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Have data in this format:

|  A  |  A' |  B  |  B' |
|-----|-----|-----|-----|
| 0.4 | 0.2 | 0.4 | 0.3 |
| 0.3 | 0.3 | 0.3 | 0.5 |
| 0.1 | 0.2 | 0.6 | 0.2 |

Note that A + A' =/= 1. In other words, we have a given proportion, A, another proportion, A', and that's it. The rest is unknown but can be assumed to be the remainder until we reach 1. So we can assume that there is some A'' = 1 - A - A'.

What we need to do is compare if A and A' are "similar" to B and B', but we don't have any information about the size of the populations.

Some additional info: These are proportion of portfolio allocations into different security types. So A could be Stocks, A' could be Bonds, and A'' could be everything else. We want to compare the portfolio of A to the portfolio of B.

Thanks!

vdiddy
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    Do you want to perform a hypothesis test / are you hoping for a p-value, or do you just want a meaningful way to compare how similar they are? Is each row an independent observation? – gung - Reinstate Monica Apr 22 '15 at 21:12
  • Hi. Yes, each row is independent. We are hoping for a p-value to determine if similar or not, so that would be ideal (if it exists in this situation). If that's not possible, I am open to exploring another meaningful way. – vdiddy Apr 22 '15 at 21:20
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    Broadly speaking, there's likely to be little that can be done. If the proportions are accurately given to sufficient figures, it may be possible to identify useful lower bounds on the $n$ (e.g. if you have a proportion like "0.2142857" then the smallest $n$ consistent with that is 14). In your case you'd be using information on both A, and A' to get lower bounds on the row-n. In rare situations, that may be enough to obtain usable upper-bounds on the p-value. If you have other, external information about $n$ (like 'We know $n$ must be at least 50'), then much more might be done. – Glen_b Apr 23 '15 at 02:25

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