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REPORT FOR ANALYTICAL CHEMISTS Table 3. Comparison of Precisions for (P = 0.68) Single airid D uplicate Spectra η 2 = 25 Element Vinatr. 2 V„hem. 2 Vsampl. VT 2 VT Duplicate Single Κ Μη Κ Μη 9 25 9X2 25 Χ 2 27 24 27 24 364/25 1176/25 364/25 1176/25 50.56 7.1 96.04 9.8 59.56 7.7 121.04 11.0 Table 4. Background Readings 9B(MII) - θ Β (Μη) 0B(K) 0B(K) 25.9 26.3 -0.4 26.9 25.9 + 1.0 25.9 26.0 -0.1 26.7 26.1 +0.6 26.5 26.4 +0.1 25.8 26.0 -0.2 26.1 27.4 -1.3 27.5 26.3 + 1.2 26.2 26.1 +0.1 25.8 25.8 0.0 three measurements may be ex- pected to deviate from the mean by more than one standard deviation. It is more usual to accept a P level of 0.95 which means that one meas- urement in twenty, on the average, will deviate from the mean by more than two standard deviations). It is important to note that the errors and therefore variances refer to single herbage samples; i.e., accord- ing to the above scheme of analysis the analytical results obtained for Κ and Mn in a single (chemical) sample drawn at random from the field will be reproducible to within ± 20 per cent and ± 35 per cent, respectively. We could reduce this error in one of two ways: (i) we could draw η χ random samples (i.e., Pi, P 2 , . . . P nl ) and submit each to an analy- sis : the average of the ni analytical results would be accurate to within ν τ -=- \ / n i , i.e., the total variance would now become 400/ni for Κ and 1225/t for Mn; or (ii) we could select n 2 random herbage samples, form a homogeneous composite from these, and submit only one aliquot from this composite to anal- ysis: the analytical results ob- tained would be precise to within ± [Va„ai. 2 + v samp i. 2 /n 2 P per cent, i.e., the total variance would become [36 + 364/n 2 ] for Κ and [49 + 1176/n 2 ] for Mn. The choice of procedure must be left to the analyst, and that choice will be governed by the relative magnitudes of the analytical and sampling errors, the time factor in analysis and sampling, and the degree of re- producibility desired. These con- siderations will therefore determine the values for n! and n 2 . In the original investigation I used a 25- times replication at the sampling stage (i.e., n 2 = 25) so that the limits of reproducibility in the final result were those shown in the upper half of Table 3. Now in the instrumental assay employed for determining cations in plant extracts, as depicted in Fig- ure 1, it has always been specified that duplicate spectra be recorded for each portion of solution to be examined. The idea behind this is to increase the reproducibility of the instrumental performance. But however much this may be justified in practice from the purely analyti- cal point of view, is there really any justification for such replication when we view the process of de- termination as a whole? In Table 2 the instrumental variances for Κ and Mn are respectively 9 and 25, and these refer to results evaluated from duplicate spectra. Suppose we were to record only one spectrum per portion of solution to be ex- amined; this would be equivalent to doubling the instrumental variance. Hence if we evaluate our final re- sult from a single spectrum only, but still using a 25-times replica- tion at the sampling stage, we should then obtain the precisions given in the lower half of Table 3. It is seen that the v T differences as between single and duplicate in- strumental assays are not suffi- ciently large to justify a preference Brookfield Synchrolectric Viscometer Chemists' best friend keeps on getting better Today, "Brookfield Viscosity" is the universal language of viscosity measurement. Keeping pace with the science of Rheology isthe Brook- field Synchrolectric Viscometer. There are now nine models in the Brookfield line, one of which has the exact number speeds, speed range and centipoise range to meet your requirements. Whether you work with Newtonion or non- Newtonion materials . . . whether you work in the ultra-low viscosity range of 0 to 10 centi- poises up to 64,000,000 centipoises there's a Brookfield instrument for you. Why not take a look at the new Brookfield Viscometer and Automatic Viscosity Measuring Instrument brochure. We will be pleased to mail you one. Brookfield Stoughton 16, Mass. ENGINEERING LABORATORIES INCORPORATED Circle No. 24 on Readers' Service Card 28 A • ANALYTICAL CHEMISTRY
