# Normality Test

Six Sigma – iSixSigma Forums Old Forums General Normality Test

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• #45473

Ropp
Participant

Just come across this on my Black Belt prepartion exam and need some help.
A normality test gives a p-value of 0.2. What conclusions would you draw? If your data was NOT normal, What action would you take?

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#148688

BTDT
Participant

Dave:This one is a common question. The null hypothesis is “The data is normal”. A p-value 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 non-parametric tests (eg. Mood’s median), the practical alternative is to find out why the data is non-normal.Cheers, BTDT

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#148689

annon
Participant

Your normality test (MTB) null assumes normality.  When your p-value 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 non-normality.  When your p-value is greater than your alpha, you fail to reject the null, working off the assumption that normality does exist for your distribution.  So when p-value = .2 with an alpha of .05, you appear to be workign with a normally distributed data set.
When your data is non-normal, you can do several things:

Do nothing…many if not most distributions depending on your environment are indeed non-normal. 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 non-normality…(mean comparisons, for example).
Use non-parametric testing (mann-whitney, 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 box-cox 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.

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#148697

The Force
Member

p>0.05 to accept the normality
if it’s not normal — you can do any or all of the ffg:
– apply the central limit theorem
– transform the data
– consider the non-normality as is and use tests for non normality moving forward (weibull, non- parametric, among others)

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#148704

Ashman
Member

Read 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.

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#148709

Ropp
Participant

Steve, thanks for the reply, but at green belt preparing to get bb conversion that was little above my head

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#148712

Steve’s Mom
Member

I am so embarassed by my little boy Stevie. I don’t know why he gives such dumb advice.

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#148724

Ropp
Participant

Its not your fault somebody in the hospital must have dropped the big mouth on his head from a great height

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#148729

Craig
Participant

I would also check for outliers and see how much they are influencing the p-value. In some cases you will be able to remove them if you have assignable cause.

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#148737

Robert Butler
Participant

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.

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#148739

Frank Fields
Participant

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.

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#148759

Craig
Participant

Frank,
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?

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