The Analysis of Means and Ranges

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Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.


Dr. Bill McNeese
BPI Consulting, LLC

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Comments (2)

  • DaleWFebruary 12, 2019 Reply

    Hi Bill,I found Dr. Wheeler's attempt to replace ANOVA with adapted SPC charts very interesting.  I applaud you for making his approach more available to others with your SPC for Excel add-in. For his example, we might ask whether his range-based ANOM-ANOR charts are telling us more or less than conventional ANOVA methods do.  I would say that they are giving us similar information, but here classic ANOVA is more powerful at putting a p-value on whether there is any hint of unequal variance (no, p=0.759 by Bartlett's test) and at detecting which subsets are different: (Two, Four > One, Three at overall alpha=0.05 by Tukey Grouping).  Modern software can provide graphs which convey overlapping CI on variances and non-overlapping 95% CI on effects nearly as clearly as adapted SPC charts will.I think that the more interesting situation occurs when there is unequal variance among subgroups.  Then, how do ANOR charts compare to conventional equality of variance tests for detecting it, and are ANOM charts made markedly more robust by using average range instead of pooled variance for detecting differences between subgroups?  I suspect that you might be writing about this in the future?

    • billFebruary 17, 2019 Reply

      Hi Dale, 
      I have not done much work at looking at the issue of unequal variances but it is definitely something worth looking at – i image Dr. Wheeler has done it someplace.  I like the simplicity of this method – and how visual it is.

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