Non Normal Data

Sally,
Your dilemma is not a new one.  Believe it or not, in many cases the non normal tools are easier to apply than the ones for normal data.  You really need to take a course in non parametric statistics and distributions.  If your schedule is like mine, attending a course that lasts longer than one or two days at the most is almost impossibility.  If you are really comfortable with the parametric tools, especially hypothesis testing, then here is my short cut of non parametric analysis.
Get yourself a copy of the Minitab Handbook from Amazon or Minitab.  Look at all the tool listed in the non-parametric tools section.  Most are easy to understand and use (approx 2-4 evening’s work).  The help in Minitab is excellent. 
Next got to the distributions section of that book and read about how to use the probability density function, inverse probability function and the cumulative probability density calculators.  These three calculator features will allow you to calculate probabilities (areas above a point) of many known distributions.  The normal happens to be just one of many important distributions that quality improvement folks typically encounter.  You need to also become familiar with the distribution identify features found in the Reliability/Survival tools in Minitab.  To keep your learning curve even shorter, use the probability distribution tool under the Graph tab, it is simpler to start using rather than going to the Reliability/Survival tab. 
Last but not least, I have been in your situation many years ago, so if you still have questions, please contact me at [email protected].  I have several other excel developed macros and links that would facilitate your learning.  Hope this helps.
 

Sally ,
       The book I would like to recommend is “Rapid Statistical Calculation” By M.H. Quenouille . Its an old book I think published 1972 . A Calculation of Distribution -Free and Easy Methods for Estimation and Testing .
Regards,
Arvin 

Hi
There is an excellent resource for your situation. It is:
Handling Non-Normal DataBy Shree Padnis
https://www.isixsigma.com/library/content/c020121a.asp
Read this one and you will find it really good.
Shereen A. MosallamSix Sigma Master Black Belt

Sally ,
One way to handle this situation is make subgroups ( may be week , month , person etc) & take average & then your data will be the Xbars of the subgroups. Atleast on some cases I could get rid of non normality problem with these technique. Thanks to CLT !
 
Alek

BMG’s stuff is trivial.
Do they teach analysis of distribution vs what should be expected? That is where the greatest gains are and I only know of two places it is taught these days. Neither is BMG.

In case of non-normal data there are some general guidelines to follow to go ahead with the analysis. Consider the list below as a starting point
 
1.      Check if you can group your data in rational subgroups. In that case you don’t need to force the normality to calculate the process capability
2.      Consider whether you have sufficient resolution, you could have a problem due the rounding
3.      Investigate outliers
4.      Be cautious of small sample sizes: a small sample from a normal population could test as non-normal
5.      Check you have a multimodal distribution (get help with a probability plot). In that case you could segment data and get normal distribution for each group
6.      Check if your data fits another typical distribution using some tools like Crystal Ball. In that case you can determine the process capability referring this distribution
7.      Transform your data: log, sqrt, Box-Cox etc., but only if you have already made sure that you don’t have outliers, small (negligible) departures from normality etc
8.      Use percentiles for calculating the process capability (for example 0.135% and 99.865% corresponding to +/- 3 sigma in a normal distribution)
9.      Treat your data as discrete data for process capability purposes and use parametric tests for hypothesis testing
I would always start the analysis with a run-chart and a normal probability plot
 
 
 

My suggestion is to be cautious in case of small samples. Whatever the test you are perfoming, the confidence is small, so in case my sample looks normal or non normal I’d be careful before making any decision
Of course if you run a simulation with Minitab or Crystal Ball you get almost always normal data, but it is true also the converse. Try to run a simulation with 10 samples assuming a non normal distribution and you’ll see that your small sample looks almost always normal . Would you conclude that you have normal data?
So, to conclude: I wouldn’t assume that my data is not normal because the Anderson Darling tells me that on a sample size of 7 or 10.
 
 

Your assumption is that the extraction is done in a perfectly random way. In that case (easy to simulate with CB or Minitab) I said you are right. 
Unfortunately, especially when dealing with historical data whose source and collection method is uncertain, is not unlikely to have a non-normal distribution even if the population must be normal by its nature. In that case, despite of any statistical test, I don’t rely on what any test may tell me. I simply know that my data should be normal and therefore I investigate why it is not. Outliers?  Rounding problems? Not “first attempt data” in a machining process? Data invented by operators to avoid scraps? I simply don’t know, but I want to investigate better before starting any further analysis (for example process capability)This is my approach, much more based on physics than on statistics. Maybe it’s wrong, but since I’m an engineer and not a statistician I prefer relying more on physics than on statistics based on a small sample