-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Hi Ed,
> only prepared one sample, so if on that particular instance I > picked up 4.8ul and not 5.0ul, this will translate into > systematically I don't share your opinion about a single measurement translating into a systematic error. I would call it a poorly designed experiment in case you were actually iterested in how accurately you determined the protein concentration. Best, Tim On 03/11/2013 04:46 PM, Ed Pozharski wrote: > 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. > - -- - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.12 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iD8DBQFRPhm5UxlJ7aRr7hoRAuoSAJwN9zAJj2qbZBNMlF0cJ0goszaqWQCg2hFp 9u+slrVyYEYbCf2D2/SOVTg= =UACi -----END PGP SIGNATURE-----
