Normality Test
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 This topic has 11 replies, 9 voices, and was last updated 14 years, 11 months ago by Craig.

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December 8, 2006 at 4:39 pm #45473
Just come across this on my Black Belt prepartion exam and need some help.
A normality test gives a pvalue of 0.2. What conclusions would you draw? If your data was NOT normal, What action would you take?
0December 8, 2006 at 4:47 pm #148688Dave:This one is a common question. The null hypothesis is “The data is normal”. A pvalue above 0.05 indicates it is safe to assume it is normal for subsequent tests.If the normality test fails, then the statistical alternative is to use nonparametric tests (eg. Mood’s median), the practical alternative is to find out why the data is nonnormal.Cheers, BTDT
0December 8, 2006 at 5:00 pm #148689Your normality test (MTB) null assumes normality. When your pvalue is less than the alpha value that you selected, (an alpha of .05 is common) you reject the null of normality and work off the assumption of nonnormality. When your pvalue is greater than your alpha, you fail to reject the null, working off the assumption that normality does exist for your distribution. So when pvalue = .2 with an alpha of .05, you appear to be workign with a normally distributed data set.
When your data is nonnormal, you can do several things:Do nothing…many if not most distributions depending on your environment are indeed nonnormal. Learn from it. Determine how you are going to analyze your data and if the assumption of normality is critical…..many tests are robust to a violation of nonnormality…(mean comparisons, for example).
Use nonparametric testing (mannwhitney, moods, etc). This simply uses the median instead of the mean in its calculations.
If you must work with the assumption of normality, you can transform the data using a boxcox transformation, etc
You can also subgroup your data set, invoking the CLT to normalize it to some degree. For example, take 150 observations in a given sample and subgroup them serially using (n=3) for 50 averaged data points. Plot these. You should see your data set move closer to normal. The larger you n, the closer to normality your distribution will move.
Good luck and verify. It has been awhile since I thought about this stuff.
0December 8, 2006 at 6:36 pm #148697
The ForceMember@TheForce Include @TheForce in your post and this person will
be notified via email.p>0.05 to accept the normality
if it’s not normal — you can do any or all of the ffg:
– check your subgrouping
– apply the central limit theorem
– transform the data
– consider the nonnormality as is and use tests for non normality moving forward (weibull, non parametric, among others)0December 8, 2006 at 8:24 pm #148704Read past threads. You don’t need to know if a distribution is normal. Even 3200 data points will only guarantee any distribution out to +/2.95 sigma.
Try fitting your data to a Burr distribution … it will always give as good as or better fit than Normal.
You will never know the exact distribution.0December 8, 2006 at 10:05 pm #148709Steve, thanks for the reply, but at green belt preparing to get bb conversion that was little above my head
0December 8, 2006 at 11:39 pm #148712
Steve’s MomMember@Steve'sMom Include @Steve'sMom in your post and this person will
be notified via email.I am so embarassed by my little boy Stevie. I don’t know why he gives such dumb advice.
0December 9, 2006 at 10:54 am #148724Its not your fault somebody in the hospital must have dropped the big mouth on his head from a great height
0December 9, 2006 at 2:33 pm #148729I would also check for outliers and see how much they are influencing the pvalue. In some cases you will be able to remove them if you have assignable cause.
0December 10, 2006 at 12:54 am #148737
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Dave, as has been noted by others, for a generic normality test a p value of .2 indicates you do not have sufficient evidence to reject the assumption of normality.
The real problem arises with the second part of the question. If your quote is the entire question then the best answer to the second part is – note the fact that your data failed a particular test for normality and go find something else to work on.
If you were curious as to what the data looked like (I usually am) you could generate a histogram of the data and normal probability plot just to get a sense of what it looks like but in the absence of any specific need/requirement/objective there really isn’t anything else to do.0December 10, 2006 at 2:58 am #148739
Frank FieldsParticipant@FrankFields Include @FrankFields in your post and this person will
be notified via email.Your histogram gives you information about your data distribution.
Attempting to fit normal distributions or other curves adds no value and tells you no useful information.
Your six sigma consultants will tell you all sorts of useless stuff to try to get you to buy unnecessary software.0December 10, 2006 at 4:39 pm #148759Frank,
I am curious as to what value even a histogram adds based on your philosophy? Do you do anything useful once you observe the shape of the data distribution?0 
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