Randy says:
<The smaller the proportional effect of the treatment, the larger an "n"
(number of colonies in the trial) you need.>
A useful statistic that anyone with an Excel spreadsheet can produce is
called 'coefficient of variation' or 'relative standard deviation'. In
general, biologists tend to cite CV values, chemists like RSD. No matter, its
the same statistic.
To calculate CV or RSD, enter your values, calculate the mean and standard
deviation for the data set, divide the SD by the Mean and multiply by 100.
This gives you a ratio expressed as a percent.
Since this ratio is a relative ratio, the units of measurement are not
important. The lowest possible value is 0, the highest is usually 100 -
although for very noisy data, the SD may exceed the mean, and the CV or RSD can
be higher than 100.
Now that you have your CV or RSD - however you want to call it, the
interpretation is easy. The smaller the ratio, the less noisy (variable) the
measurement. Higher values are noisy. The higher the CV or RSD, the more
colonies you are going to need for a valid test.
As an example, when analyzing for inorganic elements like copper, zinc,
lead, etc. - these metals occur in bees at ppm concentrations - for example,
80-100 ppm zinc is normal. The analytical instrument can easily detect ppm
concentrations. So, when I set up standards and run them through the
instrument, I expect to see the instrument output values that are very close to
the standard, and the CV or RSD may be as low as 1. If its above 5%, I go
back and re-calibrate the instrument.
Now, if I'm looking for pesticides in bees or pollen, I've a very complex
matrix, and I'm interested in looking at concentrations of pesticides as low
as 1 ppb. That is far more difficult to accomplish, and the GC/MS
instrument is not likely to be able to match a standard at 1% or even 5%. As long
as its below 15%, most labs will proceed. That's why EPA Superfund labs
often run triplicate analyses - analyze the same sample three times, and
take an average to get the reported result. That 10-15% CV or RSD is
unavoidable, so don't depend on one analysis result - especially if there are
millions of dollars in cleanup costs at issue.
Now, as per bees. We've done CV or RSD on multiple colonies for lots of
metrics - such as size of bee population, amount of brood, amount of honey,
etc.
Most of the bee population metrics come in at about 25-35%. Honey stores
are more variable, expect 60-70% or more.
Toxic chemicals in control colonies (far removed from any source of the
toxin) may fall below 5%. Variation in toxic chemicals in areas with HIGH
chemical exposure may yield 5-10% - since all of the colonies are exposed.
But, if the toxic chemical is patchy - in different nearby fields, or if a
plume from an industrial source blows one way today, another tomorrow, then
the CV or RSD can exceed 100%.
One final example - pesticides in soils (or fertilizer, etc.). These tend
to be VERY patchy, and several samples from the same field may yield a CV
of as high as 200 to 300%. Getting a fix on the representative value for
the field is a huge problem.
Jerry
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