I want to compare a set of frequencies and determine the p-value of their dependence. One of them is the null distribution of frequencies and the other is the distribution that I want to test. The data look like this:
nucleotide background selected 1 0.1489113 0.06074766 2 0.1428619 0.04205607 3 0.1189465 0.63084112 4 0.1209048 0.05140187 5 0.1218093 0.07476636 6 0.1282073 0.04205607 7 0.2183589 0.09813084
I cannot use the $\chi^2$ test because the numbers are less than 1. I've tried to take the $\log_2$ of the ratio, but I end up with some negative numbers so the $\chi^2$ is a no go again. How can I conduct a test of independence with these values and compute a p-value?
EDIT, additional informations:
basically i'm working on DNA sequences. i have a background pool of sequences that act like a null distribution and from this background i have selected a number of sequences for a particular biological function. now, i wanted to compare the distribution of mutations in a small sequence of 7 nucleotides in the pool of selected sequences versus the background.
To achieve this, i've taken all the instances where this sequence is present with one mutation in both pools and determined the frequency of mutation for each nucleotide (e.g. number of mutations at a given nucleotide / total number of mutations over all nucleotides), that is how i end up with those frequencies.
now my aim was to show that the pattern of mutation is indeed much different in the selected pool with respect to the background (63% of the mutations in the selected pool happen in the 3rd nucleotide, and the other nucleotides undergo visibly less mutations than in the background)
to provide further information, the selected column describes the frequency of 214 mutations over the 7 nucleotides while the background column describes the frequency of 120508 mutations over 7 nucleotides.