Measure of precision

Linnig, F. J., and J. Mandel, Which Measure of Precision AnaZ. Chem., 36 25A (1964). Mark, H., and J. Workman, Statistics in Spectroscopy, Academic Press, San Diego, CA, 1991. Meier, P. C., and R. E. Zund, Statistical Methods in Analytical Chemistry, Wiley, New York, 1993. 

Constructing a Precision Control Chart The most common measure of precision used in constructing a precision control chart is the range, R, between the largest and smallest results for a set of j replicate analyses on a sample. 

The previous discussion demonstrates that measurement of precise isotope ratios requires a substantial amount of operator experience, particularly with samples that have not been examined previously. A choice of filament metal must be made, the preparation of the sample on the filament surface is important (particularly when activators are used), and the rate of evaporation (and therefore temperature control) may be crucial. Despite these challenges, this method of surface ionization is a useful technique for measuring precise isotope ratios for multiple isotopes. Other chapters in this book discuss practical details and applications. 

The square of the standard deviation is called the variance. A further measure of precision, known as the Relative Standard Deviation (R.S.D.), is given by ... 

The standard deviation s is the square root of the variance graphically, it is the horizontal distance from the mean to the point of inflection of the distribution curve. The standard deviation is thus an experimental measure of precision the larger s is, the flatter the distribution curve, the greater the range of. replicate analytical results, and the Jess precise the method. In Figure 10-1, Method 1 is less precise but more nearly accurate than Method 2. In general, one hopes that a and. r will coincide, and that 5 will be small, but this happy state of affairs need not exist. 

The closeness of agreement between independent test results obtained by applying the experimental procedure under stipulated conditions. The smaller the random part of the experimental errors which affect the results, the more precise the procedure. A measure of precision (or imprecision) is the standard deviation. 

It is difficult to comprehend why this measure has not been applied in analytical chemistry. Instead of this, in the last decades the signal-to-noise ratio has increasingly been used. Signal-to-noise ratio, see Eq. (7.1), is the measure that corresponds to r in the signal domain. In principle, quantities like S/N (Eq. (7.1)) and / (Eq. (7.7)) could represent measures of precision, but they have an unfavourable range of definition, namely range[r = range[S/N] = 0... oo. 

Useful measures of precision could be derived from relative dispersion measures, namely by their differences from 1, e.g., the precision of an analytical procedure... 

We turn now to several effects that give qualitative and sometimes quantitative information on hydrogen in specific forms or complexes but that are usually less convenient to apply to the measurement of precise depth distributions or total amounts than are the procedures discussed above. 

Precision is the closeness of agreement between independent test results obtained under stipulated conditions. Precision depends only on the distribution of random errors and does not relate to the true value. It is calculated by determining the standard deviation of the test results from repeat measurements. In numerical terms, a large number for the precision indicates that the results are scattered, i.e. the precision is poor. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability and reproducibility are the two extreme conditions. 

Two other terms that you will come across when working with chemical data are repeatability and reproducibility. Again, these two terms can easily be confused and you should learn to distinguish between them. They are both measures of precision. 

The numerical difference between the highest and lowest results in a set. It is a measure of precision. Deviation (e.g. From the Mean or Median)... 

Measurement of precision. Measurement of data quality is valuable for both the analyst and the data user. Least-squares curve-of-best-fit statistical programs usually provide some information on precision (correlation coefficient, standard error of estimate). However, these are not sufficiently quantitative and often overstate the quality parameters of the data. 

The simplified term (standard deviation of the residuals divided by the estimated slope of the calibration line), the procedural standard deviation, will often be accepted as a measure of precision. 

If a sample is analyzed by a number of laboratories for comparative purposes the precision measure used is reproducibility R, which is the largest measure of precision normally encountered. Reproducibility R is the precision taken under conditions where test results are obtained with the same method on identical test items in different laboratories with different operators using different equipment. 

The statistical prediction error does not account for biases in concentration or pathlei h changes. The (SS ) matrix depends only on the pure spectra, and the re ual spectra only depends on how well dS can find a linear combination of pures to fit the sample spectrum. In other words, the statistical prediction error is a measure of precision, not accuracy. 

It is not possible at this stage to say precisely what we mean by small and large in this context, we need the concept of the confidence interval to be able to say more in this regard and we will cover this topic in the next chapter. For the moment just look upon the standard error as an informal measure of precision high values mean low precision and vice versa. Further if the standard error is small, it is likely that our estimate x is close to the true mean, p,. If the standard error is large, however, there is no guarantee that we will be close to the true mean. 

So we need to have some measure of precision and reliability and this is provided by the standard error ofxj — X2. Again we have a formula for this ... 

The most critical part of the method selection is determining the relative merits of seemingly diverse HPLC separations. Unfortunately, there is no standard against which all HPLC methods for vitamins are presently compared. However, there are indicators of assay reliability for which the analyst should look. These include measures of precision, accuracy, and reproducibility recoveries from spiked food samples linearity of calibration limits of detection measures of peak purity comparisons with existing recognized methods and results of collaborative or interlaboratory trials (9,10). 

The following are the AOAC definitions of the sources of variability in measures of precision taken from Reference 14 ... 

Replicability - "That measure of precision that reflects the variability among independent determinations on the same sample at essentially the same time by the same analyst."... 

Reliability, that part of robustness associated with ongoing performance, can be summarized as the "ability of method or technique to successfully perform a required function under stated conditions for a stated period of time." The work presented in this paper in the "Results and Discussion" section focuses predominately on measures of precision. Some anecdotal information -essentially censored data - is presented for reliability. 

Another scale of measurement of precision is standard error of mean (.M) which is the ratio of the standard deviation to the square root of number of measurements ( ). 

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