Box 5-2 The Horwitz Trumpet Variation in Interlaboratory Precision

Coefficient of variation of interlaboratory results as a function of sample concentration (expressed as g analyte/g sample). The shaded region has been referred to as the Horwitz trumpet because Of the way it flares open. [From W. Horwitz, Evaluation of Analytical Methods Used for Regulation of Foods and Drugs. Anal. Chem. 1982, 54.67A] 

Interlaboratory tests are routinely used to validate new analytical procedures—especially those intended for regulatory use. Typically, 5 to 10 laboratories are given identical samples and the same written procedure. If all results are similar, and there is no serious systematic error, then the method is considered reliable.  

The coefficient of variation (CV) is the standard deviation divided by the mean CV = six. Usually the coefficient of variation is expressed as a percentage of the mean CV(%) = 100 X six. The smaller the coefficient of variation, the more precise is a set of measurements. 

In reviewing more than 150 interlaboratory studies with different analytes measured by different techniques, it was observed that the coefficient of variation of mean values reported by different laboratories increased as analyte concentration decreased. At best, the coefficient of variation never seemed to be better than5 

When the concentration of analyte is 1 ppm, the coefficient of variation between laboratories is 16%. When the concentration is 1 ppb, the coefficient of variation is 45%. If, perchance, you become a regulation writer one day, acceptable analyte levels should allow for variation among laboratories. The Gaussian distribution tells us that approximately 5% of measurements lie above x + 1.65,s (Section 4-1). If the target allowable level of analyte is 1.0 ppb, the allowed observed amount might be set at 1 + 1.65 X 0.45 ppb, or about 1.7 ppb. This level gives a 5% rate of false positives that exceed the allowed value even though the true value is below 1.0 ppb. 

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