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I have 2 subjects. I used to take a single measurement (20 samples) per subject and use a t-test to compare the means.

Now I want to add more measurements. I'm going to have 5 measurements per subject.

I could do 5 t-tests and report the difference for each measurement, but that feels wrong.

Is there a better way to analyze this?

Thanks in advance for any pointers!

P.S. Not sure how important this is, but it seems important to me to note that the "measurements" aren't completely independent. In this case, measurements are composite workloads (with some small level of overlap) and the subjects are processing units.

John
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  • Are the measurements you are taking on the same outcome variable measured multiple times (e.g. subject weight measured 5 times) or are they different measures on a subject (e.g. weight, height, blood pressure, etc.)? – StatsStudent Mar 05 '15 at 22:58
  • They are different measures! I do 20 samples of each measure, so 100 data points per subject. – John Mar 06 '15 at 00:48

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Since you are taking 20 samples of each measure, you are correct that you are not dealing with independent data. You will need to use methods specifically used in the analysis of longitudinal or correlated data such at generalized estimating equations (GEE) or mixed effects models. In addition to the correlated data, you have multivariate data. There are two ways you can handle this. The simpler method is that you'd handle each different measure as a different analysis. The more complex method involves handling your entire analysis as a multivariate analysis since you have different measurements. Using the multivariate approach, you can use multivariate models for clustered data. Here is a paper that demonstrates some of these methods and can give you a flavor for the analysis: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2888330/

StatsStudent
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  • Thanks... I was looking for multivariate t-test, T^2, just didn't know about it. By the way, I didn't mean that my samples were not independent, but that the variables (measurements) were. Sorry about my poor terminology (obviously not a statistician :-). – John Mar 06 '15 at 16:15
  • If each of your samples are indepdent than you can use the Hotelling T^2 test. – StatsStudent Mar 06 '15 at 17:10