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I have a group of 8 subjects. For each subject I measure their heart rate 30,20, and 10 min before and after they take a drug. I then average the heart rate measurements in each subject to get one value for before and after the drug was taken. As a result, I have 8 before and 8 after averaged heart rate values. I want to compare whether there is a difference in heart rate after the drug was taken. What test would be recommended in this scenario?

I currently use JMP software and conducted an ANOVA on the groups using 'fit Y by X' and received an F value of 0.157. However, when I blocked by the subjects, and used the 'Fit Model' option, the F value was 0.035. If I blocked by subject and used the 'fit Y by X' and conducted an ANOVA, this also yielded significance. One method returned a significant result while the other did not. Why is this? Which is correct? Is it correct to block in this scenario? Also, which statistical test should I use?

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No am not familiar with JMP software. The first analysis you describe assumes that the after measurements are independent of the before measurements and this is clearly not the cases (you have paired data). Blocking by subject will provide you with the correct test of the effect of the treatment. A simpler approach, however, is a paired t-test. This tests the null hypothesis that the average within-subject change over time is zero. There are plenty of examples and info on the paired t-test online.

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