# Significance Testing for Poisson Data

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• #52820

Ken Feldman
Participant

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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#186325

Ken Feldman
Participant

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#186340

Xgames
Member

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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#186343

Lee
Participant

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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#186344

newbie
Participant

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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#186347

Mikel
Member

Wrong

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#186348

Mikel
Member

Wrong

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#186349

Xgames
Member

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#186351

Taylor
Participant

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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#186352

Ken Feldman
Participant

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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#186373

Dreemr
Participant

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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