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I work in exercise physiology, but have very little experience in statistical analysis with anything more complicated that T-Tests and correlation analyses. So this question might be a bit broad, but I'm happy to rephrase it if need be.

I have a series of subjects who each completed 3 exercise tests. The tests export raw data every 5 seconds. Results can vary by time (how long the subject was exercising) and/or by intensity (how hard the subject worked during the test). Here's a couple of examples of some "typical" results:

Varied in time and intensity Varied much more in intensity

Visually, they don't look all that dissimilar, and I can use time to exhaustion and VO2Peak (the highest point on each line) to compare maximal performance, but I'm wondering if there is a good statistical test to actually compare the lines, given that they don't always have a consistent slope.

I'm not well-versed in much of this, but any suggestions on where I can look at I'll be happy to do! I looked at this page, which seems like it could be something that might be useful, but frankly the discussions are a bit over my head.

Currently, I'm only using Excel, but I'll obviously have to use something more complex in the future.

EDIT: To be more specific I think looking at the integral of the curves (thank you whuber) and the progression of curves would be useful. Due to the nature of the exercise tests, we expect that the slope of the curves will change at some point (you can see that at about point 65 of the green line in the first graph), so calculating how the slopes change, and then performing some statistical analysis on the slopes and the timing of the changes would be outstandingly helpful.

kjetil b halvorsen
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Jeff Cournoyer
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  • Questions about statistical testing come only after you specify *what properties* of these curves you wish to compare. I would guess you might be interested in peak volume, time of peak volume, time to exhaustion, and possibly the integral (total volume), but that's just a guess: *you need to tell us what is relevant.* Once you have done that, do you need some "test" (and if so, what hypothesis or hypotheses do you wish to test)--or do you really just need to describe and explore your data? – whuber Sep 17 '21 at 14:33
  • That makes sense -- thank you. So I'll edit my question, but I have been able to calculate peak volume, time of peak volume and peak exhaustion (that is the VO2Peak, and is easily exported). Looking at the integral would be great, as it represents capacity for total work. And I would want to see how the progression of the series differ from one another. – Jeff Cournoyer Sep 17 '21 at 16:40
  • Identifying the "progression" is a matter of changepoint analysis (search our site). Assuming there are more than three curves, the very first analysis I would do--after plotting all the curves in a way to make them visually comparable--would be to digest each one into the statistics of interest (it sounds like four or five will do) and make a scatterplot matrix of them to start exploring their relationships, find geometric outliers, and see their univariate distributions. What happens next depends on what questions you have in mind and what questions that initial examination might prompt. – whuber Sep 17 '21 at 17:29

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