I have two small samples denoting if something occured or not. For example:
$s_1=\left(1,1,1,0,0,1\right)$
$s_2=\left(1,0,0,0,0,1,1,0\right)$
I want to test if proportions of occuring $1$ are the same. I cannot use proportion test for two samples, as samples are too small. Can I use Chi square homogenity test and get the robust outcome?
Best Answer
The reason your sample size is a problem for a chi-square test or a test of proportions that relies on approximation to a Normal distribution is that these tests use asymptotic results. In other words, they are built on the assumption that you have "large enough" sample size.
A test that is similar to the chi-square test, but does not rely on asymptotic assumptions, is Fisher's exact test described here: http://en.wikipedia.org/wiki/Fisher%27s_exact_test