Salve,
I would like to solicit opinions on a certain question about the
relationship between statistical and systematic error. Please read and
consider the following in its entirety before commenting.
Statistical error (experiment precision) is determined by the degree to
which experimental measurement is reproducible. It is derived from
variance of the data when an experiment is repeated multiple times under
otherwise identical conditions. Statistical error is by its very nature
irremovable and originates from various sources of random noise, which
can be reduced but not entirely eliminated.
Systematic error (experiment accuracy) reflects degree to which precise
average deviates from a true value. Theoretically, corrections can be
introduced to the experimental method that eliminate various sources of
bias. Systematic error refers to some disconnect between the quantities
one tries to determine and what is actually measured.
The issue is whether the classification of various sources of error into
the two types depends on procedure. Let me explain using an example.
To determine the concentration of a protein stock, I derive extinction
coefficient from its sequence, dilute it 20x to and take OD measurement.
The OD value is then divided by extinction coefficient and inflated 20
times to calculate concentration.
So what is the statistical error of this when I am at the
spectrophotometer? I can cycle sample cuvette in and out of the holder
to correct for reproducibility of its position and instrument noise.
This gives me the estimated statistical error of the OD measurement.
Scaled by extinction coefficient and dilution factor, this number
corresponds to the statistical error (precision) of the protein
concentration.
There are two sources of the systematic error originating from the two
factors used to convert OD to concentration. First is irremovable
inaccuracy of the extinction coefficient.
Second: dilution factor. Here main contribution to the systematic error
is pipetting. Importantly, this includes both systematic (pipettor
calibration) and statistical (pipetting precision) error. Notice that I
only prepared one sample, so if on that particular instance I picked up
4.8ul and not 5.0ul, this will translate into systematically
underestimating protein concentration, even though it could have equally
likely been 5.2ul.
So if pipetting error could have contributed ~4% into the overall
systematic error while the spectrophotometer measures with 0.1%
precision, it makes sense to consider how this systematic error can be
eliminated. The experiment can be modified to include multiple samples
prepared for OD determination from the same protein stock.
An interesting thing happens when I do that. What used to be a
systematic error of pipetting now becomes statistical error, because my
experiment now includes reproducing dilution of the stock. In a
nutshell,
Whether a particular source of error contributes to accuracy or
precision of an experiment depends on how experiment is conducted.
And one more thing. No need to waste precious protein on evaluating
error of pipetting. I can determine that from a separate calibration
experiment using lysozyme solution of comparable concentration/surface
tension. Technically, a single measurement has accuracy of said 4%
(padded by whatever is error in extinction coefficient). But one can
also project that with actual dilution repeats, the precision would be
this same 4% (assuming that this is a dominant source of error).
So, is there anything wrong with this? Naturally, the question really is
not about extinction coefficients, but rather about semantics of what is
accuracy and what is precision and whether certain source of
experimental error is rigidly assigned to one of the two categories.
There is, of course, the wikipedia article on accuracy vs precision, and
section 3.1 from Ian's paper (ActaD 68:454) can be used as a point of
reference.
Cheers,
Ed.
--
Edwin Pozharski, PhD, Assistant Professor
University of Maryland, Baltimore
----------------------------------------------
When the great Tao is abandoned, Ideas of "humanitarianism" and
"righteousness" appear.
When intellectualism arises It is accompanied by great hypocrisy.
When there is strife within a family Ideas of "brotherly love" appear.
When nation is plunged into chaos Politicians become "patriotic".
------------------------------ / Lao Tse /
