the interaction mean: It means the effect of treatment differed as a function of time. This is almost certainly the outcome you desire.

Is the significance of the factor treatment (between) sufficient to be to say that one group is superior to other one, that one treatment is better: Almost certainly not. As mentioned in the comments this might suggest that your groups were actually different at pre - intervention.

The between-within group interaction can be interpreted as such: does the difference between moments (within) depend on the treatment group that they are in (between)?

The math behind this is very simple but important. Let's say you only had moments 1 and 2. We would find the interaction by subtracting moment 2 from moment 1, and use that value as a dependent variable in the model. So your dependent variable is now the difference between moment 2 and moment 1, and your independent variable is still the treatment group. Now if you run this model and interpret it normally, the interpretation will be very similar to above; just interpreted in terms of how the effect of the within-subjects variable is dependent on the between-subjects variable.

So if you have a significant interaction for time spent using technologies when comparing moments 1 and 2, that means that the difference between these moments for time spent using technologies depends on the between-subjects variable (treatment) that they receive.

To answer your second question, your between-subjects results and interaction results are complementary but tell you rather different things. These are not 2 between-interactions like interpreted elsewhere on this page. The between-subjects test can tell you if treatment 1 is more effective than treatment 2. So, on average across moments, this would tell you if treatment x is more effective than treatment y in a statistically-significant manner. The interaction would then tell you if the difference between these moments depends on the treatment they receive.

The interaction is not necessarily important in determining whether the treatment is effective or not, but if you're interested how the treatment affects how participants' time spent using technologies changes between moments, it is ideal.

PS: I know that this question is extremely old, but this is the first and most relevant result from search engines and I haven't seen a fully-correct answer yet.