This is similar to the question Measuring the "distance" between two multivariate distributions, except that I want to measure distance between two data sets. I can imagine simply computing the mean, standard deviation, and other summary statistics and then somehow aggregating the differences for each distribution, but that does not seem very theoretically sound.
I wonder if there is a generally accepted method for doing this measurement.
Best Answer
I think your question is essentially the same as Can I use Kolmogorov-Smirnov to compare two empirical distributions?, for which the Kolmogorov-Smirnov test is commonly used. The KS test statistic is a natural measure of the distance between two samples. For more details, please see Kolmogorov–Smirnov test on Wikipedia.