I found a function in JMP and was wondering when to apply the Transformed Ranks option within the Analysis of Means menu. I read the reference from Nelson et. al, provided by JMP, but I am still not quite sure if I apply it properly. Unfortunetaly, I do not really find any other references which are useful. If I compare groups (measurements instruments with same sample set) with non-normal distributed residuals and are not able to transform the data to a normal distribution it seems that this is the only analysis I can run in JMP to compare the Mean. For me personally the approach to assign ranks makes sence in my example.
To my example:
I want to report if groups (measurement instruments) match to the overall mean and afterwards conduct a wilcoxon test fo each group to the overall mean. The graphical output matches with the non-parametric test. If limits are exceeded the p-value is <0.05.
Can I use this test to compare measurements instruments with the same sample set and derive a statement about statistical matching to the overall mean? I already conducted technical matching analysis using Bias / Tolerance ratio but was wondering if this could be added to my analysis as an add-on.
Can you share a plot of the residuals that exhibit the non-normal distribution? A histogram and a normal quantile plot would help.
What have your tried in order to transform the data to normal?
How many replicate measurements do you observe? How many items are in your sample? How many instruments are included?
You are trying to show that the mean of the measurements is close to the standard value across the items and intruments? Lack of significance in a test for a difference is not the proper analysis. You might want to use an equivalence test instead.
Since the question is about the measurements, please see Help > Books > Quality and Process > chapters about Measurement System Analysis and Variability Chart might be helpful.