Analysts averaging

In general, the computation of an instantaneous specific production rate is not particularly useful. Quite often the average production rate over specific periods of time is a more useful quantity to the experimentalist/analyst. Average rates are better determined by the integral approach which is illustrated next. 

A method recommended for adoption as official, first action (27). The method in which methimazole is separated from tablet excipients by column chromatography on Celite 545 with chloroform as the eluent and then quantitatively measured and identified by IR spectrophotometry. This method was studied collaborative-ly by 10 analysts average recoveries from two simulated and two tablets mixtures ranged from 96.6% + 1.0 to 101.1% + 0.9 (28). 

Material Manganese, % Number of Analysts Average Absolute Error Average Relative Error, %... 

Sometimes just one determination is available on each of several known materials similar in composition. A single determination by each of two procedures (or two analysts) on a series of material may be used to test for a relative bias between the two methods, as in Example 2.4. Of course, the average difference does not throw any light on which procedure has the larger constant error. It only supplies a test as to whether the two procedures are in disagreement. 

We can establish a range of pHs over which the average analyst will observe a change in color if we assume that a solution of the indicator is the color of HIn whenever its concentration is ten times more than that of Im, and the color of In ... 

Single-operator characteristics are determined by analyzing a sample whose concentration of analyte is known to the analyst. The second step in verifying a method is the blind analysis of standard samples where the analyte s concentration remains unknown to the analyst. The standard sample is analyzed several times, and the average concentration of the analyte is determined. This value should be within three, and preferably two standard deviations (as determined from the single-operator characteristics) of the analyte s known concentration. 

After the average crude oil price increased from 3.18 per barrel in 1970 to 21.59 in 1980, many analysts forecast skyrocketing energy prices for the remainder of the centuiy. The middle price path of the U.S. Energy Information Administration in 1979 projected a nominal price of 117.50 per barrel in 1995 Such forecasts seemed to be soundly based not only in recent experience but also in the economic theoiy of exhaustible resources. As a consequence, U.S. industries invested heavily in energy conseiwa-tion measures, with the result that industrial consumption of energy decreased from 31.5 quads in 1973 to 27.2 in 1985. Some of this investment was probably not warranted on economic efficiency gi ounds because prices ceased to rise after 1981, and even plummeted to 10 per barrel in 1986. 

Standard life is described as the average lifetime that is acceptable to any plant failure analyst or troubleshooter. Therefore, if we arrive at defect limits in machinery within the maintenance program, we have also reached the standard life of all the failure modes in the plant. Do we now ... 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

For many, this book will at least offer a glimpse of the nonidealities the average analyst faces every day, of which statistics is just a small part, and the decisions for which we analysts have to take responsibility. 

Accuracy (systematic error or bias) expresses the closeness of the measured value to the true or actual value. Accuracy is usually expressed as the percentage recovery of added analyte. Acceptable average analyte recovery for determinative procedures is 80-110% for a tolerance of > 100 p-g kg and 60-110% is acceptable for a tolerance of < 100 p-g kg Correction factors are not allowed. Methods utilizing internal standards may have lower analyte absolute recovery values. Internal standard suitability needs to be verified by showing that the extraction efficiencies and response factors of the internal standard are similar to those of the analyte over the entire concentration range. The analyst should be aware that in residue analysis the recovery of the fortified marker residue from the control matrix might not be similar to the recovery from an incurred marker residue. 

In biochemical engineering we are often faced with the problem of estimating average apparent growth or uptake/secretion rates. Such estimates are particularly useful when we compare the productivity of a culture under different operating conditions or modes of operation. Such computations are routinely done by analysts well before any attempt is made to estimate true kinetics parameters like those appearing in the Monod growth model for example. 

A central concept of statistical analysis is variance,105 which is simply the average squared difference of deviations from the mean, or the square of the standard deviation. Since the analyst can only take a limited number n of samples, the variance is estimated as the squared difference of deviations from the mean, divided by n - 1. Analysis of variance asks the question whether groups of samples are drawn from the same overall population or from different populations.105 The simplest example of analysis of variance is the F-test (and the closely related t-test) in which one takes the ratio of two variances and compares the result with tabular values to decide whether it is probable that the two samples came from the same population. Linear regression is also a form of analysis of variance, since one is asking the question whether the variance around the mean is equivalent to the variance around the least squares fit. 

Bolton s opinion was bolstered in June 2005 by Senator Richard Lu-gar s survey of 85 non-proliferation and national security analysts from the United States and other nations. It was designed in part to characterize the risks related to the terrorist use of CBRN. The survey revealed that experts believe the probability of an attack somewhere in the world with a CBRN weapon was 50% over the next five years and 70% over the next ten. An attack with a radiological weapon was seen as the most probable with the likelihood of an attack with a nuclear or biological weapon considered about half as plausible [37]. The average probability of a nuclear attack in the next ten years was nearly 30%, with experts almost evenly divided between terrorist acquisitions of a working nuclear weapon versus self-construction [37]. The average risk estimate over ten years for major chemical and biological attacks was 20%. Senator Lu-gar concluded The bottom line is this for the foreseeable future, the United States and other nations will face an existential threat from the intersection of terrorism and weapons of mass destruction. ... 

In actual practice, it is common to keep the transformation factors constant throughout the analysts. Engineering judgment is used to select the appropriate factors, depending on the predominant response mode anticipated. A trial and error approach may be used to evaluate the response mode behavior. An average of the clastic and plastic transformation factors is sometimes used. 

The results of Analyst-1 lie on either sides of the average value as shown by two cross-signs on each side which might have been caused due to random errors discussed earlier. It is quite evident that there exists a constant (determinate) error in the results obtained by the Analyst-2, and (/ / /) In case, Analyst-3 had performed the estimations on the very same day in quick succession i.e., one after the other, this type of analysis could be termed as repeatable analysis . If the estimations had been carried out on two separate days altogether, thereby facing different laboratory conditions then the results so obtained would be known as reproducible analysis . 

Example The normality of a solution of sodium hydroxide as determined by an analyst by FOUR different titrations are found to be 0.5038 0.5049 0.5042 and 0.5039. Calculate the mean, median, average deviation, standard deviation and coefficient of variation. 

Greef, R., Peat, R., Peter, L. M., Pletcher, D. and Robinson, J., Instrumental Methods in Electrochemistry, Ellis Horwood, Chichester, 1990. The Southampton Electrochemistry Book - now out of print, but well worth a look. Its treatment is considerably less mathematical than Bard and Faulkner s text (see above) and, in consequence, is more readable for the average student and analyst. Some of the book is just about suitable for undergraduate work, although most of its content should be thought of as being postgraduate level. 

Interaction of Analyst with Other User. A number of statements have already been made on this topic. One aspect yet to be addressed is the desire for results to be expressed in a single number. "1 think it is a serious problem. 1 have lots of people who say they want an average they don t want three numbers nor ten numbers. They want one number they call average. ... 

As an example, the results obtained for method precision and capability are presented in Table 10 for a Gage R R study performed for an oral film-coated tablet in four different labs, using six sample batches, and analyzed in replicate by two analysts in each lab. The %P/T metric was calculated according to the Ph. EUR specifications 95-105% and according to the USP specifications 90-110%. The method standard deviation (apart from the process standard deviation) is also presented, together with average assay results and confidence intervals thereof per lab and for all labs together. 

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