# Is the Cohen's D a suitable test for my dataset?

I have two variables (A and B). A has 3,000 samples; B has 500,000. They represent cumulative solar radiation (summer 2000) in Alta Valtellina (Italy), divided in two major areas (A and B) which I need to compare. Below are the histograms of my datasets:

As far as I know, a two-sample t-test won't be ideal here because my samples are too large (see my previous question). So I thought about using the Cohen's D test. Running the kstest I know the distribution of these variables is not normal (output is 1, meaning "rejecting the Null Hypothesis that data is normally distributed"). Does the Cohen's D test needs the data to be normally distributed (I could not find a reference for this)?. If so, should I have to transform my data, or would someone suggest a better test for my case?

EDIT

At present I am writing a scientific paper, and only with a good justification like a statistical test (or a statistical comparison) I woul be able (or not) to say that my datasets differ from each other at a certain degree. If they are different (what I expect from the figure above, but I might be wrong), I would use the statistics of A (which is a sample of solar radiation pixels of a large area) to classifiy the remaining pixels of my study area (if they are similar to A I would assign them the same classification of A; B otherwise).

• If you think your samples are "too large" for a hypothesis test, you probably shouldn't be using hypothesis tests even if the sample were smaller. The samples being large doesn't indicate a problem with testing as such, it simply highlights more clearly that it answers a different question than the one you really intend to ask. – Glen_b Sep 9 '15 at 4:45
• As I want to find "large" differences in my datasets rather than looking at "tiny" ones, I think I'd better use the Cohen's D rather than the t-test, as the latter works with standard errors which gets really small for large dataset (denominator is high -> SE gets tiny). Would the Cohen's D be a reasonable choice in my case? Also, please take a look at my previous question (linked above), to better understand why I might prefer not using the t-test for my case (the situation is similar), but I am afraid I could not use the Cohen's D if my data is not normally distributed, could I? – umbe1987 Sep 9 '15 at 7:30
• Note that $\bar{x}_1$ and $\bar{x}_2$ will be so near to normally distributed as makes no odds. Further note that Cohen's d is actually $\frac{\bar{x_1}-\bar{x_2}}{\sigma}$ and you don't know $\sigma$ (i.e. Cohen's $d$ as he defined it - see Cohen (1992), Table 1** - is not a sample quantity!). Even if you ignore what Cohen is actually doing and replace $\sigma$ by $s$, in what sense does "Cohen's d" qualify being called a test rather than simply an estimate of the effect size? Does Cohen's arbitrary classification into small, medium and large really correspond to what you need here?...ctd – Glen_b Sep 9 '15 at 8:19
• ctd... ** see also Cohen "Statistical power analysis for the behavioural sciences", 2e., p274, where he explicitly states that $\sigma$ in Cohen's $d$ is a population quantity. What Cohen is doing is discussing effect size in the context of a power analysis, which is conducted before the data are even collected. What you're doing is calculating something after the data are collected. – Glen_b Sep 9 '15 at 8:36
• The point I was making about Cohen is that you're not using a test, you're simply making a comparison. Are you after an actual hypothesis test, or not? – Glen_b Sep 9 '15 at 22:34