HORRAT value

Calculated repeatability, intermediate precision, and reproducibility values can be compared with those of existing methods. If there are no methods with which to compare the precision parameters, theoretical relative reproducibility and repeatability standard deviations can be calculated from the Horwitz equation and the Horrat value (Table 5). Horwitz RSD values are reported in Table 6. Higher variability is expected as the analyte levels approach the detection limit (see below). Next to the Horwitz equation, the AOAC s Peer Verified Program proposes its own levels of acceptability of %RSD as a function of analyte concentration level [56,72]. 

Horrat value = RSDr (trial)/RSDR(Horwitz) < 2 RSDr and RSDr values according to AOAC peer-verified program... 

Precision calculated values of RSD must be in compliance with Horwitz (Horrat) values... 

Results aimed at Precision multiple results, both repeatability and reproducibility >%RSD is compared to theoretical Horwitz Horrat values Trueness Single result per test material, > calculation of Z score as measure for bias... 

It is now generally accepted practice that HORRAT values of 2 or less indicate that the method is of adequate precision. Hence, in our example, this is clearly so. 

The concept of HORRAT values was introduced by Horwitz etal. (1989). The HORRAT value is the ratio of RSDr obtained from the actual experimental data from intcriab-oratory data to the PRSDr calculated from the Horwitz formula ... 

When the value of RSD and the mean value of the analyte concentration have been established, the Horwitz ratio, HORRAT, can be calculated. 

From these simple calculations the ANOVA table can be constructed together with the HORRAT ratio. An important difference from the conventional ANOVA table is that it allows for the sample variation to be accounted for. The general ANOVA table and calculated values for S samples are shown in Tables 28 and 29 but the example uses only two. However, if more than two samples are desired/available the procedure can be extended. 

It is readily apparent that the HORRAT ratio of 2.89 indicates that the method is not sufficiently precise for inter-laboratory work. However, inspection of the ANOVA table shows a large value for the mean square due to the samples, MSs. This is an indication that they may not have been homogeneous and that the method may in fact be satisfactory. This demonstrates a major advantage in partitioning the variances between laboratory, sample and error rather than the traditional within- and between-laboratories method. 

All of the foregoing calculations are simply to trim the data set by removing outliers in accordance with the set criteria. All that remains is to calculate the mean value for the sample, the repeatability and reproducibility of the trialled method and the HORRAT ratio. These values can be calculated using a one way ANOVA method similar to that described in Table 29 and given in Table 33 and the final values in Table 34. 

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