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 https://stats.idre.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.