GENEALOGY-DNA-L Archives

From: "John F. Chandler" <>
Subject: [DNA] Some more replies
Date: Sat, 3 May 2003 18:40 EST
In-Reply-To: fauxdk@yahoo.com message <20030503202440.59567.qmail@web41206.mail.yahoo.com> of Sat, 3 May 2003 14:24:38 -0600

David wrote:
> For example, with respect to the contour rings
> seen on the triangle plots sent with the results for those people tested by
the
> DNAPrint test, if the red dot (MLE - most likely estimate) is surrounded by a
> band that is 1 / 2 as likely as the MLE, and another band that is 1 / 100 as
> likely, I can't get it through my thick head why one should put much if any
> faith in the latter, even if there are imprefections

Part of your confusion stems from the fact that this likelihood is a
probability density for a continuous variable. In other words, the
probability of getting a value within a little box divided by the area
of the box. If you consider the area of the red dot and the area of a
thickened yellow line running along the outer contour, I think you can
convince yourself that there could easily be 100 times the area in the
thick line as in the equally thick dot. The obvious consequence is that
the total probability of getting a value somewhere on the line is at
least comparable to the total probility of getting a value somewhere on
the dot.

-----

Tom wrote:
> You say that if all the confidence contours
> converge in the corner, one is just as likely to be 0% NA (or whatever)
> as 15% (or whatever).

No. There is an important distinction between the two ways of
describing differences (i.e., in terms of relative likelihood and
in terms of significance). I said that, if the contour lines all
converge in the corner, then there is no statistical significance to
the difference between the dot and the corner. In other words, the
most likely value can be different from zero without beging
*significantly* different from zero. However, that does not mean
that a zero value is just as likely as the non-zero result. That's
the one thing you definitely cannot say. According to the calculations,
the red dot *is* the most likely single value and is more likely than
any other single value (all things being equal). One point that I made
several weeks ago and not since: all things are generally not equal, and
you may have your own source of information about your genetic makeup
that you can and should fold into the calculations. If you *know* you
have a couple of great grandparents who were, say, "mostly Indian", then
you would have your own version of the triangle plot with your own red
dot somewhere around 20% NAM and 80% EUR and your own contours of
confidence around that point. DNAprint doesn't have that information,
but you do (assuming you can place some kind of numeric values on your
knowledge). Thus, the most likely estimate available to *you* is the
properly weighted average of their result with your result. By the
nature of things, the result of combining two independent sources of
information will give a more robust answer than either source by itself
(unless the two sources disagree so violently that you know one of them
has to be dead wrong).

> What if the first (black) contour doesn't
> converge with the other two contour lines? That is, it stays away from
> the corner.

In that case, you can say that the red dot is significantly different
from zero (aside from possible systematic errors).
-----

Roy wrote:
> Admittedly I am "dense" at this, but what means (below) "then your
> result is not statistically distinguishable from 0"? Does it mean that
> Andi's 8% NA could just as likely be 0%.

Same answer as for Tom above. It means that you can't rule out zero
as the answer, even though 8% is more likely.

> My own triangle has African at the top; European at bottom left;
> East-Asian at bottom right. The Red Dot is smack-dab on the left
> (upright) line about 10% of the way up from the bottom, and the three
> confidence rings (not segments of a circle, but of a long elipse)
> more-or-less converge in the European corner (the inner one about 2% up
> from the corner) and intersect the (upright) line at varying distances
> up that line - between 20% to 25% of the way up.

Therefore, your result is about 10% African, 90% European, and the
statistical uncertainty is about 8%. The systematic error is anybody's
guess. There could be some East Asian in there, too.

> I was expecting a certain percentage of NA. So, since my confidence
> rings "run into the side and converge in the corner" (as explained
> below) then........What?

Well, I guess that means you didn't get any plot showing NAM on one
corner? I would hope that means that plot would have shown contours
hugging even closer to the EUR-AFR edge, but it's unfortunate that
you came away with no report at all on the uncertainty of the NAM
percentage. As far as the meaning of the results you got: you can say
with 99% confidence that your percentage of African ancestry is between
0% and 25%, that your European ancestry is between 75% and 100%, and
your East Asian is between 0% and some upper bound that you can read
off the plot (sounds like 5-10% from you description). The upper limit
on Native American is probably lower than for East Asian, but it's
not actually specified.

John Chandler

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