I'm new to JMP, and trying to determine which test is appropriate for my study. I have matched biological measurements at two time points (before and after a meal) for 25 individual donors. Each donor has a single data point per time point. The population has a large standard deviation for most of these measurements, and usually the results do not have a normal distribution. Some observations have a few outliers. I have attached a sample graph depicting my data.
Is it appropriate to analyze the data with a simple t-test or Wilcoxon test via the Fit Y by X menu? Or should I perform the analysis using the Specialized Modeling > Matched Pairs > Wilcoxon Signed Rank approach? The main question in this study is whether or not the biological measurement (ie, yield) changes after eating a meal. I'm not particularly interested in donor-specific responses, more the trend of the population as a whole. Any advice on which test to use, and how to execute that test in JMP, would be greatly appreciated!
Maybe I'm misunderstanding, but if your question is "The main question in this study is whether or not the biological measurement (ie, yield) changes after eating a meal." Wouldn't you really want to compare the delta between before and after, not before vs after? While your sample data may be non-normal (it looks like a gamma distribution to me), your delta distribution is most likely normal with a more reasonable std deviation. Assuming this is the case you could just test the delta distribution mean against the null hypothesis that it's mean is 0 (or there are no changes after eating a meal.)
Great explanation, thank you for making that so clear! I also have additional measurements with three time points (morning, noon, evening) - in this case, would it be valid to compare the deltas between each pair individually (T1-T2... T2-T3... T1-T3)? Or is there a different test that I should be using? Thank you so much for your guidance, I'm new to this and it is very helpful!
That all depends on the question you are trying to answer. If you are trying ask "Which meal affects yield the most: breakfast, lunch or dinner?", then you would do a t-test of the deltas, of course this would require 6 measurements. Since you have three, I'm guessing the question is, "Is there a difference in yeild at different times of day?" In this case, I would do both a parametric test (t-test) checking the power to determine if it has any merits based on the central limit theorem and a non-parametric test (Wilcoxen, ect.) to cover my basis. You can also apply a transformation to the data (e.g. log(yeild)) to see if it approximates normallity better.