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Archiver > GENEALOGY-DNA > 2003-01 > 1041782354


From:
Subject: Re: [DNA] Y test - random samples
Date: Sun, 5 Jan 2003 10:59:14 EST


In a message dated 01/04/03 6:11:00 PM Pacific Standard Time,
writes:

> I read it as 99.7 percent and 99.8 percent probability that 2 people,
> randomly selected, WON'T MATCH ALL markers on 9 out or 9 or 11 out of 11
> markers. Is that what it says?

Yes, although with rounding it would be 99.8 and 99.9 percent.

> I'd be interested in knowing what is the probability of matching less than 9
> markers.... eg. the probability that two people taking a 9 marker test test
> would match 8 out of 9, or 7 out of 9, or 6 out of 9, or 5 out of 9 markers

Interesting question, but I don't know of any way to calculate it. We'd
probably have to have access to the raw data and run some random simulations
on it. But the odds of getting partial matches do increase considerably.
There are nine different ways two samples could match 8 out of 9 markers.
There are 36 different ways two samples could match on 7 out of 9 markers,
84 different ways two samples could match on 6 out of 9, and 126 different
ways two samples could match on 5 out of 9.

Those numbers come from the combinatorial formula, N! / (K! * (N-K)!), where
N is the total number of markers and K is the number of markers which match.
If you have Excel, the spreadsheet formula is

=COMBIN(N,K)

or you can use the scientific calculator that comes with Windows to compute
the factorials.

However, the theoretical number of combinations probably would not be
observed in practice, because the Y chromosome is inherited as a unit. For
example, DYS388=14 and DYS390=22 are the modal values for Hg2, and DYS388=12
and DYS390=24 are the modal values for Hg1. It would be quite unusual to find
DYS388=14 and DYS390=24 in one sample, so that puts some constraints on the
combinations you could find in the Y-STR database.

Still, the bottom line is that it much, much easier to find partial matches.

Ann Turner
GENEALOGY-DNA List Administrator
>http://lists.rootsweb.com/index/other/Miscellaneous/GENEALOGY-DNA.html
DNA preservation kits: >http://www.dnafiler.com

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