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Matched Pairs Analysis when the Difference is a Function of the Mean

What inspired this wish list request? I love the Difference vs Mean plot in this platform, but many times the difference may be a function of the mean. What next?

 

 

What is the improvement you would like to see?  I would like to be able to fit a line of Difference vs mean and see if it is significant, better yet, have JMP do it and suggest a different analysis like % Difference vs Mean (Available in JMP 18), and see if this one has a trend also. If it does, suggest another approach. At a minimum provide a way to output the data used in the plots to a data table so I can check myself. I think the Galton.jmp sample data file is a good example where people will get the incorrect conclusions. The Matched pairs analyses leads one to believe the difference is not significant, when in fact some assumptions of the paired t-test are violated, and this is not the correct conclusion. The assumption that the difference is random about an average difference is not true in this case. 

 

 

Why is this idea important?  This will lead JMP users to the correct analysis in cases where the paired t-test assumptions are violated.