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I have to do an hypothesis test for two series, both distributed as a Poisson. The first groups has its mean, and the second another one: i have to test the significance of this difference. Which test should i use?

The t-test for the difference between two means? I try the U-test, but I don't think it's ok cause it's only for continuous distribution, not discrete as Poisson ones.

kjetil b halvorsen
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Daniele
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You can analyze categorical predictors in regression models--including those using Poisson-distributed outcomes. You just need to ensure that you code the categorical variable appropriately (e.g., using dummy, effect, or contrast codes) in order to fit a model that yields interpretable/sensible intercept and slope estimates. Good descriptions of the various coding strategies can be found in West et al. (1996) and Cohen et al. (2013)

References

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.

West, S. G., Aiken, L. S., & Krull, J. L. (1996). Experimental personality designs: Analyzing categorical by continuous variable interactions. Journal of personality, 64(1), 1-48.

jsakaluk
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  • thanks for your answer, but i didn't find free stuff about the ones that you write about. What can you think about a simple statistical test, is there a good one? thanks – Daniele Oct 17 '17 at 08:03
  • West et al. (1996) is currently freely available on google scholar through a link from semanticscholar.org. And I'm afraid that if you're insistent on having a Poisson-distributed outcome, a Poisson regression with a singleton categorical predictor (dummy, effects, or contrast coded) is as simple as you're likely to find. – jsakaluk Oct 17 '17 at 16:29
  • thanks for your availability. I don't undestand why are you telling me about a "Poisson regression" instead of using a test for the difference between two means. I have 2 groups of data, with different lenght, and i have to verify to a significance test between these 2 mean. How can i do that with a dummy variable? Sorry for my question, i'm quite new in this kind of analysis. – Daniele Oct 17 '17 at 16:43
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    A comparison between two groups can always be represented as a regression model. Just represent the groups with a *dummy variable*, which is 0 for one group, 1 for the other. The a model of form $y_i=\beta_0+\beta_1 \mathbb{I}_i+\epsilon_i$ represents the means of the two groups, respectively $\beta_0$ and $\beta_0+\beta_1$ – kjetil b halvorsen Nov 06 '18 at 19:50