# [Clips] Read two biometrics, get worse results - how it works

dan at geer.org dan at geer.org
Thu Oct 20 11:42:19 EDT 2005

```RAH, et al.,

It is true that one can combine two diagnostic
tests to a worse effect than either alone, but
it is not a foredrawn conclusion.  To take a
medical example, you screen first with a cheap
test that has low/no false negatives then for the
remaining positives you screen with a potentially
more expensive test that has low/no false positives.
There is a whole health policy & management
literature on this.  I reproduce the barest
precis of same below, assuming the reader can
manage to view it in a fixed width font while
respecting my hard carriage returns as writ.

--dan

cheat sheet on terminology of medical diagnostic testing
_________________________________________________________________

\  the true situation
\
\    +       -
+-------+-------+---
|       |       |
+ |   a   |   b   |  a+b
what the         |       |       |
diagnostic       +-------+-------+---
test returns     |       |       |
- |   c   |   d   |  c+d
|       |       |
+-------+-------+---
|       |       |
|  a+c  |  b+d  |   t

true positives
a = positive testers who have disease

true negatives
d = negative testers who are without disease

false positives
b = positive testers who are without disease

false negatives
c = negative testers who have disease

prevalence
(a+c)/t = fraction of population that has disease

sensitivity
a/(a+c) = what fraction of those with disease test positive

specificity
d/(b+d) = what fraction of those without disease test negative

predictive value positive
a/(a+b) = what fraction of positive tests have disease

predictive value negative
a/(a+b) = what fraction of negative tests are without disease

Notes:

Information retrieval people know sensitivity as "recall" and
predictive value positive as "precision."

Screening with a cheap test with high sensitivity then an expensive
test with high specificity is often the best (most cost effective)
strategy.

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