You always hear of one-in-million or billion chances but it would seem, by
simple analysis, that this is not true, and would certainly explain why the
FBI is fighting against people being able to do studies such as are quoted
in this article. But you really don't need to do any studies. That
statistics are pretty simple.
For those of you who are computer-wise, DNA matching is apparently a binary
coded system. "9 loci" matches are frequently used to find matches.
I don't know where the numbers come from that I hear in the court
cases...but this is how it quite apparently works. As the article below
pointed out -- they found 122 matches in the Arizona database of 65,000
where there was a 9-loci or more match. This very closely matches the
following table that I calculated based on simple binary probabilities
showing # of loci, cumulative probability, and resulting number of average
matches expected at each loci match level:
1 0,5 32500
2 0,25 8125
3 0,125 4063
4 0,0625 2031
5 0,03125 1016
6 0,015625 508
7 0,007813 254
8 0,003906 127
9 0,001953 63
10 0,000977 32
11 0,000488 16
12 0,000244 8
9 loci or better" numbers gives you 63 likely matches -- The 122 in the
study may well be due to the lack of independence -- e.g.. relatives and the
distribution of the actual DNA samples (which one would have to do a study
to find out).
Given the current U.S. population of 305 million then, how many matches
would there be in the U.S.? At 9 loci or more you would expect 595,703
matches. Proof beyond doubt? Hardly. At 12 loci it would be 74,463 and at
13 loci 37,231.
This is why DNA evidence alone is NOT a sure thing and should never be used
as the sole evidence in a case. So the next question would be -- if I
already have a suspect and his DNA matches -- how good is that? That
question is simply, "what are the odds that a specific DNA sample will match
somebody else in the database?" For the U.S. population that turns out to
be 1-in-546 or a 99.82% match at 9 loci and 1-in-8192 at 12 loci or a 99.99%
match. As a juror I don't think I would see much difference between 99.82%
and 99.9988%. And stating it as 1-in-8192 puts a whole different spin on
99.99%.
DNA can be used to EXCLUDE beyond any doubt. But it cannot be used to
INCLUDE beyond any doubt. Question being what is "reasonable doubt"
statistically? As a defense lawyer you might be able to say "in this city
of 65,000 alone there are approximately 122 people with the same DNA profile
as my client" -- that would be the 9-loci case -- or "8 people' at 12 loci.
That sounds like reasonable doubt to me and would make me completely
discount the DNA evidence. Without other supporting evidence I would never
convict somebody on DNA alone.
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