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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