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Archiver > GENEALOGY-DNA > 2006-02 > 1139874465

From: "Diana Gale Matthiesen" <>
Subject: RE: [DNA] Earliest common ancestors for 37/37 and 43/43 matches
Date: Mon, 13 Feb 2006 18:47:45 -0500

Yes, of course the individual odds are based on the number of possible outcomes,
not the size of the group. But the size of the group in these examples had been
arbitrarily set to equal the number of possible outcomes, plus one (n+1). My
point was that the groups set up in the example were EXTREMELY non-random (the
odds against such a group occuring randomly really are astronomical), and that
in a truly random sample n+1 would not guarantee a match, which is what was
being said.

In other words, I would, indeed, attach significance to two people in my project
sharing a 37/37 match one step from their progenitor, regardless of whether my
project had ten members or ten thousand.

> -----Original Message-----
> From: John Chandler [mailto:]
> Sent: Monday, February 13, 2006 5:34 PM
> To:
> Subject: Re: [DNA] Earliest common ancestors for 37/37 and
> 43/43 matches
>
> Diana wrote:
> > The probability that two people in a group of 367 have
> > the same birthdate is 1/367 times 1/367 or 1 in 134,689 thousand.
>
> Not at all. Leaving aside the question of whether 365 or 366 is the
> best number to use, what you're proposing has nothing to do with the
> size of the group. The odds you're quoting are for the situation of
> picking out two specific people at random and asking if they both have
> the same birthday as YOU. That has nothing to do with the birthday
> "paradox", which calls for asking everybody in a randomly chosen group
> and finding out if at least two of them have the same birthday as each
> other, not specifying WHICH two people in advance. Any two will do,
> and any birthday will do. Essentially, you've demonstrated why this
> thing is called a "paradox".
>
> > In the case of STR testing for 37 markers, where 74
> one-step mutations are
> > possible from a common origin, the chance of two
> individuals having the same
> > mutation is 1/74 times 1/74 or 1/5476.
>
> Again, no. You've stated a number that is independent of the size of
> the group, and therefore does not take into account any part of the
> birthday paradox. The number you quote is the chance of picking out a
> specific mutation in advance and then discovering that two specified
> people (known somehow to have exactly one mutation each) BOTH have
> that exact mutation. That's not relevant.
>
> John Chandler
>
>
> ==============================