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I have 2 groups of subjects, namely:

  • Subjects that are younger than 67
  • Subjects that are older than 67

Each subject of each group wears a sensor that estimate the metabolic equivalent of tasks (METs) during a day (this measure represents how active the subject is during the day...it is similar to the energy expenditure).

For each patient I compute the average METs at each hour that means that each patient is represented by a time serie with 24 data points.

In the picture you can find the hourly averages METS for each group of subjects together with the 95% confidence intervals. This picture represent the hourly pattern of the 2 groups.

Is there a statistical test in order to compare (and emphatize differences) the 2 hourly patterns?

The question is: How can I show (using a statistical test) that there are significant differences between the hourly pattern of people older than 67 and younger than 67?

enter image description here

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    $\begingroup$ Start with forming a question. What interests you? $\endgroup$ – Aksakal Nov 3 '15 at 16:31
  • $\begingroup$ Question is now in the text $\endgroup$ – gabboshow Nov 4 '15 at 8:31
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    $\begingroup$ In general, you cannot test differences between averages without information on variation around averages. In this case, you want to compare families of curves, which is quite an advanced problem, studied under headings like functional data analysis. There are many other methods such as fitting sinusoids to each individual and looking for patterns in the coefficients. This problem starts easily (you can plot the data) and gets much more difficult very quickly. You're the researcher but a split at 67 seems quite arbitrary to me: I would want to know ages of all patients. $\endgroup$ – Nick Cox Nov 4 '15 at 8:59
  • $\begingroup$ Hi @NickCox I have information on variation around averages. Those are represented in the 95% confidence intervals that you can see in the picture. I know that significant hourly differences between >67 and <67 are determined as hours with non-overlapping confidence bands, but I was looking for a rigorous statistical test (with p etc..). Regarding the split at 67 it is OK for my problem. $\endgroup$ – gabboshow Nov 4 '15 at 9:03
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    $\begingroup$ Not trying to be negative, but how would MANOVA cope with cycles? It's fundamental that 1 am follows midnight. $\endgroup$ – Nick Cox Nov 4 '15 at 10:50
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Why don't you split into few time bands of 2h duration, say 00:04, 04:06, etc. and for each band you apply a two-sample t-test for each band. You didn't mention how many patients for each group, but if they are only few a t-test should do the work. Then you will get a p-value and a confidence interval for each time band. You can reject the null hypothesis only if you can reject for all bands and use the largest p-value as p-value for the whole population.

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