compare and show significant differnce between arrival times (poisson distribution) I have the number of arrivals per hour to a center before and after the implementation of a scheduling software that allows clients schedule their own appointments. 
Both distributions are Poisson with high arrivals at the beginning of the day that reduce as the day proceeds. The goal of the program however is to the reduced the variation and have people show up more evenly through the day. Because these aren't normal, I can't just compare standard deviations or any of the normal stats tools of significance.
Is there a way to normalize the curve? (using the mean arrival per hour / log??). Or are they any other tools I can use to show the significant reduction in variability of arrival times. thank you. 
 A: (per request)
You are trying to look at the difference between two things.  When I compare two things I like to use a box-plot, or a violin plot.
Your data IS going to be different than what I simulate.  The distributions are the weakest examples of how to compare two things.  I think you are looking to compare the overall distribution, and that you want to move the peak from "opening" to later in the day.  You also want to move the "whiskers" in - aka spread out the bulk of the arrivals.
So this suggests wait time can be approximated using negative binomial distribution.  I'm going to use it to describe arrival times.  
Here is some toy code:
set.seed(1)
library(vioplot)

N = 1000 #how many samples 

#arrival time before
before <- sort(rnbinom(n=1000, mu = 5, size = 24))

#arrival time after
after <- sort(c(runif(n=N/2,min = 0, max = 12.25),
        rnbinom(n=N/2, mu = 5, size = 24)))

#comparison

vioplot(before,after,names=c("before","after"))

Here is a toy plot:

This gives you a very initial way to explore your problem.  Look at the center of the plot, the shoulders, the whiskers, and the "bout" of the violin.  
Questions you should ask yourself:


*

*How many people are in each different contributing function of the "after"?  It should change over time.  Sample size drives detection of change.  Nature of the different mode also drives detection of change.  Things change over time.  In the winter in Wisconsin a clinic is going to get online scheduled visits much more reliably than in summer - because 20-below is really really cold.

*What is the new "mean" or defining parameters in the "after" function?  What does it have to be in order to see a "statistically significant difference"?  If everyone does it but the parameter change is small, then it drives detection.  

*What does it have to be to see a "technically significant
difference"?  Technical and statistical aren't always the same.  A 1% change that math likes isn't going to change your bottom line by 50%.  

