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I have an extremely large data set, but I'll simplify it down as, although I think I should use a chi squared test, I've run into difficulties applying it:

Let's say I have a list of 20 different 'foos'.The number of 'foos' that bind 'bars' has a normal frequency distribution. Some 'Foos' bind to various 'bars'. Let'say I have 500 'bars' Some 'foos' come from within 'bars', but some do not.

How would I go about to testing whether 'foos' preferentially bind to 'bars' that they reside in?

##### EDIT 
|---------------------------------| <= chromosome

|----------* ** **-----------------| <= miRNA (foo) within chromosome (no gene)

|------0000000000-------------| <= gene (bar) within chromosome (no miRNA within it)

|-----------0000** ***0000--------| <= miRNA within a gene within a chromosome

I'm looking at miRNA gene target bindings. When the miRNA's are translated, they usually target various genes (or more specifically their protein products). I have the gene targets of each miRNA, determined using an algorithm called 'miranda'. I want to see whether the miRNA that is synthesised from inside a gene preferentially binds that gene across all thousands of miRNA and their different gene targets (as some of them will bind to the gene from which they arise by chance).

Initially I thought about taking the observed probability that a 'foo' within a 'bar' binds that 'bar' and subtracting that from the probability that a 'foo' would bind a 'bar'. Is this correct? It seems that I'm not really using that much data...

Is this the right way to go?

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    $\begingroup$ I've read this twice and still cannot picture your situation at all. A small example of data (like yours) and/or some simple notation beat a lengthy word picture every time, so please don't tell us what you have, show us. $\endgroup$
    – Nick Cox
    Commented Mar 10, 2014 at 14:47
  • $\begingroup$ Apologies, I've edited the post although I'm struggling to make it abstract enough so that any statistician can look at it, but also making it informative enough $\endgroup$
    – Mark Ramotowski
    Commented Mar 10, 2014 at 15:26
  • $\begingroup$ Thanks for the editing. You've clarified it to the extent that (a) some people should now be able to recognize what you're doing (b) I'm now clear that they don't include me. Is pure chance really a benchmark here? I'll be signing off here, but quite what your null hypothesis is may not be clear even to people working with similar data. $\endgroup$
    – Nick Cox
    Commented Mar 10, 2014 at 15:31
  • $\begingroup$ If you want to draw an ASCII-art illustration, indent it 4 spaces so characters are constant-width, and everything lines up $\endgroup$
    – Glen_b
    Commented Mar 10, 2014 at 18:07
  • $\begingroup$ I indented 4 spaces, as @Glen_b suggested. Whether everything else should line up I leave as a question beyond my rudimentary biology. $\endgroup$
    – Nick Cox
    Commented Mar 10, 2014 at 18:26

1 Answer 1

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The answer in fact did not require a chi-squared test. The best thing was to randomise the data and see if the actual probability that the miRNA targeted their own gene was more than if it was at random.

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