ANOM with Transformed Ranks technical details

[#1]

Dear JMP Users,

I try to understand the theory behind ANOM with Transformed Ranks. JMP help is limited and gives refrance to Nelson et al. (2005). But can not reach this, if any one know how this test works, how upper and lower limit desicions valculates easily, i am happy to hear that.

[#2]

I could use some help here too. I have a dataset of 30 groups of skewed data samples, and I sense that ANOM using TRs is the right way to go. But I am coming up short on documentation. 

[#3]

Hello Both.

So, I would use ANOMTR if I suspect that the distribution of the data from which I am sampling is "non-normal".  So not that my sample is non-normal (since samples tend to be small and it is hard to know much about a distribution from a handful of data points) but that the distribution from which I am sampling is far from normal. If I am unsure I might run both procedures and see how different the conclusions are...I of course graph all of the data was well to try to understand whatever it is that I am investigating.

See if this is helpful - there is a technical report on robust ANOM that I can't find at the moment but can look harder if you want further details.

Karen

The ANOM book can be found here: ASA-SIAM Series on Stats and Applied Probability .

The help for the transformed ranks with the stats details is here JMP ANOM with TR Details 

From the ANOM Book:

[#4]

Thanks for the book image capture @KarenC . That was just enough explanation to figure it out. The authors Nelson et al actually have a website that shows those formulae, but without the supporting text I couldn't figure them out.

I was able to duplicate the results of JMP's ANOM on Transformed Ranks by using the standard ANOM on values that I transformed myself  -- that is, after calculating the ranks, transforming the ranks to the Eij values, and then doing standard ANOM on those. Sure enough...same results as produced by the ANOM with Transformed Ranks directly. 

Having said all that, it would be nice if JMP included a more thorough explanation within the online documentation rather than sending users to a bookseller. Maybe that was the contractual agreement with the developer of the ANOM method.

Sorry to the OP if I hijacked your question. I won't "resolve" it since it may not be resolved from your POV. 

[#5]

Happy to help. I had forgotten all about that website: ANOM website. The primary use of that site would be to see the list of technical research papers around ANOM. As to the JMP documentation, I can assure you (as one of the et.al. authors) that there was no contractual agreement with us per the documentation. The ANOM book was not written to make money but to provide a practitioners guide to a methodology for which (at the time) there was no such book. As to JMP documentation, it is a guide to the software with lots of stats details, but not always every detail we need or want. So we have the references provided and then this great community to help us dig further into technical details when needed. 

[#6]

Whoa! I didn't realize you were THE Karen C! Thanks again for the explanation. By chance do you know if the Minitab implementation of ANOM is the same?

[#7]

I have no idea as to the Minitab implementation.