# Testing for Normality

Six Sigma – iSixSigma Forums Old Forums General Testing for Normality

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• #44540

michael spearman
Participant

Question to all Blackbelt….. The question was served up, when do you test Continuous data for Normality??????? Or do you even run Normality??????
I say- you run Normality on all Continuous Data, before pursing other testing possibilities…
Just a thought

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#142895

Hans
Participant

One key point: In regression the assumptions are that the error is normally distributed. You may want to check a couple of other threads where I extensively go into the history of the “normality myth”. Good luck.

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#142896

michael spearman
Participant

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#142899

Ken Feldman
Participant

With the software available today, doing a normality test is a mere click of a button.  I always do it if for no other reason than to see what I have.  Since, as Hans points out, normality is often an underlying assumption of many statistical tests, re: ANOVA and t test it’s good to know.

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#142917

howe
Participant

Normal distributions don’t exist in the real world.
XbarR and XmR control charts don’t need them.

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#142924

Ken Feldman
Participant

Original poster didn’t mention anything about control charts. I agree that control charts are quite robust to normality so it is rarely a factor. But, if the poster wanted to do some hypothesis testing then the knowledge of the distribution would be important. While the normal distribution is hypothetical we merely worry about how close to it is our data. That’s all a normality test is telling you.

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#142929

michael spearman
Participant

In control charts normality is assumed, before we have the process in that phase, the phase Darth mention (By the way is the way i would do it) the raw data phase (hypothesis testing). Control chart data has been normalized already to me, thats what I would believe.
Just a thought ………..
Thank you Mike, Darth and Hans. Good topic for the exchange of data and ideals

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#142941

Hans
Participant

Michael,
I would like to emphasize Mike’s suggestion to get the Wheeler and Chambers book on control charting. Unfortunately, some other textbooks confound control charting with the type of measusrement error theory that brought about the normal curve. Wheeler and Chamber cite Shewart’s original research on the robustness of control chart in regards to non-normality and add a few distributions that Shewart did not include in his original work. If you really want to dive into the subject, there is a book by Dover on Shewart’s Washington lectures that summarize his book 1931 book in a more comprehensive and less mathematical fashion.
In any case, you can’t go wrong with normality. But don’t get to upset about non-normality when control charting. You are dealing with process statistics (i.e. time related data), not population statistics (cross-sectional data). In any case, good luck!

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#143237

vishwanath
Member

hi,
instead of havings confushion on Normality data, its always better to check the normality before MSE & once you confirm the normality of data, then you can go for Process Capa & process behavior chart (control chart).
its always better to project the imprvement in adequesy of measurement system.

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#143297

Jonathon Andell
Participant

Before I start to pontificate, bear in mind Diamond’s quote, which goes something like this: “The objective is to understand the process, not the data.”When dealing with continuous data, I always include the following in my analysis:1. Control Chart. Even if the underlying data come from a non-normal distribution, it’s vitally important to use our eyes and brains to detect special cause patterns – especially since special cause can be the reason for apparent non-normality. Besides, control charts are pretty robust against minor violations of the normality assumption.2. Histogram and probability plot. Each has the potential to reveal useful information. If the probability plot has “stair-steps” and parallel lines, you may be dealing with bimodality – another frequent reason that agrregate data appear non-normal.3. If the above all show a reasonably stable process and a single distribution, then I would consider using a distribution ID utility. Some just provide tabular outputs like Anderson-Darling or other statistics. If that’s what you use, be sure to build distribution-specific probability plots of the leading contenders, and use your eyes to see if anything is amiss.Bear in mind: selecting the “right” distribution ought to incorporate consideration of what kinds of natrual phenomena tend to generate which distributions. James King’s book “Probability Charts for Decision Making” has some good tables for that purpose.The above procedure can be done in 15-30 minutes with the right software, and it leaves you with reasonably sound statistical understanding. Better still, it maximizes your chance to learn more about the process, which is the real point of all this work.

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