How to check goodness of fit of new data to a previously developed model? I have a model created from a prior dataset and I want to know if it can be used on my current dataset.  
The original model gives the expected percentage of times an email is opened x hours after it is sent.  I have data for another type of email showing how many emails were opened x hours after it was sent.  What should I do to determine whether I can use the first model for the second dataset?
 A: Since your model gives the expected proability that an email will be opened at most X hours after it is sent, you can use the Kolmorogov-Smirnov goodness of fit test.
To use the test, treat the model as your null hypothesis cumulative distribution function. Now, create the empirical distribution function of your data, EDF(T), which is just the number of emails sent at most T hours after they were sent. 
Calculate the Kolmorgov-Smirnow statistic using the above two inputs (null distriution, and EDF) and compare to the proper cutoff value (for your desired significance level). 
EDIT 1: Based on the discreteness of the data, another possibility it to use a chi-square goodness of fit test. Just form a bin for every 1 hr increment and use the model estimate for the probability and the total number of samples to get your expected counts for each bin. Then calculate the actual counts for each bin and compute the chi square statistic and check for significance, per the link. The chi square test does not require continuous distributions, so it won't require simulation to determine appropriate cutoff values.
