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I have data on two groups of subjects. Each group was measured three times, and there were four dependent variables all measuring the level of fitness (score of a person's heart rate in five stages of the test, minutes they achieved, distance they achieved and rated perceived exertion).

My hypothesis is that there will be a significant difference in group A's fitness level compared to group B. group A is in advanced training programme and group B is in a 'normal' training programme and their fitness is measured before training, at 4 weeks and at 6 months follow-up.

I'm leaning toward one-way repeated measures ANOVA, but I'm also starting to wonder if I should be using one-way repeated measures MANOVA because I have 4 dependent variables. Or does this not matter? Could I still use repeated measures ANOVA?

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    $\begingroup$ What model/hypothesis do you want to fit/test? $\endgroup$
    – Nick Stauner
    Commented May 17, 2014 at 10:01
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    $\begingroup$ Hi nick, thank you for your comment. My hypothesis is that there will be a significant difference in group A's fitness level compared to group B. group A is in advanced training programme and group B is in a 'normal' training programme and their fitness is measured before training, at 4 weeks and at 6 months follow-up $\endgroup$
    – Emma
    Commented May 17, 2014 at 10:23
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    $\begingroup$ Okay, but how do you want to handle "fitness level"? Do you have a measurement model in mind that combines your four dependent variables? They are not four levels of one variable BTW; might want to check your understanding of the difference between levels and variables, unless I'm misunderstanding what you've written. If you don't have anything like a latent factor model in mind for combining the four dependent variables, you'll probably need to test your hypotheses for each separately, or need to develop a latent factor model, which could be tricky. $\endgroup$
    – Nick Stauner
    Commented May 17, 2014 at 10:31
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    $\begingroup$ @HorstGrünbusch hi there, thanks for your comment. I think my own understanding of what a dependent variable with 4 levels means was wrong. I should say 4 dependent variables as appose to one dependent variable with 4 levels $\endgroup$
    – Emma
    Commented May 17, 2014 at 11:04
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    $\begingroup$ So you measured the fitness level 4 times? Your first comment suggested 3 measurements: Baseline, 4 weeks, 6 weeks. So I got confused. You are sure that fitness level is metric, e.g. data from a bicycle ergometer? And: Have a look at this older question, please. $\endgroup$
    – Horst Grünbusch
    Commented May 17, 2014 at 11:20

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It sounds like you're looking to test one basic hypothesis on four similar variables. Setting aside the thought of estimating a latent fitness factor from these four variables, you can approach this with a mixed effects MANOVA. Because you expect fitness in general to change differently for your two groups, and you have four indicators of fitness, you can test your hypothesis of group differences on each of your four dependent variables while controlling for multiple comparisons using MANOVA.

As I understand your problem, you want to include a random effect for individuals measured repeatedly. Your fixed effect is training program. You have four dependent variables. You expect no group differences at the first measurement, but expect group differences at the second, and I'm guessing you expect those differences to be stable until the third measurement. You can test group differences and the group variable's interaction with measurement time in repeated measures ANOVA for each of your four dependent variables, but MANOVA makes the test more conservative by controlling for familywise error rate inflation caused by taking four separate whacks at the hypothesis.

I should warn you that these general linear models are conventionally fitted by ordinary least squares estimation, which may produce biased estimates of standard errors, and therefore biased significance test results if your data don't meet the assumptions...and real data often don't. Also, there's some controversy regarding the utility of controlling for familywise error inflation. If you want to make sure you're choosing the right analysis for your purposes and care to study related issues, @HorstGrünbusch's link to this question is definitely a good one to follow too:

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  • $\begingroup$ Thank you so much for explaining it to me in detail, you have cleared up a lot of the confusion. Much appreciated! :) $\endgroup$
    – Emma
    Commented May 17, 2014 at 19:09

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