Statistical analysts

Air pollution control statistical planners, agricultural biologists, biologists, computer specialists, economists, management analysts, mathematicians, microbiologists, ph)rsicists, phytotoxicologists, researchers, research analysts, research scientists, research specialists, scientists (environmental and unspecified), statisticians, and statistical analysts. 

Royal Society of Chemistry, Analytical Methods Committee, Robust statistics, Analyst, 114 (1989), 1693 D1697. 

Statistical analysts can provide numbers that characterize the data set. Two of the most common numbers provided are called the "mean" and the "median." The mean is an arithmetic average of the data. It provides insight into the data set. 

World Resources Institute is an independent non-profit organization with a staff of more than 100 scientists, economists, policy experts, business analysts, statistical analysts, mapmakers, and communicators working to protect the Earth and improve people s lives. 

A statistical analysis allows us to determine whether our results are significantly different from known values, or from values obtained by other analysts, by other methods of analysis, or for other samples. A f-test is used to compare mean values, and an F-test to compare precisions. Comparisons between two sets of data require an initial evaluation of whether the data... 

If systematic errors due to the analysts are significantly larger than random errors, then St should be larger than sd. This can be tested statistically using a one-tailed F-test... 

An alternative approach for collaborative testing is to have each analyst perform several replicate determinations on a single, common sample. This approach generates a separate data set for each analyst, requiring a different statistical treatment to arrive at estimates for Grand and Csys-... 

A variety of statistical methods may be used to compare three or more sets of data. The most commonly used method is an analysis of variance (ANOVA). In its simplest form, a one-way ANOVA allows the importance of a single variable, such as the identity of the analyst, to be determined. The importance of this variable is evaluated by comparing its variance with the variance explained by indeterminate sources of error inherent to the analytical method. 

Once a significant difference has been demonstrated by an analysis of variance, a modified version of the f-test, known as Fisher s least significant difference, can be used to determine which analyst or analysts are responsible for the difference. The test statistic for comparing the mean values Xj and X2 is the f-test described in Chapter 4, except that Spool is replaced by the square root of the within-sample variance obtained from an analysis of variance. 

The most useful methods for quality assessment are those that are coordinated by the laboratory and that provide the analyst with immediate feedback about the system s state of statistical control. Internal methods of quality assessment included in this section are the analysis of duplicate samples, the analysis of blanks, the analysis of standard samples, and spike recoveries. 

Rectification accounts for systematic measurement error. During rectification, measurements that are systematically in error are identified and discarded. Rectification can be done either cyclically or simultaneously with reconciliation, and either intuitively or algorithmically. Simple methods such as data validation and complicated methods using various statistical tests can be used to identify the presence of large systematic (gross) errors in the measurements. Coupled with successive elimination and addition, the measurements with the errors can be identified and discarded. No method is completely reliable. Plant-performance analysts must recognize that rectification is approximate, at best. Frequently, systematic errors go unnoticed, and some bias is likely in the adjusted measurements. 

Analysts should review the technical basis for uncertainties in the measurements. They should develop judgments for the uncertainties based on the plant experience and statistical interpretation of plant measurements. The most difficult aspect of establishing the measurement errors is estabhshing that the measurements are representative of what they purport to oe. Internal reactor CSTR conditions are rarely the same as the effluent flow. Thermocouples in catalyst beds may be representative of near-waU instead of bulk conditions. Heat leakage around thermowells results in lower than actual temperature measurements. 

There are a variety of ways to express absolute QRA results. Absolute frequency results are estimates of the statistical likelihood of an accident occurring. Table 3 contains examples of typical statements of absolute frequency estimates. These estimates for complex system failures are usually synthesized using basic equipment failure and operator error data. Depending upon the availability, specificity, and quality of failure data, the estimates may have considerable statistical uncertainty (e.g., factors of 10 or more because of uncertainties in the input data alone). When reporting single-point estimates or best estimates of the expected frequency of rare events (i.e., events not expected to occur within the operating life of a plant), analysts sometimes provide a measure of the sensitivity of the results arising from data uncertainties. 

