# Repeated Measures ANOVA or ANCOVA?

We recently conducted an repeated measures experiment consisting of two conditions. Each condition consistent of three tasks. The tasks are seen as random factors because they are not comparable among themselves. We measured the task completion time.

I have seen something similar, that was evaluated using ANCOVA, but I don't understand why you would use ANCOVA and not a Repeated Measures ANOVA.

Is ANCOVA more suitable due to the fact, that each task is different?

I am really new to Statistics. Maybe somebody can shed some light on that topic for me?

• Have you seen this thread? Can you elaborate on what is the difference to your case or why you are not satisfied with the answers given there? Commented Feb 19, 2014 at 14:14
• @amoeba Yes I have seen this thread. I was wondering why someone would use ANCOVA, because I would have choosen anova. Commented Feb 20, 2014 at 19:36
• Well, it seems to be a contentious question with different people arguing in favour of different options. If you read the comments in that thread, you will find three or more CV threads linked there with very relevant discussions as well. At the moment your question sounds like an exact duplicate, so unless you revise it you are unlikely to get interesting answers. Commented Feb 20, 2014 at 19:45
• @amoeba Thank you for your comment. However I think the other thread had a completely different setup, because they measured a pre and post value to a condition and therefore the pre value could be seen as covariant. This is something I get (even though most people say, just use the difference). However I don't understand why someone would do it in a experiment like the one described above. Because I can't see the covariant. Commented Feb 22, 2014 at 11:04
• All right, then maybe you could revise your question and provide more precise details about the experiment, because currently it is not clear enough. What are your "conditions" (if not pre and post, as I thought)? What are your tasks? How many tasks/conditions each subject participates in? What is your research question? Commented Feb 22, 2014 at 13:38

When repeated measurements are taken on subject - either over time or with different conditions - then the within-subject correlation must be accounted for.

Repeated measures ANOVAs accomplish this by adjusting for the contributions of each individual as fixed effects in the model (a dummy variable for each individual). The ANCOVA approach deals with the inter-dependence by testing the effect of the treatment on the post-measure while adjusting for the initial measurement as a fixed effect.

However, ANCOVA would only be suitable for Pre vs. Post because the model readily describes the relevant question: "After controlling for initial levels, did the treatment(s) increase or decrease the dependent variable relative to the control group(s)?" The limitation, as discussed in the above threads, is that ANCOVA cannot determine if the dependent variable differed by treatment at baseline. This generalizes poorly to your experimental design.

You are interested in whether the condition affects the outcome across each task (main effect of condition) and, perhaps, whether the effect of the condition varies with the task (interaction). This would be similar to the Pre/Post case in needing to know whether the outcome varied by treatment at baseline and at the end, which ANCOVA cannot determine. Furthermore, it's unclear how the ANCOVA would be specified with more than two tasks. Is the effect of treatment on time in Task A adjusted for Task B and C, or is the outcome Task B and adjusted for A and C? Although I suppose this kind of comparison could arise in some circumstances.

Thus, ANCOVA is fine for Pre/Post comparison, but repeated measures ANOVA would be more suitable for your design.

• I am not sure I follow your logic. If, as you say, ANCOVA is fine for Pre/Post comparison, than what feature of the OP's design makes it not fine? Is it that the two conditions are not Pre and Post? OP never specified what they are, but let's say they are "drunk" and "sober", or "sunny weather" and "rainy weather". What's the difference to Pre/Post situation? Commented Feb 24, 2014 at 16:12
• The OP described the design as 3 tasks that are not comparable among themselves, so I think that it's safe to assume that it doesn't follow a Pre/Post not-necessarily-in-time scenario as you describe. This of course could be addressed empirically if the OP clarifies the design. Commented Feb 24, 2014 at 19:43
• Yes, OP wrote that the three tasks are not comparable, but did not say anything about conditions being not comparable. Tasks can be chopping an onion, reading a book and whatever else (following your question above), but if all of them are done in two conditions, then I fail to imagine an example where it would not be equivalent to Pre/Post case... Commented Feb 24, 2014 at 23:23
• @amoeba Thanks for the discussion. Well I should have stated that more precisely. The participants where asked to search for objects using two different approaches, but due to the fact that each object is hidden differently hard (you can't compare how hard objects are hidden, at least I don't know any scale and setting up a scale would be nuts). Also each object has a different distance from the starting point of each search. So the tasks can't be compared. A participant needed to do 6 search tasks. 3 with each approach. My current analysis is a 2-side-t-Test on each search task. Commented Feb 26, 2014 at 12:41
• @Robin: If you are satisfied with the answer provided by Moose, then you can accept it and we don't need to discuss it any further. As for me, I am still confused with both your experiment, and Moose's answer. Commented Feb 26, 2014 at 14:23

I have often read and heard that a) repeated measure ANOVA and b) ANCOVA , the two analyses answer different research questions.

Sometimes, it's not rare seen Researcher disagreeing with the supervisor based on which Analysis would do the right justice to the research question. I believe that when your research objective is about the mean gain, growth, or change comparing two groups in a pre-post test research (or two groups; of intervention and placebo) the repeated measure ANOVA (time*subject interaction) really messure this changes. As @moose, it is safe to limit the use of ANCOVA to comparing means of two groups, where you have group(intervention) A, B, C, etc you really need the ANOVA.