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Significance Testing for Poisson Data

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  • October 22, 2009 at 1:55 pm #52820

    Darth
    ★ 10 Years ★
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    I have three sets of Poisson data and I need to test whether there is a significant difference between the three sets. The data is clearly Poisson so using a normal approximation is out of the question. Any thoughts on doing an “ANOVA” type analysis but with the severely skewed count data….93% of the counts are 0 just to give you an idea. Thanks.

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    October 22, 2009 at 10:10 pm #186325

    Darth
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    Hey stop fooling around and somebody please answer this question. Thanks.

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    October 23, 2009 at 3:05 pm #186340

    Xgames
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    With lots of data (greater than 25 or 30), the central limit theorem takes cares of things (when checking for differences between the means).

    ANOVA is pretty robust to normality, though….the assumption in the model is for the residuals to be normal.  If they’re grossly skewed, then will most likely need to do a transformation on the data.

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    October 23, 2009 at 5:55 pm #186343

    Lee
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    A bit rich for my blood at this time, but look at http://www-stat.wharton.upenn.edu/~lzhao/papers/newtest.pdf
     

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    October 23, 2009 at 6:01 pm #186344

    newbie
    ★ 10 Years ★
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    Hey Doc,
    I assume you transformed it and/or ran the ANOVA / Moods Median for the helluva it….anything interesting result?
    With 93% of the data being zero, I assume your data is counting  occurances of some event in a given time period/sample area  (ie 93% of the time, there is no occurance of a given event).  
    If so, would it be practical/useful to translate your poisson data into a continuous format, such as a MTBF or ‘Mean Time Betweeen Events’ in this case?  
    Just a thought….good luck.

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    October 23, 2009 at 6:30 pm #186347

    Mikel
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    Wrong

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    October 23, 2009 at 6:31 pm #186348

    Mikel
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    Wrong

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    October 23, 2009 at 7:27 pm #186349

    Xgames
    ★ 10 Years ★
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    Please enlighten me Stan…..

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    October 23, 2009 at 8:24 pm #186351

    Taylor
    ★ 10 Years ★
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    Doc
    You should be able to perform ANOVA and get Some kind of a result. Have you tried performing standard deviation of runs?
     

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    October 23, 2009 at 10:31 pm #186352

    Darth
    ★ 10 Years ★
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    Xgames, thanks for trying to provide input but as Stan said, you are a bit off.I said the data was counts/Poisson which is discrete data. The Central Limit Theorem has little to with discrete data let along hypothesis testing.While it is true that ANOVA is pretty robust with respect to the assumption of normality again I was clear that the data was significantly skewed which occurs with the Poisson especially for small counts.The issue of normality of residuals is in regards to regression not hypothesis testing, especially for non continuous data.There is occasion when counts are large that the Poisson can be approximated by the normal distribution and the analysis becomes easy. That is not the case here. The counts are small and as I described a lot of zeros. Transformation will not work.Thanks anyway.

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    October 26, 2009 at 1:57 pm #186373

    Dreemr
    ★ 10 Years ★
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    I think the most appropriate test may be the Chi-Square Goodness of Fit.  In the end it is count data it just is not proportional.

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