The function of the analyst is to obtain a result as near to the true value as possible by the correct application of the analytical procedure employed. The level of confidence that the analyst may enjoy in his results will be very small unless he has knowledge of the accuracy and precision of the method used as well as being aware of the sources of error which may be introduced. Quantitative analysis is not simply a case of taking a sample, carrying out a single determination and then claiming that the value obtained is irrefutable. It also requires a sound knowledge of the chemistry involved, of the possibilities of interferences from other ions, elements and compounds as well as of the statistical distribution of values. The purpose of this chapter is to explain some of the terms employed and to outline the statistical procedures which may be applied to the analytical results. 

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. 

The comparison of more than two means is a situation that often arises in analytical chemistry. It may be useful, for example, to compare (a) the mean results obtained from different spectrophotometers all using the same analytical sample (b) the performance of a number of analysts using the same titration method. In the latter example assume that three analysts, using the same solutions, each perform four replicate titrations. In this case there are two possible sources of error (a) the random error associated with replicate measurements and (b) the variation that may arise between the individual analysts. These variations may be calculated and their effects estimated by a statistical method known as the Analysis of Variance (ANOVA), where the... 

Correctly used, statistics is an essential tool for the analyst. The use of statistical methods can prevent hasty judgements being made on the basis of limited information. It has only been possible in this chapter to give a brief resume of some statistical techniques that may be applied to analytical problems. The approach, therefore, has been to use specific examples which illustrate the scope of the subject as applied to the treatment of analytical data. There is a danger that this approach may overlook some basic concepts of the subject and the reader is strongly advised to become more fully conversant with these statistical methods by obtaining a selection of the excellent texts now available. 

This book, written by two passionate analysts, treats the application of statistics to analytical chemistry > 2 in a very practical manner. A minimum of tools is explained and then applied to everyday, that is, complex situations. The examples should be illuminating to both beginners and specialists from other fields in their quest to evaluate data and make decisions. 

There are innumerable references that cover theory, and still many more that provide practical applications of statistics to chemistry in general and analytical chemistry in particular. Articles from Analytical Chemistry were chosen as far as possible to provide world-wide availability. Where necessary, articles in English that appeared in Analytica Chimica Acta, Analyst, or Fresenius Zeitschrift fiir Analytische Chemie were cited. 

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. 

Narrow limits any statement based on a statistical test would be wrong very often, a fact which would certainly not augment the analyst s credibility. Alternatively, the statement would rest on such a large number of repeat measurements that the result would be extremely expensive and perhaps out of date. 

Results from the analysis of the RM and the certified value and their uncertainties are compared using simple statistical tests (Ihnat 1993,1998a). If the measured concentration value agrees with the certified value, the analyst can deduce with some confidence that the method is applicable to the analysis of materials of similar composition. If there is disagreement, the method as applied exhibits a bias and underlying causes of error should be sought and corrected, or their effects minimized. 

A form of this approach has long been followed by RT Corporation in the USA. In their certification of soils, sediments and waste materials they give a certified value, a normal confidence interval and a prediction interval . A rigorous statistical process is employed, based on that first described by Kadafar (1982,), to produce the two intervals the prediction interval (PI) and the confidence interval (Cl). The prediction interval is a wider range than the confidence interval. The analyst should expect results to fall 19 times out of 20 into the prediction interval. In real-world QC procedures, the PI value is of value where Shewhart (1931) charts are used and batch, daily, or weekly QC values are recorded see Section 4.1. Provided the recorded value falls inside the PI 95 % of the time, the method can be considered to be in control. So occasional abnormal results, where the accumulated uncertainty of the analytical procedure cause an outher value, need no longer cause concern. 

The reasons for such vagueness may lie in a combination of factors, the lamentable level of proper understanding of statistics amongst many analysts and, as mentioned above, the inconsistent and complex manner in which many certification bodies use statistics to produce their certified values and the willingness of journals to accept papers that lack proper validation of restdts and do not describe the proper use of CRMs. 

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