Statistician

So basic is the notion of a statistical estimate of a physical parameter that statisticians use Greek letters for the parameters and Latin letters for the estimates. For many purposes, one uses the variance, which for the sample is s and for the entire populations is cr. The variance s of a finite sample is an unbiased estimate of cr, whereas the standard deviation 5- is not an unbiased estimate of cr. 

An important part of planning an experimental program is the identification of the variables that affect the response and deciding what to do about them. The decision as to how to deal with each of the candidate variables can be made jointiy by the experimenter and the statistician. However, identifying the variables is the experimenter s responsibiUty. Controllable or independent variables in a statistical experiment can be dealt with in four different ways. The assignment of a particular variable to a category often involves a trade-off among information, cost, and time. 

After the preceding considerations have been taken into account, a test plan is developed to best meet the goals of the program. This might involve one of the standard plans developed by statisticians. Such plans are described in various texts (Table 1) and are considered only briefly here. Sometimes, combinations of plans are encountered, such as a factorial experiment conducted in blocks or a central composite design using a fractional factorial base. 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

W. C. Marshall, Graphical Methods for Schools, Colleges, Statisticians, Engineers and Executives, McGraw-HiU Book Co., Inc., New York, 1921, pp. 

From a modehng standpoint statisticians would define this problem as a two-population test oihypothesis. They would define the respective sample sheets as two populations from which 10 sample thickness determinations were measured for each. 

When the estimates are well founded, the skewness may be preserved by using a distribution such as the Gompertz. The median of that curve occurs a.sy = 0.5 c, while the point of inflexion corresponds to the mode at y = c/exp (1) = 0.3679 c. The statistician Karl Pearson suggested as a simple measure of skewness... 

An appreciation of statistical results can be gained from a study conducted to support the first application of computer control for an ethylene oxide production unit at Union Carbide Corporation in 1958. For the above purpose, twenty years of production experience with many units was correlated by excellent statisticians who had no regard for kinetics or chemistry. In spite of this, they did excellent, although entirely empirical work. One statement they made was ... [ethane has a significant effect on ethylene oxide production.] This was rejected by most technical people because it did not appear to make any sense ethane did not react, did not chemisorb, and went through the reactor unchanged. 

As expected, a lot of work, estimation and guessing goes into model development. In this estimation the developer should rely on the help and advice of both a chemist knowledgeable about similar mechanisms, and a statistician versed in the appropriate mathematics. 

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. 

To call in the. statistician after the experiment is done may be no more than asking him to perform a postmortem... 

This table is derived from Table III of R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research, published by Oliver Boyd Ltd, Edinburgh, and by permission of the authors and publishers, and also from Table 12 of Biometrika Tables for Statisticians, Vol. 1, by permission of the Biometrika Trustees. 

The data in the training set are used to derive the calibration which we use on the spectra of unknown samples (i.e. samples of unknown composition) to predict the concentrations in those samples. In order for the calibration to be valid, the data in the training set which is used to find the calibration must meet certain requirements. Basically, the training set must contain data which, as a group, are representative, in all ways, of the unknown samples on which the analysis will be used. A statistician would express this requirement by saying, "The training set must be a statistically valid sample of the population... 

Many analytical practitioners encounter a serious mental block when attempting to deal with factor spaces. The basis of the mental block is twofold. First, all this talk about abstract vector spaces, eigenvectors, regressions on projections of data onto abstract factors, etc., is like a completely alien language. Even worse, the techniques are usually presented as a series of mathematical equations from a statistician s or mathematician s point of view. All of this serves to separate the (un )willing student from a solid relationship with his data a relationship that, usually, is based on visualization. Second, it is often not clear why we would go through all of the trouble in the first place. How can all of these "abstract", nonintuitive manipulations of our data provide any worthwhile benefits ... 

Many people use the term PRESS to refer to the result of leave-one-out cross-validation. This usage is especially common among the community of statisticians. For this reason, the terms PRESS and cross-validation are sometimes used interchangeably. However, there is nothing inate in the definition of PRESS that need restrict it to a particular set of predictions. As a result, many in the chemometrics community use the term PRESS more generally, applying it to predictions other than just those produced during cross-validation. 

Again with the analytical chemist in mind, we have not treated all topics equally. The electronics expert is likely to feel we have skimped, especially in Chapter 2 Chapter 4 is oversimplified statisticians will find much missing from Chapter 10 and other important developments could have been treated in Chapters 9 and 11. 

The second perspective might be that of the leader of some large project where chemical analyses are just a side issue, where sample numbers are large and chemical niceties might be completely swamped by, say, biological variability here a statistician will be necessary to make sense of the results in the context of a very complex model. Chemistry is a bit harder to relate to than many other industries in that the measured quantities are often abstract, invisible, and only indirectly linked to what one wants to control. 

Thus, one can be far from the ideal world often assumed by statisticians tidy models, theoretical distribution functions, and independent, essentially uncorrupted measured values with just a bit of measurement noise superimposed. Furthermore, because of the costs associated with obtaining and analyzing samples, small sample numbers are the rule. On the other hand, linear ranges upwards of 1 100 and relative standard deviations of usually 2% and less compensate for the lack of data points. 

Statisticians advise look for a simpler problem when confronted with the complexity and messiness of practical chemistry. 

Chemists are frustrated when they learn that their problem is mathematically intractable. All sides have to recognize that the other s mental landscape is valid and different and that a workable decision necessitates concessions. The chemist (or other namral scientist) will have to frame questions appropriately and might have to do some experiments in a less than straightforward manner the statistician will have to avoid overly rigorous assumptions. 

Research use of analytical results in the framework of a nonanalytical setting, such as a governmental investigation into the spread of pollution here, a strict protocol might exist for the collection of samples (number, locations, time, etc.) and the interpretation of results, as provided by various consultants (biologists, regulators, lawyers, statisticians, etc.) the analytical laboratory would only play the role of a black box that transforms chemistry into numbers in the perspective of the laboratory worker, calibration, validation, quality control, and interpolation are the foremost problems. Once the reliability and plausibility of the numbers is established, the statisticians take over. 

Because the number of data points is low, many of the statistical techniques that are today being discussed in the literature caimot be used. While this is true for the vast majority of control work that is being done in industrial labs, where acceptability and ruggedness of an evaluation scheme are major concerns, this need not be so in R D situations or exploratory or optimization work, where statisticians could well be involved. For products going to clinical trials or the market, the liability question automatically enforces the tried-and-true sort of solution that can at least be made palatable to lawyers on account of the reams of precedents, even if they do not understand the math involved. 

In a (laboratory) world increasingly dominated by specialization, the vendor knows what makes the instrument tick, the technician runs the samples, and the statistician crunches numbers. The all-arounder who is aware of how these elements interact, unfortunately, is an endangered species. 

On the other side, many models of a different type are currently used in the biological sciences These can be envisaged as complicated (mathematical) extensions of commonsense ways to analyze results when these results are partially hidden behind noise, noise being inescapable when dealing with biological matters. This is the area currently occupied by most statisticians Using empirical models, universally applicable, whose basic purpose is to... 

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