Test whether two samples differ

You have two datasets collected from two versions of a system, or from two cities. The variable of interest may be continuous, skewed, heavy-tailed, or categorical, and the sample sizes may be different. 1. How would you test whether the two samples come from the same underlying distribution? Discuss the right test choices for continuous versus categorical data, and for univariate versus multivariate settings. What assumptions do the common tests make, and how would you interpret statistical significance versus practical significance? 2. What sampling methods do you know, and when would you use each one in practice for data collection or offline evaluation?