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Re: Blade article
Just a note...it would be nice to send Tom Henry these comments. I know
he (like most reporters) is eager to correct any errors in reporting so
they aren't promulgated in future stories. Tom's email is
thenry@theblade.com
I've cc'ed him on this response...I'm not sure if he's on the beachnet
listserv.
--
Christine Manninen
GLIN Webmaster: www.great-lakes.net
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Taylor, Christopher wrote:
> This IS a great explanation of what a geometric mean is, and why it is used
> in microbiological statistical studies. Makes perfect sense to me. However,
> to a non-scientific/non-math oriented consumer it is very confusing. Many
> people have no idea what a standard deviation, a mean or a log
> transformation is. How then, do you easily explain to this person what a
> geometric mean is(when they don't understand logs or means)? I know this is
> basic to those of us in the field, but to the average consumer, it's very
> advanced voodoo statistics! :-)
>
> The author I was referring to in my previous post was the author of the
> Blade article, Tom Henry. I know he understands what a geometric mean is,
> but he will probably never be able to get the column space to explain it..
> Therein lies the problem.
>
> I had also mentioned that the only thing I could think of that would be
> "other factors" was Tom Henry's way of implying the geometric mean's
> "elevating low numbers and reducing high numbers"(quoted from below). Not
> sure that's what he was really trying to say, but it was all I could think
> of!
>
> Chris Taylor
> Chief Chemist
> Toledo Water Plant
> 419-245-1717
>
>
>
> -----Original Message-----
> From: Richard L Whitman [mailto:rwhitman@usgs.gov]
> Sent: Wednesday, September 01, 2004 10:52 AM
> To: Shannon Briggs
> Cc: beachnet@great-lakes.net
> Subject: Re: Fwd: RE: Blade article
>
>
>
> I am not the author of the article referred to paper, but I can explain why
> one uses geometric means.
>
> A simple arithmetic means, also called an average, is an estimate of the
> population and assumes that the samples are representative of the true
> population. Since this almost never completely true, we invented
> statistics to help us estimate of the characteristics of the population
> (range, variation, distribution, mean, trends).
>
> E. coli, like most biological populations, are not normally distributed,
> they are most often clumped (clustered, contagious, patchy, etc). In
> statistical terms, this means the variance exceeds the mean. There are
> several solutions to this. One way is to take the median. This is the
> sort of thing they do with people's incomes or home prices. That is
> because while most of us are average, those mega-rich really skew the mean
> upwards. There are two more ways that we use to make the sampled
> population more normal.
>
> Composite sampling from many places on the beach will give you a better
> representation than single samples. This is not without cost though, you
> lose information on the variation which is important for most statistical
> testing. Here is a seemingly unlikely example, but I've seen this sortof
> data often. You took 5 samples each reading 50, 50, 100, 100, 1000. The
> compositing of those samples would yield 260 cfu/100ml, a beach closure.
> If you had taken the samples individually you would have found that the
> standard deviation was 414 and you would know that there was a problem with
> your estimate of the average. We look at sampling strategy closely in the
> August issue of Env. Sci and Tech. Julie Kinzelman and Al Dufour have
> worked with composite samplings a lot and have some actual data on this.
>
> The second way to deal with the extremes, is to log transform the data.
> Microbiologist traditionally use 10 based logs. This has the effect of
> elevating low numbers and reducing high numbers. In effect, this allows
> for a more bell shape distribution, a population characteristic that is
> necessary for most traditional statistical testing.
>
> The geometric mean can be computed by:
> 1. taking the logarithm of each
> number
> 2. computing the arithmetic mean of
> the logarithms
> 3. raising the base used to take the
> logarithms to the arithmetic mean
>
>
>
>
> Here is an example
>
>
>
> X
> Log(X)
> 1
> 0.0000
> 2
> 0.30103
> 3
> 0.47712
> 10
> 1.00000
> Geometric mean = 2.78
> Arithmetic mean = 0.44454.
> 10.44454 = 2.78
>
>
>
> If any one of the scores is zero then
> the geometric mean doesn't make any
> sense and cheat by adding a constant to
> every number. The geometric mean for
> the example I gave intially is 120,
> swimmable.
>
>
>
>
>
> The geometric mean is always lower than
> the arithmetic mean, so the criteria is
> different. EPA can explain how they
> derived the 126 CFU/100 ml. Hopes this
> helps a bit.
>
>
>
>
>
>
> Richard Whitman
> Chief, Lake Michigan Ecological Research Station
> 219-926-8336 Ext. 424
>
> 1100 North Mineral Springs Road
> Porter, IN 46304
>
>
>
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