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I am using around 200 variables to compare 2 populations, group A and group B. Here's a representation of what the data looks like

Var1    VarA    VarT    Var3    group
2       0.56    10       152    A
3       0.43    11       187    A
5       0.25    15       149    A
7       0.12    12       132    A
2       0.78    8        132    A
1       0.55    7        178    A
0       0.35    7        240    A
0       0.36    7        205    A
0       0.3     6        137    A

Var1    VarA    VarT    Var3    group
5       0.24    10       205    B
8       0.76    8        120    B
7       0.43    9        531    B
4          0    5        203    B
5       0.52    11       215    B
2       0.63    14       224    B
1       0.46    12       211    B
2       0.64    1        212    B
6       0.55    7        134    B
5       0.78    7        222    B

I was trying to find the variable that shows the biggest difference between these 2 groups, by comparing the data column-by-column (e.g. "VarT" from group A with "VarT" from group B). I am working in R.

I found the statistical distance tests (such as Kullback–Leibler divergence, Cramér–von Mises, Bhattacharyya distance and Kolmogorov–Smirnov test) useful in this case. The problem I am having is that I cannot decide which test to use, what are the preferences among these tests? Unfortunately I wasn't able to find any comparisons between these tests. My data is numerical only with no NA values, and it is highly variable.

Direction towards other methods for testing the "overlap" between the 2 distributions in each variable are welcome.

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  • $\begingroup$ Hypothesis testing and calculating distances is not quite the same. So I wonder if you could be more precise? $\endgroup$ – Michael M Oct 8 '13 at 10:18
  • $\begingroup$ Thanks for your repy, I am looking for calculating the distance, I picture it in my mind as drawing each pair of similar variables (from A and B) as 2 distribution curves, and measure the area of overlap. I would like to pick the variables with the smallest overlap area. $\endgroup$ – Error404 Oct 8 '13 at 10:27
  • $\begingroup$ You could try MANOVA (Multivariate ANOVA) or even logistic regression. $\endgroup$ – kjetil b halvorsen Aug 29 '18 at 8:13

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