Is there any significance test to compare count data measured at pre and post from the same subjects? For example, compare the number of car accidents of a group of drivers at their first year of driving and second year of driving. If we assume that:

$Y_{i1} \sim Poisson (\lambda_1); Y_{i2} \sim Poisson (\lambda_2)$

How may we test the following hypothesis when $Y_{i1}$ and $Y_{i2}$ are paired:
$H_0: \lambda_1 = \lambda_2 $.

  • $\begingroup$ stats.stackexchange.com/questions/9561/… and ucs.louisiana.edu/~kxk4695/JSPI-04.pdf $\endgroup$
    – user158565
    Oct 21, 2018 at 20:50
  • $\begingroup$ @a_statistician Neither of those references appears to apply to paired data. $\endgroup$
    – whuber
    Oct 21, 2018 at 21:02
  • 1
    $\begingroup$ "from the same subjects" This phrase is not very clear. Suppose you observed 100 drivers in first year, in second year you still follow-up these 100 drivers. Question is what kind of data you have, just counts of accidents during two different year, $Y_1$ and $Y_2$? or you keep the record for each driver separately, such as $(Y_{i1}, Y_{i2}), i = 1,...,100$. For first situation, the linked method works. for second situation, Poisson regression in needed. $\endgroup$
    – user158565
    Oct 21, 2018 at 21:10
  • 1
    $\begingroup$ 1. Your title asks about equality of variables but your body text is about equality of their means (and by extension, their distributions). Please edit your title to reflect what you're actually asking. 2. You will probably need some kind of model for the joint distribution so any kind of application-specific information that would help narrow that selection may be important. $\endgroup$
    – Glen_b
    Oct 22, 2018 at 3:00
  • $\begingroup$ @Glen_b 1. Updated. 2. I am not sure how to find a joint pmf when they are paired. It would not be a problem if the two variables are independent as sum of two poisson follow a poisson with mean ($\lambda1 + \lambda2$). $\endgroup$ Oct 22, 2018 at 3:28


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