How do you show that two populations are statistically similar? 
Possible Duplicate:
Testing hypothesis of no group differences 

Suppose I have $k$ samples from 2 independent experiments (service times by 2 methods) and their means are similar. How do I statistically show that both methods have similar service times?
 A: You can use equivalence testing here.  Since you are testing to see if the two population distributions are similar I think it is a mistake to base conclusions off of a two sample t-test.
Here is the approach.  Take the ratio of the two service times and construct the CI for a given significance level.  
Now, the hard part, you need to scientifically determine what cutoffs indicate they are the same (the cutoffs do not come from the data).  For example the FDA might specify the 90% CI of the ratio must be in the range of .80 to 1.25 to consider two drugs equivalent.  
If your entire CI is within the cutoffs then you can conclude the two distributions are similar.  If part of the CI is in the cutoff and part outside the results are inconclusive.  If the entire CI is outside the cutoffs then you can conclude they are different.
A: You have two distributions of service times. What you want is to compare those distributions and check whether they are really different.
There are a few statistical tests that can do this for you each with different drawbacks (e.g. sensitivity to changes in scale, location, etc.)
Have a look at the Kolmogorov-Smirnov test or Mann–Whitney U
A: Set a high alpha level and show that you fail to reject the null.
