Independence test for values between 0 and 1 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. 
 A: I'd suggest you forget about the frequencies and work with the raw counts (i.e. don't divide by 214 and 120508). 
First put these data into R. You can do it eighter directly or by use of R for Excel (which works only on 32-bit MS Office for Windows). I'll assume you put the 7 counts of background in variable B, and 7 counts of selected in variable S. Remember, that R is case-sensitive!
Run this code:
S<-c(23,123,54,235,23,32,123) #sample data.
B<-c(65,345,65,35,786,43,234) #sample data.
library(dgof) #Required to use a more accurate version of the ks.test.
ks.test(rep(1:7,times=S),rep(1:7,times=B))

The subexpression rep(1:7,times=S) converts counts into the actual observations by simple replication.
A: Good comment by Tito, pointing out that you may want to make sure that your frequencies are coming from a number of trials that are similar (ideally identical).
I recommend multiplying each proportion that you have by X, and setting the number of trials to X also. 
If you have an identical number of trials for each variable, then X = the number of trials. You can then run your chi-squared. If there are differing numbers of trials, then I'm not sure.
Hope this helps.
