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Re: [Phys-l] Below Detection Limit (was Another uncertainties question...)



Thanks again --

The thing that helped me most was simply recognizing that I was asking the wrong question. I was asking for a concrete, scientific answer to what was really question of purpose. (As so often happens when we try to answer non-scientific questions with science, the answer was tortured for me.) It was sorta a scientific "not enough information" situation in my case, but apparently that's not what I wanted to hear so I banged my head on for awhile when the answer should have been obvious. In any case, the discussion helped clarify my thinking...

BTW... as we've looked into it more, we have indeed found some cases where by state ecology rules non-detects actually are NOT counted as zero, but rather half the threshold detect, for purposes of moving avgs, etc... One may speculate that this might have been put in place to keep people from improving their average by using a crummier test. I dunno... But this is purely speculation on my part. Or of course, those reasons pointed out by John.

There may well be other ways as well, of course, as has been pointed out. But the moral for me is that it does appear to be important to read the fine print in any governing laws if you find your self in such a situation, or consider the purpose behind your question, as your mileage may vary ;)
Happy monday, all -

Jason




John Denker wrote:
On 01/25/2008 03:15 PM, Edmiston, Mike wrote in part:

In the legal situations the answer is clear... the "below detection
limits" must count as zero.

Not necessarily. Even if we restrict attention to legal situations,
the answer depends on who has the burden of proof. Not all "legal situations" are the same.

You can't cite a violation and issue a fine when there is no evidence
that the company was actually in violation. The "not detected" readings
have to be averaged as zeroes.

That applies in situations where *you* have the burden of
proving a violation.

The situation is very different in situations where the company
has the burden of proving compliance. The company has to treat an undetectable quantity as being equal to D (the detection threshold) because it can't prove otherwise.

I don't know what happens outside of environmental permit compliance,
but I have worked on a liaison committee between the refinery, the
health department, and the Ohio EPA for the past 20 years, and it is
clear that for average values calculated for legal permit compliance
purposes, the "not detected" values are averaged as zeroes. I don't see
how it could be any other way.

There's more to physics than legal technicalities.

The physics works like this:

a) One hypothesis is that a "no detect" report corresponds to a raw reading of zero.

b) Another hypothesis is that a "no detect" report corresponds to a raw reading uniformly distributed on the interval (0, D) leading to an average of D/2.

c) Another hypothesis is that a "no detect" report corresponds to a raw reading always infinitesimally less than D.

It would be rash to /assume/ hypothesis (a) describes reality. Ditto
for hypotheses (b) and (c).

I'm not suggesting that we replace one ill-founded assumption with
another. I'm suggesting that a prudent person should consider /all/ the plausible hypotheses, including (a), (b), (c), and perhaps others.

This is sometimes called a what-if analysis. It is also sometimes
called scenario planning. The objective is to make decisions that
produce acceptable results no matter which of the plausible
scenarios comes to pass.
http://en.wikipedia.org/wiki/Scenario_planning

1) It may be that D is small enough (mercaptan) that all three scenarios are equivalent. But maybe not. 2) When D is large (carbon monoxide) it might be fatal -- literally -- to assume an undetected quantity should be treated as zero.

This is why scenario planning is important. It gives you a systematic
method for making good decisions in the face of uncertainty.

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Jason Alferness
University of Washington
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