Statistical procedures

The quotation attributed to Benjamin Disraeli, There are three kinds of lies lies, damned lies and statistics, is unfortunately often quoted to dismiss statistical findings. And perhaps an opposite view is like dreams, statistics are a form of wish fulfillment. J. Baudrillard 

There are numerous statistical methods for parametric and nonparametric analyses, and the choice is often made locally (Table 14.1 also see the reference section). Waner 

Some Statistical Tests Applied in Toxicology Studies 

Duncan s multiple test range Dunnett s test 

Fisher s least significant difference (LSD) test Linear regression to test for dose-effect trends Pairwise comparison Pearson s correlation coefficient Student s t-test Williams s t-test 

Here j is the orbital energy of the ith occupied MO. Large electron charge densities and low energies would contribute to electrophilic attack near that atom. There is an analogous nucleophilic quantity, SM,ki involving the unoccupied MOs. 

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Even Hartree-Fock calculations are diflTicult and expensive to apply to large molecules. As a result, fiirther simplifications are often made. Parts of the Fock operator are ignored or replaced by parameters chosen by some sort of statistical procedure to account, in an average way, for the known properties of selected... 

Decision Process. In many cases, the decision regarding the need for exposure reduction measures is obvious and no formal statistical procedure is necessary. However, as exposure criteria are lowered, and control becomes more difficult, close calls become more common, and a logical decision-making process is needed. A typical process is shown in Eigure 2. Even when decision making is easy it is useful to remember the process and the assumptions involved. Based on an evaluation, decisions are made regarding control. The evaluation and decision steps caimot be separated because the conduct of the evaluation, the strategy, measurement method, and data collection are all a part of the decision process. 

Parameter Estimation. WeibuU parameters can be estimated using the usual statistical procedures however, a computer is needed to solve readily the equations. A computer program based on the maximum likelihood method is presented in Reference 22. Graphical estimation can be made on WeibuU paper without the aid of a computer however, the results caimot be expected to be as accurate and consistent. 

Attention should be paid to the sufficiency of the study with respect to determining significance and assessing ha2ard, eg, whether the number of control and test animals is sufficient to allow detection of biological variabiUty in response and for comparative statistical procedures. 

As usually the statistical properties of the experimental data are poorly known, nobody can guarantee that the standard statistical procedures give the tmstworthy results. The history of chemical data treatment exemplifies impressively the persistent stmggle for obtaining more and more reliable meaningful information from the experimental data. 

The report is concentrated at a few procedures of data treatment that allow overcoming some drawbacks of standard statistical procedures. The main attention is paid to the problems of the regression analysis, especially to the Quantitative Stmcture-Activity Relationships (QSAR). 

Individuals differ in their sensitivity to odor. Figure 14-7 shows a typical distribution of sensitivities to ethylsulfide vapor (17). There are currently no guidelines on inclusion or exclusion of individuals with abnormally high or low sensitivity. This variability of response complicates the data treatment procedure. In many instances, the goal is to determine some mean value for the threshold representative of the panel as a whole. The small size of panels (generally fewer than 10 people) and the distribution of individual sensitivities require sophisticated statistical procedures to find the threshold from the responses. 

Further statistical procedures can be applied to determine the confidence limits of the results. Generally, only the values for the mean and standard deviation would be reported. The reader is referred to any good statistical text to expand on the brief analysis presented here. 

McBean, E.A., and Rovers, E. (1998) Statistical Procedures for Analysis of Environmental Monitoring Data and Risk Assessment, Prentice Hall, New York. 

The Committee is unable to determine whether the absolute probabilities of accident sequences in WASH-1400 are high or low, but it is believed that the error bounds on those estimates are, in general, greatly understated. This is due in part to an inability to quantify common cause failures, and in part to some questionable methodological and statistical procedures. 

Lower confidence limit (LCL) A statistical procedure to estimate whether the true value is lower than the measured value. 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

There are statistical procedures available to determine whether the data can be fit to a model of dose-response curves that are parallel with respect to slope and all share a common maximal response (see Chapter 11). In general, dose-response data can be fit to a three-parameter logistic equation of the form... 

There are statistical procedures available to choose models (hypothesis testing), assess outliers (or weight them), and deal with partial curves. 

Analysis of variance (ANOVA), a statistical procedure that quantifies differences between means of samples and the extent of variances within and between those means to determine the probability of there being a difference in the samples. 

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. 

These new statistical procedures permit reexamination of a number of reaction series to reach more definite conclusions than formerly concerning the occurrence, accuracy, and significance of isokinetic relationships and possible values of the isokinetic temperatures. In this section, the consequences of these findings will be discussed and confronted with theoretical postulates or predictions. 

J.R. Piggott, Statistical Procedures in Food Research. Elsevier, London, 1987. 

K.A. Gomez and A.A. Gomez, Statistical Procedures for Agricultural Research, second edition Wiley, New York, Chapter 2, pp. 7-83 (1984). 

Besides visual inspection, there are several statistical procedures for detecting outliers (Barnett and Lewis, 1978). These tests are based on the examination of the residuals. Practically this means that if a residual is bigger than 3 or 4 standard... 

Denormalization of data is needed when a statistical procedure requires that the information to be analyzed must be on the same observation. Procedures in SAS that perform data modeling are often the ones that require denormalized data, as they require that the dependent variable be present on the same observation as the independent variables. For example, imagine that you are trying to determine a mathematical model that predicts under what conditions a therapy is successful. That model might look like this ... 

Do not denormalize data unless required by statistical procedures or if SAS BY processing of the data will meet your needs. Sometimes you can see just by looking at the reporting desired that denormalization is not required. For example, look at the following table requirement ... 

Determine what statistics you need in your table by looking at the listing destination output of your statistical procedure. 

If you cannot find what you need in an output data set from the statistical procedure, use ODS OUTPUT to send your statistics to a data set. To determine... 

SAS has always had and will maintain a central role in the data management, analysis, and reporting of clinical trial data. Because of the strong suite of SAS statistical procedures and the power of Base SAS programming, SAS remains a favorite of statisticians for the analysis of clinical trial data. Several companies have built their clinical trial data management and statistical analysis systems entirely with SAS software. More recently, SAS has offered SAS Drug Development as an industry solution that provides a comprehensive clinical trial analysis and reporting environment compliant with 21 CRF-Part 11. 

A second advantage of using the FDA reports is that the agency carefully scrutinized the data that the drug companies had sent them. They examined the design of each of the studies and appraised the statistical procedures that were used to analyse the results. They asked the companies to provide more information and conduct additional data analyses where they deemed these to be needed. Most importantly, they excluded from consideration inadequate and poorly controlled trials. This enabled us... 

ANOVA was developed by Fisher [1925,1935] as a statistical procedure that investigates influences (effects) of factors on a target quantity y according to a linear model which holds in the simplest case... 

It must be emphasized that the availability of the SMO and 2D autocovariance function methods as two independent statistical procedures to estimate the same parameter, in, the number of proteins, is a helpful tool to verify the reliability of the results obtained. In the case of the 2D PAGE map of colorectal adenocarcinoma cell line (DL-1) an excellent agreement was found between the values obtained from the SMO method—m = 101 10 and m = 105 10—and the 2D autocovariance function procedure—m = 104 10 (Pietrogrande et al., 2006a). 

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