Tests for Significance

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    Paul McDaniel

    We have implemented a process improvement.  We have run with the new process for 30 days and are unsure of the process accomplishments.  So for each of 30 days I have an mean value and std dev of the data for that day.  Samples made each day are 10 units.We have dug up a control group data set from the past.  We have 10 days of data in that control group (mean and std dev each day) for 10 days.It seems that conducting a means test does not account for the variation seen over each day.  For the means test we want to declare our population statistics to be the average of the means and the std deviations of the production runs vs textbook indications we should average our means and take a std dev of the means.By the way, when we analyze our data by taking the average and std deviation from the mean values, we reject our hypothesis that the process was improved.  When we average our means and use the std dev (averaged) from the 10 units run each day, we fail to reject our hypothesis.  So we are probably guilty of trying to make the statistics overly complicated to prove our point.



    I might be being a bit simple here but:
    1. have you control charted your data yet, old versus new to see what it looks like (Xbar , S chart). Does it even look like it might be different?
    2.A means test such as ANOVA and test for equal variance should tell you statistically whether you have changed your process or not.
    Whenever you can, plot your data in an appropriate form and just have a look at it, try and understand what you have before you try applying statistics, it saves a lot of time in the end.



    Hi Paul,
    I do not understand your hypothesis: It should be that your process was not improved. It will be easier to reject this hypothesis (thus saying that you really have got an improvement) when using the stdev of the means as this will be approx sqrt(10) smaller than your real stdev. So I think your way to use the stdev of the daily results comes closer to reality but still might not really count for the total variation. Don´t you have all the data? If not you could try a MonteCarlo-Simulation for the 30 “new” and the “10” old day´s do simulate all this data and compare then with t-test or Anova and F-Test.
    Before that I agree with the statement to have a look on the data graphically…:)
    regards, m

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