Selecting PRoper Test of significance

Six Sigma – iSixSigma Forums Old Forums General Selecting PRoper Test of significance

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    While studying a process characterstic  it was quite evident that duing initial stages the process is not stable and after a time delay the process stabilises. Therefore when a capability study is done the process is found not to be  capable. I divided the data into two groups : one before the process is stable and one after the process is stable. The capability study showed that the process is capable once the process is stable . How ever I wanted to study if the two sets of data are significantly different.
    The Glitch in this is the data does not seem to be normal . I only have 18 data points in each set of Data.
    What does the forum think is the best way to prove significance or What test statistic to choose


    Mike Carnell

    There are lots of options.
    You can transform the data to make it normal. For some reason this one just rubs me wrong. There is life after failing a normality test. 
    You can test the difference in variances using a Levene’s Test. No assumptions about normality.
    You can test meadians rather than means using the Mann-Whitney, Moods Median, or Kruskal-Wallis tests. (Non parametric tests)
    There are other options but if you do these you can run them on Minitab. It will let you run the various test pretty simply without a lot of work. That way you can spend a little time understanding the analysis and decide if you have any confidence in these types of tests.
    If you don’t have Minitab you can download it from the web. It doesn’t last forever (just a trial copy) so don’t store anything in there you want to keep.
    Good luck.


    Carl H

    As Mike stated, there are options for comparing means/medians of two groups which are not each Normally distributed. 
    Another quick manual test is the TUKEY end count test.  Dot plot the two groups.  Count the points from the “low” group that are lower than the lowest value from the “high” group.  Count the points from the “high” group that are higher than the highest value from the “low” group. Add these together;  If sum is >6 you have ~95% confidence there is difference in means (ref 1)
    If you are really after differences in varaition, test for equal variances in MINITAB should help.  Levenes test output should be used for non normal data.  Without MINITAB you could do this by hand using F test and F table.  With 18-1 = 17 DOF, I get about 2.2-2.5 as critical value from table.  If you are not good at F table lookups (like me), a quick formula for critical F is 10 / sqrt ((N1 + N2)/2)) where N is sample sizes (ref 1).  From this I got 2.35, which is in the ball park.
    Since you stated that the data was not in control, simple run charts of each data set in time order may tell you about their relative differences even if mean and varaition are the same.
    (1) Basic Statistics, Kiemele, Schmidt, Berdine



    When analyzinga process for any reason you need to create a sampling plan. The purpose forthis plan is to gather as much information as you can about the conditions , personnel, machines, environment, time of day etc. The data set should be much larger than 18 points. ( If this is financialy possible) Take data for several days or weeks depending upon the frequency of repetition ofthe process.
    With a substantial data set you can perform a myriad of queries rooting out the cause of your deviations.



    Can F test be used being a non normal data. Or is is a good enough approximation

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