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Skewness or Kurtosis usage?

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  • #30801

    Ron Tozydlo
    Member

    Does anyone use skewness or kurtosis?  Wheeler states that “skewness and kurtosis statistics are practically worhtless.”

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    #80874

    Robert Butler
    Participant

    From MIL-HDBK-5H  pp. 9-30 we have the following:
    ” The quantities (skewness corrections) added to the tolerance-limit factor, k99 and k90, represent adjustments which were determined empirically to protect against anticonservatism even in the case of moderate negative skewness.  Skewness is not easy to detect, and negative skewness in the underlying distribution can cause severely anticonservative estimates when using the normal model, even when the Anderson-Darling goodness-of-fit test is used to filter samples.  These adjustments help to ensure that the lower tolerance bounds computed maintain a confidence level near 95 percent for underlying skewness as low as -1.0.  For higher skewness, the procedure will produce significantly greater coverage.”
      Since an awful lot of people use the Mil Handbook I guess that the answer to your question is that a lot of people use skewness, or at least have to take it into account. 
      I can think of a few instances where I had to worry about kurtosis but these would only constitute personal use as opposed to general use of the property.

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    #80886

    Zilgo
    Member

    Skewness and curtosis are like the 4th dimension of statistics.  Just as it is more difficult to imagine objects in 4D space, it is difficult to interpret skewness and kurtosis in a statistical setting.  Most distributions that you will come across (unless you are in a REALLY technical setting) won’t be greatly affected by S & K.
    They exist and are important, but in better than 95% of situations you will be in, they will not play a major role.

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    #80918

    Eileen
    Participant

    Ron,
    Yikes! I wonder what Don Wheeler was thinking?
    The measures for skewness(asymetric) and kurtosis(peakness or slope of the sides of the distribution) are used extensively where process capabilities are determined. The most common method for determining the best model (or distribution) for your data is the four moments test (or versions thereof). The four moments – mean, variance, skewness, kurtosis- are calculated and then fitted to the closest mathematical function. A very popular method for fitting distributions to data sets is the Johnson curves, also based on the four moments.
    Many processes are not normally distributed. You need to know what function fits the data so you can correctly calculated Cp and Cpk or at least determine the expected percentage of the distribution outside the specifications.
    Eileen-Quality Disciplines
     

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    #80925

    Zilgo
    Member

    Of course, most of the time you can transform a non-normal distribution and make it normal, thereby making you worry about the four-moments tests and anything else having to do with moment generating functions is mostly unncessary.  In the event that you get a dataset that cannot be transformed to be sufficiently normal, then skewness and kurtosis will play a bigger role.  But I would bet that in better than, say, 95% of cases, a Box-Cox or a log transformation will get your data looking suffiently normal.

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    #80953

    Ron Tozydlo
    Member

    Thank you Robert and Eileen for your replies.  After reading your responses and reviewing Mr. Wheeler’s condemnation, I think he believes that because the statistical software programs on the market offer these two tools, novices may be steered to using them incorrectly.
     

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    #81014

    Hemanth
    Participant

    Hi,It is a valid question, I have shared one of my observation under the https://www.isixsigma.com/st/normality where these tools may be misleading (I am still trying to figure out if the dataset is statistically normal or not..), I would be greatful if you could lead me to some literature on this topic.

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    #81022

    Robert Butler
    Participant

     Hemanth, if you are looking for appropriate reading material I would recommend Statistical Models in Engineering by Hahn and Shapiro.  Chapter 6 is an excellent discussion of the Johnson distribution which Eileen referenced.  Given that this distribution enjoys widespread use a read of Chaptrer 6 will not only give you an understanding of that method of empirical distribution fitting it will also show you the importance of skewness and kurtosis to this fitting method.
      Chapter 7 is titled “Drawing Conclusions About System Performance from Component Data” and it explains those situations where an investigator would  need a measurement of skewness and kurtosis.
      The quick take away from Chapter 7 is that these two measurements are important when you need to have an understanding of the tails of your distribution.  “…the normal distribution approximation is frequently least adequate at the extreme tails of a distribution.”

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    #81086

    Ron Tozydlo
    Member

    Hemanth,
    Don Wheeler discusses how these statistics can be misused on page 46-54 of Advanced Topics of Statistcal Process Control, SPC Press, Inc., 1995.  I will be reviewing the book referenced by Robert.  Thank you Robert.

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    #81087

    Hemanth
    Participant

    Hi all,
    Thanks for your inputs.
    regards
    Hemanth

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