HORRAT:  More convenience or more confusion?

In the Berlin-Proceedings of ICUMSA (22nd conference) results of a "Workshop on Collaborative Studies" are given, with a table "Analyte concentration" on page 75. This table is reproduced here, but with one additional column entitled "Max. Acceptable RSDR(%) = 2H(%)".

Analyte concentration

Conventional	Fractional	Log C	Expected RSDR(%) = H(%)	Max. Acceptable RSDR(%) = 2H(%)
100%	C = 1	0	2	4
10%	C = 0.1	-1	2.8	5.6
1%	C = 0.01	-2	4	8
0.1%	C = 0.001	-3	5.6	11.2
0.01%	C = 0.0001	-4	8	16
0.001%	C = 0.00001	-5	11	22
0.0001%, 1 ppm	C = 10-6	-6	16	32
0.1 ppm, 100 ppb	C = 10-7	-7	23	46
0.01 ppm, 10 ppb	C = 10-8	-8	32	64
0.001 ppm, 1 ppb	C = 10-9	-9	45	90
Formulas:			2(1-0.5*log C)	2 * 2(1-0.5*log C)

On page 75 of the proceedings, just three lines below the corresponding table, "Horwitz Ratio or HORRAT" are printed in bold (should be 2 or less), apparently to stress its importance. An alternative variant to check an RSDR(%) from a collaborative test is mentioned near the bottom of the same page, but without bold letters as the second of two suggestions: "In a collaborative test, the RSDR actually calculated from the result should not exceed two times H." This proposed limit "two times H" is visible from the new table column. All different variants of RSDR (observed, expected, acceptable) have the same dimension (% of the mean = corresponding to a C.V.) and equal dimensions are advantageous for a quick understanding of the figures in the table. Within a final table of a collaborative test it is possible to end up like a balance, with an actual line (%), followed by a limit line 2H(%), and the reader will see clearly if the limit is kept or not. The introduction of a dimensionless "HORRAT" (observed RSDR, divided by expected RSDR) is unnecessary. With reporting of HORRAT values chemists may loose their feeling about "what is acceptable?", and the convenience of a uniform limit of 2 is unimportant, compared to this. During conference lectures tables are usually shown for seconds rather than minutes and therefore it would be better to show figures as uniformly as possible:  a) in the dimension of the mean (Sr, SR, r, R) and  b) in % of the mean (RSDr, RSDR, H, 2H). Figures with uniform dimensions can quickly be understood and compared during projection on the screen. Dimensionless HORRAT figures are additional confusing figures in a projected final table. If HORRAT and RSDR are of similar range, it is difficult for a reader to find the orientation quickly, in order to compare HORRAT with a (mostly hidden) reference value of 2. If the reader concentrates on HORRAT, he will lose his own feeling about too high values of RSDR.

2004-08-11       G. Pollach