Non Normal data
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 This topic has 6 replies, 6 voices, and was last updated 15 years, 2 months ago by Chris Seider.

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March 6, 2007 at 9:53 am #152779
accringtonParticipant@accrington Include @accrington in your post and this person will
be notified via email.Can you explain what you want to do with the data?
0March 6, 2007 at 10:10 am #46304
CK HariParticipant@CKHari Include @CKHari in your post and this person will
be notified via email.Hi,
I would like to know the methods of dealing Non normal data.
Thanks,
Hari CK0March 6, 2007 at 10:18 pm #152816Hi
What sampling strategy did you use? If you had used rational subgrouping then chances are that you would have got normal data as (read central limit theorem). You probably took whatever data was available and did a normality test on that…
Now if you do not have normal data then you measure of central tendency cannot be the mean and your measure of variation cannot be standard deviation (which measures to use would depend on the kind of distribution you have)
If you want to do hypothesis testing with non normal data then you use non parametric tests (moods median, kruskall wallis etc)
Basically do not fear that you have got non normal data but also do some intelligent sampling and data collection to begin with so that you have a better representation of data0March 7, 2007 at 12:48 am #152823There is no such thing as perfectly normal data. You will never know precisely your data’s distribution. Shewhart developed control charts without any assumption of data distribution. Note that Shewhart did not rely on the Central Limit Theorem.
Histograms also do not require any assumption of data distribution.0March 7, 2007 at 1:56 am #152825What??? No mention of Don Wheeler??? Are we converting you Steve???
0March 7, 2007 at 3:54 am #152826
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Interestingly enough I reread Shewhart’s book today for a paper I am writing. He did mention a number of times that he was not concerned about nonnormality in the population because using rational subgrouping and subgroup averages, the issue was moot. However, he does not ignore the concept of the CLT.
On page 289 Shewhart says, “We are now in a place to consider an additional and very important reason for choosing the average xbar of a sample to detect a change delta xbar and the standard deviation sigma to detect a change delta sigma. The previous discussion has been limited to the assumption that the universe or distribution of standard quality is normal.
In Part IV, however, we saw that, no matter what the nature of the distribution function of the quality is, the distribution function of the the arithmetic mean approaches normality rapidly with increase in n, and in all cases the expected value of the means of samples of n is the same as the expected value Xbar of the universe.”
This type of comment appears a few times in his book. I think it is fair to say that the control chart works independent of the CLT and is robust to normality although Shewhart did not ignore the idea of the CLT in selecting the mean of samples as his format for identifying common cause and assignable cause.0March 7, 2007 at 4:50 am #152830
Chris SeiderParticipant@cseider Include @cseider in your post and this person will
be notified via email.I love nonnormal data……If you have inputs recorded along with your nonnormal output then you can identify some of the reasons (often referred to special causes) much easier….
Do not be afraid….
good luck0 
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