SEM is a very basic statistic. If one calculates the average = mean, one
can easily compute the Standard Error of the Mean.
Simply stated, the large the SEM, the more variable or 'noise" there is in
the data. It is common to see the mean or average presented with the
associated standard deviation SD or standard error in tables and figures in
scientific papers.
To help you understand this statistic, I suggest you look at the mean and
SE and calculate another statistic, the relative standard deviation as
follows:
In _probability theory_ (http://en.wikipedia.org/wiki/Probability_theory)
and _statistics_ (http://en.wikipedia.org/wiki/Statistics) , the relative
standard deviation (RSD or %RSD) is the _absolute value_
(http://en.wikipedia.org/wiki/Absolute_value) of the _coefficient of variation_
(http://en.wikipedia.org/wiki/Coefficient_of_variation) . It is often expressed as a
percentage. A similar term that is sometimes used is the relative variance
which is the square of the coefficient of variation._[1]_
(http://en.wikipedia.org/wiki/Relative_standard_deviation#cite_note-0) Also, the relative
standard error is a measure of a statistical estimate's reliability obtained by
dividing the _standard error_
(http://en.wikipedia.org/wiki/Standard_error_(statistics)) by the estimate; then multiplied by 100 to be expressed as a
percentage.
The relative standard deviation is widely used in _analytical chemistry_
(http://en.wikipedia.org/wiki/Analytical_chemistry) to express the precision
and repeatability of an _assay_ (http://en.wikipedia.org/wiki/Assay) .
100 × [(standard deviation of array X)/ (average of array X)] = relative
standard deviation expressed as a percentage_[2]_
(http://en.wikipedia.org/wiki/Relative_standard_deviation#cite_note-1)
So, when you do this, you will get a % number from 0 (unlikely, unless
every measurement is exactly the same) to greater than 100, maybe as high as
200-300%. The smaller the %, the better the data.
When I run known chemicals of known concentrations to calibrate an
instrument, say 5 ppb, 10 ppb, 15 ppb, 20 ppb - I expect to get an RSD or CV of 5%
or less.
If I take a field collected sample (ONE SAMPLE) of bees or pollen, mix it
well, and split it into three samples, for organic pesticides I expect to
get an RSD or CV of less than 15% (the larger number is due to uneven
mixing, interferences from the sample matrix, instrument sensitivity, any
weighing error, differences in moisture content, etc.) - for complex chemicals in
complex matrices like bees, pollen, or nectar, lots of variable affect the
accuracy and precision of the instrumental results.
The point is that there is variability in the analysis results that is
unavoidable - one works to keep this as low as possible.
Now, if I go out into a large field and take soil samples from different
parts of the field and analyze them, I expect the variation to go up - say
we''re looking at pesticides in soil. Plowing, irrigation, wind, leaching,
rain, irrigation, spray consistancy, overlap, all contribute to making the
conc of pesticide in soil at any one spot different than in another spot.
One expects to see center of field different from edges or corners, but in
reality, two samples taken just a foot or two apart can vary a lot. For
pesticides in soils, RSDs or CVs of over 100%, as high as 300-500% are common.
Same for pollen stored in combs - move over a few inches or to another comb
in same hive, you may get a very different number.
All of this causes those of us doing this kind of work to get headaches.
The problem is designing the experiment to deal with this variability.
The more variable the results (as seen by stats such as SEM), the more
samples you need to take, and one may need to move to a more sophisticated
sampling design, such as stratified sampling. In fact, done properly, one
usually wants to do some preliminary trials to obtain results that can then be
processed statistically. Those results can be used to compute how many
samples one needs to take to overcome the inherent variability in the measure
(s).
This usually comes down to asking the question ' What is a Representative
Sample', which, unfortunately, many forget.
Jerry
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