Transcript of Brookfield ENGINEERING LABORATORIES INCORPORATED
REPORT FOR ANALYTICAL CHEMISTS
Table 3 . Compar i son of Prec is ions for (P = 0 . 6 8 )
S ing l e ai rid D upl icate Spectra
η2 = 25
Element Vinatr.2 V„hem.2 Vsampl. V T 2 V T
Duplicate
Single
Κ Μη Κ Μη
9 25
9 X 2 25 Χ 2
27 24 27 24
364/25 1176/25 364/25
1176/25
50.56 7.1 96.04 9.8 59.56 7.7
121.04 11.0
Table 4. Background Readings 9B(MII) -
θΒ(Μη) 0B(K) 0B(K)
25.9 26.3 - 0 . 4 26.9 25.9 + 1.0 25.9 26.0 - 0 . 1 26.7 26.1 +0.6 26.5 26.4 +0 .1 25.8 26.0 - 0 . 2 26.1 27.4 - 1 . 3 27.5 26.3 + 1.2 26.2 26.1 +0 .1 25.8 25.8 0.0
three measurements may be expected to deviate from the mean by more than one standard deviation. I t is more usual to accept a P level of 0.95 which means that one measurement in twenty, on the average, will deviate from the mean by more than two standard deviations). It is important to note that the errors and therefore variances refer to single herbage samples; i.e., according to the above scheme of analysis the analytical results obtained for Κ and Mn in a single (chemical) sample drawn at random from the field will be reproducible to within ± 20 per cent and ± 35 per cent, respectively.
We could reduce this error in one of two ways: (i) we could draw η χ random samples (i.e., Pi, P2, . . . Pn l) and submit each to an analysis : the average of the ni analytical results would be accurate to within ν τ -=- \ / n i , i.e., the total variance would now become 400/ni for Κ and 1225/t for Mn; or (ii) we could select n2 random herbage samples, form a homogeneous composite from these, and submit only one aliquot from this composite to analysis: the analytical results obtained would be precise to within ± [Va„ai.2 + v s a m pi .2/n2P per cent,
i.e., the total variance would become [36 + 364/n2] for Κ and [49 + 1176/n2] for Mn. The choice of procedure must be left to the analyst, and that choice will be governed by the relative magnitudes of the analytical and sampling errors, the time factor in analysis and sampling, and the degree of reproducibility desired. These considerations will therefore determine the values for n! and n2. In the original investigation I used a 25-times replication at the sampling stage (i.e., n2 = 25) so that the limits of reproducibility in the final result were those shown in the upper half of Table 3.
Now in the instrumental assay employed for determining cations in plant extracts, as depicted in Figure 1, it has always been specified that duplicate spectra be recorded for each portion of solution to be examined. The idea behind this is to increase the reproducibility of the instrumental performance. But however much this may be justified in practice from the purely analytical point of view, is there really any justification for such replication when we view the process of determination as a whole? In Table 2 the instrumental variances for Κ and Mn are respectively 9 and 25, and these refer to results evaluated from duplicate spectra. Suppose we were to record only one spectrum per portion of solution to be examined; this would be equivalent to doubling the instrumental variance. Hence if we evaluate our final result from a single spectrum only, but still using a 25-times replication at the sampling stage, we should then obtain the precisions given in the lower half of Table 3.
It is seen that the vT differences as between single and duplicate instrumental assays are not sufficiently large to justify a preference
Brookfield Synchrolectric Viscometer
Chemists' best friend keeps on getting better Today, "Brookfield Viscosity" is the universal language of viscosity measurement. Keeping pace with the science of Rheology isthe Brook-field Synchrolectric Viscometer. There are now nine models in the Brookfield line, one of which has the exact number speeds, speed range and centipoise range to meet your requirements.
Whether you work with Newtonion or non-Newtonion materials . . . whether you work in the ultra-low viscosity range of 0 to 10 centi-poises up to 64,000,000 centipoises there's a Brookfield instrument for you.
Why not take a look at the new Brookfield Viscometer and Automatic Viscosity Measuring Instrument brochure. We will be pleased to mail you one.
Brookfield Stoughton 16, Mass.
ENGINEERING LABORATORIES INCORPORATED
Circle No. 24 on Readers' Service Card
2 8 A • ANALYTICAL CHEMISTRY
