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Customer noticing differences in fitted distribution CI's

MikeD_Anderson

Hey all!

Have any of you seen this issue?

A customer was checking numbers between JMP 13 and 15 and noticed that the CI's for a fitted normal distribution are slightly different. I checked through the docs and couldn't come up with anything other than the changes to align the Capability calcs. At the same time, I think I recall someone (Brady?) mentioning we might see differences, but can't find anything in my notes which parts and why. Someone care to set me straight?

Thanks!

Accepted answers

jules

I've only done a little digging on this, but It appears that in JMP 15, the confidence intervals formed within the fitted normal panel use z, not t quantiles, so for small sample sizes the CIs between there and the summary stats panel can vary dramatically. For instance: take the following example with n=2

Screen Shot 2020-06-01 at 8.56.02 AM.png

The CI within the fitted normal clearly uses z, given the short width of the interval. Confirmed, as the upper limit = 0.196041+(1.96*.8326) = 1.828. But, the interval in summary stats is using t, as it should given we are estimating σ, thus the wider interval. I was not aware of this change being made, and can't quite wrap my head around why it would make sense to do it this way. But, there you have it.

example.jmp

MikeD_Anderson

Here's the word from tech support (TL;DR - Julian was dead right - nicely done, sir!)

in v13 the CI from the fitted data is calculated the same way as the summary statistic (if you look at the picture above - they match). Those are calculated using a t-statistic:

in v15, we changed to a z-statistic for the fitted normal:

However, I can't find either of those mentioned in the documentation, which is going to cause problems if people check this as part of their validation processes.

All comments

jules

Screen Shot 2020-06-01 at 8.56.02 AM.png

example.jmp

MikeD_Anderson

Thanks, @jules! Where in the docs did you find that? They’ll want to know.

Best,

M

jules

I didn't find it in the docs, it was just a guess that panned out!:):)

MikeD_Anderson

Here's the word from tech support (TL;DR - Julian was dead right - nicely done, sir!)

in v13 the CI from the fitted data is calculated the same way as the summary statistic (if you look at the picture above - they match). Those are calculated using a t-statistic:

in v15, we changed to a z-statistic for the fitted normal:

However, I can't find either of those mentioned in the documentation, which is going to cause problems if people check this as part of their validation processes.

jules

Thanks for getting confirmation on this, Mike! Did you get any explanation for why this change was made? I can't think of a rational justification (which I admit may just be my lack of imagination), but I can certainly think of instances where people will misinterpret those intervals/come to incorrect conclusions.

MikeD_Anderson

Not yet - that's part of the follow-up info I need.