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Stata FAQ
How can I test for equality of distribution?

An alternative test to the classic t-test is the Kolmogorov-Smirnov test for equality of distribution functions. In a simple example, we'll see if the distribution of writing test scores across gender are equal using the High-School and Beyond 2000 data set. We'll first do a kernel density plot of writing scores by gender.
use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear

kdensity write if female == 1, plot(kdensity write if female == 0) ///
	legend(label(1 "Females") label(2 "Males") rows(1))
 
ksmirnov write, by(female)

Two-sample Kolmogorov-Smirnov test for equality of distribution functions:

 Smaller group       D       P-value  Corrected
 ----------------------------------------------
 male:               0.2468    0.002
 female:             0.0000    1.000
 Combined K-S:       0.2468    0.005      0.003
From the test, it is apparent that the writing scores across gender do not have have the same distribution function.

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