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Math Help - Normality plot (no of errors over 2 years)

  1. #1
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    Question Normality plot (no of errors over 2 years)

    I am trying to analyse number of errors over a period of 2 years and I run a normality test for my data via minitab.

    it shows Normality plot (no of errors over 2 years)-normality-plot.jpg

    Can i conclude that the graphical representation show non-normal data ?
    then what should i do ?

    Thanks!
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  2. #2
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    Re: Normality plot (no of errors over 2 years)

    If that is a Q-Q plot then your data is not normal.

    Tell us about the dataset.
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  3. #3
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    Re: Normality plot (no of errors over 2 years)

    Month No. of errors occurred
    Jan 0
    Feb 5
    Mar 1
    Apr 0
    . 1
    . 4
    .

    etc...


    that's all. Do you need the full data ?
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  4. #4
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    Re: Normality plot (no of errors over 2 years)

    Any tip from anyone ??
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  5. #5
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    Re: Normality plot (no of errors over 2 years)

    i would like to test for special causes, but if my data is non-normal , is there any way out or I need to gather at least 30 for my sample size ?
    i can't get 30 as I only have data from 2010. and the number of errors made is less than 30.
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  6. #6
    Senior Member MaxJasper's Avatar
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    Re: Normality plot (no of errors over 2 years)

    Plot also histogram of your data. You have most of your data =0 which indicates normal dist is not a candidate and perhaps a right-skewed distribution is need like chi-square ..etc. Also check Poisson distribution. Please post a table of your complete data.
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  7. #7
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    Re: Normality plot (no of errors over 2 years)

    This is my dataset :

    Month No of Errors
    Jan 2010 2
    Feb 2010 3
    Mar 2010 1
    Apr 2010 1
    May 2010 1
    Jun 2010 4
    Jul 2010 1
    Aug 2010 1
    Sep 2010 0
    Oct 2010 2
    Nov 2010 3
    Dec 2010 1
    Jan 2011 2
    Feb 2011 2
    Mar 2011 1
    Apr 2011 0
    May 2011 5
    Jun 2011 0
    Jul 2011 0
    Aug 2011 0
    Sep 2011 1
    Oct 2011 0
    Nov 2011 0
    Dec 2011 1
    Jan 2012 0
    Feb 2012 0
    Mar 2012 0
    Apr 2012 4
    May 2012 1
    Jun 2012 1
    Jul 2012 1
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  8. #8
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    Re: Normality plot (no of errors over 2 years)

    I managed to get 2010 data till July 2012,so i believe the sample size (N=31) is now sufficient.
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  9. #9
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Normality plot (no of errors over 2 years)

    A histogram of your data indicates right-skewed data:


    Normal Q-Q diagram is:


    And variation of data form normal:


    To test whether data fits a normal distribution or a Poisson distribution:


    H0: data is normally distributed :: reject (p<0.05)
    H1: data follows a Poisson distribution :: accept (p>0.05)

    Data can also follow other distributions. You should check and select the best that fits and describes your data.

    Please notice that at p=0.01 significance level your data can be considered marginally normally distributed but not at p=0.05 significance level. However, usually as you collect more data these conditions will change.
    Attached Thumbnails Attached Thumbnails Normality plot (no of errors over 2 years)-errors_qq_normal.png   Normality plot (no of errors over 2 years)-erros_hist.png   Normality plot (no of errors over 2 years)-errors_qq_normal_det.png   Normality plot (no of errors over 2 years)-errors_h0.png  
    Last edited by MaxJasper; August 29th 2012 at 07:28 PM.
    Thanks from hazel
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  10. #10
    Senior Member MaxJasper's Avatar
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    Re: Normality plot (no of errors over 2 years)

    Problem with your Q-Q is that you plotted the data points while you should plot the Expected values.
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  11. #11
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    Re: Normality plot (no of errors over 2 years)

    Quote Originally Posted by hazel View Post
    This is my dataset :

    Month No of Errors
    Jan 2010 2
    Feb 2010 3
    Mar 2010 1
    Apr 2010 1
    May 2010 1
    Jun 2010 4
    Jul 2010 1
    Aug 2010 1
    Sep 2010 0
    Oct 2010 2
    Nov 2010 3
    Dec 2010 1
    Jan 2011 2
    Feb 2011 2
    Mar 2011 1
    Apr 2011 0
    May 2011 5
    Jun 2011 0
    Jul 2011 0
    Aug 2011 0
    Sep 2011 1
    Oct 2011 0
    Nov 2011 0
    Dec 2011 1
    Jan 2012 0
    Feb 2012 0
    Mar 2012 0
    Apr 2012 4
    May 2012 1
    Jun 2012 1
    Jul 2012 1
    1. It cannot be normal as it is discrete.

    2. Why would you even expect it to be "normal", you should be expecting it to have a Poisson distribution which would only be approximately normal when the mean number per period is large (which it is not).

    .
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  12. #12
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    Re: Normality plot (no of errors over 2 years)

    Quote Originally Posted by MaxJasper View Post
    Problem with your Q-Q is that you plotted the data points while you should plot the Expected values.
    Sorry i don't understand what do you mean. Could you please explain in detail ? Thanks
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  13. #13
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    Re: Normality plot (no of errors over 2 years)

    This is what I have got from minitab: Graph > Probability Plot.

    Normality plot (no of errors over 2 years)-prob-plot-confirmed-errors.jpg
    Attached Thumbnails Attached Thumbnails Normality plot (no of errors over 2 years)-prob-plot-confirmed-errors.jpg  
    Last edited by hazel; August 30th 2012 at 05:33 PM.
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  14. #14
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    Re: Normality plot (no of errors over 2 years)

    With Reference to
    Identifying the Distribution of Your Data - Minitab

    I do a check and I got this :

    Normality plot (no of errors over 2 years)-distribution-identi_plot-errors.jpg

    P<0.005 so it is not normally distributed. Where do i go from here ?
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  15. #15
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    Re: Normality plot (no of errors over 2 years)

    No one ?
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