Quantiles: Inclusive vs Exclusive method?

[#1]

JMP appears to use the exclusive method as the default for calculating quantiles, irrespective of the sample size (that is, odd versus even).

Excel offers one the option (QUANTILE.INC versus QUANTILE.EXC).

Which is correct when the sample size is, say, less than 50?

Does JMP permit the use of the inclusive method?

17.1.0

[#2]

Hi @34South : Which is "correct"? At the risk of being accused of being pedantic, I'll weigh in.  Estimating (as conceptually different from  "calculating") quantiles can be deceptively challenging (especially with small sample sizes). By definition, all estimates are wrong! Which is the "best" estimate is the real question. Good article here.

https://www.amherst.edu/media/view/129116/original/Sample%2BQuantiles.pdf

[#3]

Dear @MRB3855 

Thank you for this. Good to know that my confusion is not unwarranted. However, and I must admit to only being an intermediate JMP user and largely self-taught 'statistician', I do find some references that suggest the inclusive method to perhaps be the more logical choice. JMP does not seem to allow the use of alternate methods and uses the exclusive method exclusively (pardon the pun). As a JMP fanatic, how to I justify using this method when other packages appear to do otherwise?

[#4]

Hi @34South : Justification for one method over another? Good question.  JMP (Statistical Details for Quantiles (jmp.com)) uses definition 6 in the link I provided earlier. That link shows 9 different methods (here is a example based description of eight of them  https://www.resacorp.com/quartiles.htm ) for calculating percentiles, and all can be justified on some level.

You'll notice Table 1 from my earlier link provides "six desirable properties for a sample quantile". Definition 6, as JMP uses, satisfies five of them (see Table 3, and section "5. summary and conclusions"). As "justification" I'd provide that article from my previous post. As for perhaps answering "why is it different than Excel?", my first thought is; for rigorous statistical work, generally speaking, "I trust JMP far more than I do Excel"; there are lot's of reasons for that (though I do use Excel to do loads of other useful and wonderful things).  Just my 2 cents...

[#5]

The calculation/estimation distinction may be important (hopefully, somebody will be able to comment on this more authoritatively).  JMP does do quantile regression models (they are somewhat hidden in the Generalized Regression platform under the "Distribution" choice) and I would think that estimation of quantiles would be important there (instead of calculation).  So, perhaps the choice is related to more sophisticated modeling than simply wanting a number that represents the Xth percentile?

[#6]

Hi @dale_lehman  and @34South : I'd argue that the "calculation/estimation distinction" is always important; it points to the difference between sample and population. Statistical inference is all about inferring from a sample to the population. If you aren't doing that, you're just calculating numbers (e.g., descriptive statistics used to summarize a sample, which may be all you need depending on goals). As someone once said of Statistics; what is observed is interesting...but what is hidden is crucial.  OK, I'll get off my soapbox...