Hi folks,(adsbygoogle = window.adsbygoogle || []).push({});

I have what I think is quite a basic question, but I'm looking for options.

So, I have data that consists of a set of numbers (this is not a set theory question) - each number can be ascribed to one of two groups (the source of the number). Now, I have knowledge of the source of each number - but I want to set up a test case, to try and group the numbers such that they separate into their two respective groups (pretending I don't know what the true result is when I start).

Now, my question isn't about the mechanics of re-ordering data or anything of the sort - what I want to do is somehow characterise the 'errors' that the algorithm I'm working with produces. This is perhaps best described by an example: say I have a set of X's and O's (these are actually numbers, but the X and O represents the source of each number - the two groups). The set is ordered arbitrarily: XOOXOXOOOXXOOXXX. I then re-order the set based on some things I know about the numbers and get, say: XXXXOXXOXXOOOOOO.

Then, the set is split into X's and O's with two errors (the O's that are on the side of the X's). This is a pretty good result - and something that I want to quantify. I am thinking I could just do a hypergeometric probability test, splitting the entire set in half and testing the probability that each half contains as many X's and O's as it does. The problem is that I would also like the 'distance' to be important. As in,

OXXXXXXXXOOOOOOO is a worse result than XXXXXXXOXOOOOOOOO, because this O on the left has made it's way to the other end of the other group. Maybe some rank correlation approach would do this?

I want to take care and avoid doing something silly!

thank you,

N

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# Quantifying Significance In Re-ordering Of a Set

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