# Appropriate test for testing a pair of random binomial variables

I have pairs of values from two runs (replicate) for each sample along with total count for each run. I assumed each value as random binomial. I used log-likelihood ratio test to compare each pair, but my data range is wide, e.g. X1, X2 = (0,0), (0,1), (0,2), ..., (20, 20) with total counts for each run (n1, n2) range from hundreds to thousands. So my data look like:

ID    X1    X2    n1       n2
A1    0     0     119     230
A2    0     1     213     185
.     .     .      .       .
.     .     .      .       .
.     .     .      .       .
A200  15    23    2300    1735


What test will be appropriate and power for it? Already tried likelihood ratio test, how can I implement Fisher's exact test in R for it? any other test that may use X1 condition of X1 + X2!

Any help will be appreciated. I want to implement it in R, so R codes/function will be more helpful. Thanks in advance

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What is the question? What do you want to determine from these data? Are the X1 and X2 predetermined or are they observations? What do they mean? What is a "run"? Does it correspond one-to-one with a single "ID"? What does the reference to "X1+X2" mean? –  whuber Jul 1 '11 at 16:04
Do you want to run a separate test for each row or an overall test? –  Aniko Jul 1 '11 at 16:13
@Aniko, yes I want to run a separate test for each row. –  Adam Jul 6 '11 at 19:13
@whuber - X1 and X2 correspond to observed count data for lab test in run 1 and run2. Run is basically is a replicate, where a test was repeated twice. Yes it correspond one-to-one with a single ID. I assume that both X1 and X2 are iid binomial random variables. I am testing my assumption that both are from a same binomial distribution with parameter p1, and p2, where p1=p2=p. I am applying likelihood ratio test, but heard if I use a test where X1 is conditional on X1+X2 it is more powerful, which hypergeometric. (from the OP) –  chl Nov 3 '11 at 22:49
Let's see whether I get it. On row 2 you're saying that for ID = A2, $X_1$ is an observation of a Binomial($p_1,213$) variable and $X_2$ is an independent observation of a Binomial($p_2,185$) variable. You also assert all rows are independent. You wish to test whether $p_1=p_2$. You are wondering whether a test based on $\Pr(X_1|X_1+X_2)$ might be a good choice. Is all this correct? –  whuber Nov 3 '11 at 22:59
One option is the Mantel-Haenszel test. This will test/estimate the odds-ratio between x1 and x2 while allowing the margins to vary between the ID's. In R use the mantelhaen.test function.