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I have a fundamental question about applying ANOVA.

Suppose we are testing 4 drugs which reduce blood pressure. Our experiment contains 4 drugs + 1 Placebo. We give these to 3 types of patients (moderate, high, very high). Each drug is given to 18 patients which have equal number of the above types. A total of 18x5 = 90 patients are tested for over a year. Everyday we take 3 readings of their Blood pressure (morning, afternoon, night).

Now after a year, we have the individual readings, daily reading (average of 3 individual readings), weekly reading (average of all readings in a week) and similarly monthly reading.

If I do a between subject one-way ANOVA to find if there is a statistical difference in the means. Which readings should it be applied to? The individual readings-- in which case the DOF will be high, or the daily, weekly, month average. What is the fundamental theory which allows us to determine on which values the ANOVA should be run. Does it make a differance if we run it on different averages as against the raw values.

Thanks.

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  • $\begingroup$ One thing to consider is this: ANOVA assumes that the observations you use are independent, and (while I know very little indeed about blood pressure), I would imagine / guess that if you used all the individual readings, you'd struggle to justify independence. For example, if someone's blood pressure is particularly high for the first reading of the day, will it be more likely to also be higher than average for the second reading? (again, I don't know, but I'd guess that might be an issue to consider). $\endgroup$ – hodgenovice Feb 9 '16 at 18:34
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Aside from not using the raw values for legitimate reasons stated above (non-independence), the fundamental theory here depends on your question of interest: do you want to conclude drug A had superior overall long-term effects (monthly averages, blocked by subject, two-way by type and drug)? more promising trend for 'improvement' (rate of change in daily average repeated-measures analysis, ditto)? For skewed or unbalanced data, it is very likely to make a difference how you test it, thus it is very important to formulate your hypothesis prior to testing. Also, tt seems a waste to not account for maximum variability or CV, for which you could do a separate group testing.

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  • $\begingroup$ Thanks, to you and @hodgenovice. This seems to be it! The non-independence. I think the best way is to go for repeated measures analysis in such situations. $\endgroup$ – Dobeli Feb 13 '16 at 13:49

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