Statistics computer packages

Before complicated statistical models are constructed and run—increasingly easy with more and more powerful statistical computing packages—it is absolutely necessary to describe the basic characteristics of each variable—number of observations, mean, standard deviation, minimum, and maximum. That will reveal which data are below the limits of detection, are missing, are miscoded, and are outliers. If the study involves three or four key variables, associations among the variables should also be examined. Histograms and scatterplots will reveal data structures unanticipated from the numerical summaries. 

The analyst needs to understand that statistical models vary in their inferential utility. Linear models of some type or other are the most common and the most easily analyzed with statistical computing packages, but they may be only rough approximations of the real world. An oft-quoted aphorism of G.E.P. Box is that all models are wrong, some are useful. That is no doubt true, but it misses another level of detail of such models as follows. At the simplest level, a model fits the data. At the next level, a model predicts the data. At its most useful level, a model shows unanticipated features of the data and the research, and this is the ideal especially for biomarker research. The most exquisite characterization of association... 

The option to use this model is often available in statistical computer packages, and for manual calculations the arithmetic is reduced compared with the full linear regression discussed above. A caveat should be made, however, since forcing the line through the origin assumes that the measured blank value is free from experimental error and that it represents accurately the true, mean blank value. 

As with g 1, small departures of the value of g2 of a sample from zero are very likely even if the population from which the sample originated is meso-kurtic. Again, statistical computer packages offer assistance in deciding whether the sample g2 is sufficiently far from zero (either way) for this to indicate that the population distribution is probably not meso-kurtic. Table 34C of Biometrika Tables far Statisticians can also be used to interpret a calculated g2 value. 

Analysis of variance (ANOVA). A procedure, found in any statistical computer package that statistically analyzes data. Among other things, it gives a statistic called the standard error. 

The linear regression calculations for a 2 factorial design are straightforward and can be done without the aid of a sophisticated statistical software package. To simplify the computations, factor levels are coded as +1 for the high level, and -1 for the low level. The relationship between a factor s coded level, Xf, and its actual value, Xf, is given as... 

It should be emphasized, however, that most of our relationships involve, in different combinations, only three or four of the quantities on the right of Eq. (8). To develop an expression to represent a particular property we need a database of experimental values for it. For each compound in the database we compute V(r) and all of the variables in Eq. (8). A statistical analysis package is then used to identify a subset of these to which the experi-... 

The main goal of this section is to provide a summary of several of the most widely used multivariate procedures in food authentication out of the vast array currently available. These are included in well-known computer packages such as BMDP, IMSL, MATLAB, NAG, SAS, SPSS and STATISTIC A. The first three subsections describe unsupervised procedures, also called exploratory data analysis, that can reveal hidden patterns in complex data by reducing data to more interpretable information, to emphasize the natural grouping in the data and show which variables most strongly influence these patterns. The fourth and fifth subsections are focused on the supervised procedures of discriminant analysis and regression. The former produces good information when applied under the strictness of certain tests, whereas the latter is mainly used when the objective is calibration. 

USING COMPUTER PACKAGES TO GENERATE DESCRIPTIVE STATISTICS... 

Using computer packages to generate descriptive statistics... 

For some of the statistical routines that we will look at later, there is no single Cl that could encapsulate the overall significance of a data set, so computer packages only report the P value not a Cl... 

With single-precision computations, numbers with at least seven decimal places will be generated. Many statistical software packages give six places. This should be sufficient for most purposes. 

Before discussing some applications, a few basic aspects on univariate statistics will be presented. A large amount of information exists regarding this field, and more details can be found in the original literature (e.g. [70,71]). Also a variety of computer packages performing statistical data analysis is available (e.g. [71a]). 

This type of data processing and display is commonly done using computer packages for statistical data evaluations (e.g. [76]). 

Commonly used statistical computer program packages may aid in the estimation of reference limits, but these packages lack some of the techniques described here. The RefVal program, however, implements these methods completely. 

With the widespread availability of hand-held calculators, computer spreadsheets, and statistical software packages for PCs, there is no need to do the calculations outlined above by hand. 

The availability of computer packages of classification techniques has led to the waste of more valuable scientific time than any other statistical innovation (with the possible exception of multiple-regression techniques) . 

From these data, we can now make a regression diagrammatic table to see how well the model fits the data. Regression functions are standard on most scientific calculators and computer software packages. One of the statistical software packages that is easiest to use, and has a considerable number of options, is MiniTab. We first learn to perform the computations by hand and then switch to this software package because of its simplicity and efficiency. Table 2.2 presents the data. 

The emphasis in this chapter is on problems that are common in, or unique to, computer simulation relative to statistical experiments as a whole. The reader should refer to Chapters 83 to 87 of the Handbook for basic statistical methods. No specific computer hardware or software is assumed other than a language for programming the simulation experiment and possibly a statistical-analysis package capable of standard procedures such as least-squares regression. 

There is little doubt that the theory of adhesion will improve rapidly as computer calculations become more rapid and sophisticated. These improvements will take place in three areas as shown schematically in Fig. 17.13 first is the enhanced understanding of molecular adhesion forces at the atomic level second is the modeling of the statistical behavior of Brownian adhesive systems finally, the analysis of adhesion in continuum mechanics terms will increase as specific adhesion computer packages become available. 

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