The question of how large a difference between results must be to be statistically significant should be very important to consider and was to some extent discussed at the recent meeting on Quality Specifications in Stockholm. By the way, the draft consensus report from that meeting is still open for comments at Jim Westgard's homepage, easily reached through the IFCC homepage and through many national homepages as well. It is not so easy to derive the formula if you insist on t-tests and a couple of years ago I offered an alternative approach on the acb forum.
This is how the formula is derived:
Consider that you have two results, A and B, and the uncertainties uA and uB, respectively.
The uncertainty of the difference (A-B) is sqrt(uA^2 + uB^2). [I apologize for the clumsy notation due to limitations in the mail word processor].
To be significant, the difference should be larger that the uncertainty of the difference, i.e >sqrt(uA^2 + uB^2).
To reach an often used probability, the uncertainty should be multiplied by a coverage factor, for about 95 %, a factor of 2 is often used. Now, if the results that are compared are obtained with a high degree of reproducibility, it is fair to assume that uA = uB. The formula is then reduced to 2 x uA x sqrt(2), about 2,8 x uA, in practice it is often recommended to use 3 x uA, for simplicity in field (ward) work.
It is useful to remember how this formula is derived since one might face situations when uA is not equal to uB, e.g. different laboratories etc.
The situation when the difference is so large that the relative or absolute uncertainty is greatly different at those concentrations (amounts) then the difference between the measurements is mostly large enough to state that the above considerations are not very interesting.
I
t goes without saying, and it this highly dissatisfying, that reports in most cases fail to inform the user about the uncertainty of the results and therefore leave him/her without sufficient background to evaluate the significance of the difference.
Anders Kallner
Dept Clin Chem, Karolinska hospital, Stockholm Sweden
E-mail address:
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phone: +46 (0)8 5177 49 43
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