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If I have two groups of data sets. Each group has two arrays of empirical data. In the first group each array has, say, 50,000 data points, and in the second group each array has 3,000 data points. Assume all arrays follow same distribution, but they are collected from different populations. If I understand correctly, I can use some methods to find the statistic distances or divergence between the two arrays in each data group (e.g. KL divergence, Jensen-Shannon divergence). But can I compare the two divergences and say that the distance in the first group is larger/smaller than the second one. In other words, if I found that the Jensen-Shannon Divergence for the first group is 0.2 and the value for the second group is 0.1, can I say the distance between the two arrays in the first group is bigger than the distance between the two arrays in the second group? If not, is there any method allow me to do so? Is there a method that can give a universal-kind measure so I can compare distances from different set of data?

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  • $\begingroup$ I have talked to many people since but still have not figured out this problem. Any suggestion will be highly appreciated. $\endgroup$ – Ryan Wang Nov 20 '14 at 4:06

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