Statistical software package

Similarity is often used as a general term to encompass either similarity or dissimilarity or both (see Section 6.4.3, on similarity measures, below). The terms "proximity" and distance are used in statistical software packages, but have not gained wide acceptance in the chemical literature. Similarity and dissimilarity can in principle lead to different rankings. 

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... 

Both planar and curved surfaces can be fitted by statistical software packages like Statistica [1993]. In the general case, the 3-D calibration surface is given by... 

Determination of sodium in a soil extract. Using the five sodium calibration standards already prepared obtain five replicate readings for each sodium standard and calculate the mean emission intensity and RSD for each standard. Aspirate the standards in ascending and descending order of concentration. Aspirate a blank between each standard and zero the instrument. Using a statistical software package construct a... 

One can use statistical software packages to calculate the level of control the process is under, and one may, for example, use process capability indices that compare the output of an in-control process to the specification limits. Indirect proxies for controllability metrics could also be the amount of materials and/or energy consumed per kg of product caused by excursions outside the control zone. For example, a rejected batch will become waste, and additional mass and energy will be required to replace or rework the rejected batch. 

A number of custom-made statistical software packages are available commercially. The student is urged to be familiar with at least one of them because of their versatility and efficiency. 

The discipline of chemometrics provides a number of methods to deal with such problems. During the last years many of these methods became available for PCs, either by statistical software packages or by specific software developed by chemists. A variety of chemometric methods is, in principle, now available at the chemist s own desk. Although the chemist usually is not an expert in multivariate statistics he/she is forced to use such methods, because of the complexity of actual problems in chemistry. 

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. 

If the SolvStat.xls macro is used with the kinetics data of Figure 12-3, the regression parameters shown in Figure 12-13 are returned. The values in rows 42, 44 and 46 can be used to compare the results of the SolvStat macro and a commercial statistical software package. 

Table 1 Commercially available statistical software packages...

The linear discriminant function is a most commonly used classification technique and it is available with all the most popular statistical software packages. It should be borne in mind, however, that it is only a simplification of the Bayes classifier and assumes that the variates are obtained from a multivariate normal distribution and that the groups have similar covariance matrices. If these conditions do not hold then the linear discriminant function should be used with care and the results obtained subject to careful analysis. 

Multiple linear regression analysis of Equation (1) can also be used and for this kxy is determined with as many different combinations of and self-interaction coefficients (p or p ) can be measured by fitting the Bronsted or Hammett data to a binomial expression (logA = a + bx + cx ) by regular statistical software packages or by a program based on the statistical equation in Appendix 1 (Section A 1.1.4.4). 

This is the most common approach in QSAR to develop a quantitative linear correlation model, althongh not necessary always best for a given data set. The simplest means to obtain such a quantitative relationship is to nse MLR available in any statistical software package. MLR generates predictive equations of the form ... 

Since a random variable such as age can take on a number of values for a group of study participants it is of interest to know something about the relative frequency of each value. The relative frequency is the count of the number of observations with a specific value (for example, the number of 30-year-old participants) divided by the total number in the sample. An informative first step in a statistical analysis is to examine characteristics of the relative frequency of values of the random variable of interest, which can also be called the empirical distribution of the random variable. This knowledge is an essential part of selecting the most appropriate statistical analysis. Statistical software packages offer a number of methods to describe the relative frequency of values including tabular frequency displays, dot plots, relative frequency histograms, and stem-and-leaf plots. 

Note that Cochran s statistic does not use a correction factor and the denominator of the stratum weights is instead of (k - 1). We mention Cochran s statistic because it is used by some statistical software packages instead of the Mantel-Haenszel statistic. Fleiss points out that the difference between the Mantel-Haenszel statistic and Cochran s statistic is small when the sample sizes are large, but considerable when the sample sizes within each of the strata are small. 

The analysis begins with ordering all 15 observations. Note that statistical software packages order and rank the observations and do the ANOVA for you. The ordered observations from lowest to highest across the three groups are as follows ... 

The statistical software package SAS (SAS Institute Inc., Cary, North Carolina, U.S.A.) has a module [PROC MIXED (10)], which analyzes mixed effects models and provides estimates for both the fixed (shifts on the mean) and random effects (variance components estimates). 

MINITAB statistical software package (Minitah, Inc., State... 

Long and Ervin (2000) used Monte Carlo simulation to compare the four estimators under a homoscedastic and heteroscedastic linear model. The usually reported standard error estimator [Eq. (4.10)] was not studied. All heteroscedastic estimators of performed well even when heteroscedasticity was not present. When heteroscedasticity was present, Eq. (4.11) resulted in incorrect inferences when the sample size was less than 250 and was also more likely to result in a Type I error than the other estimators. When more than 250 observations were present, all estimators performed equally. Long and Ervin suggest that when the sample size is less than 250 that Eq. (4.16) be used to estimate . Unfortunately no pharmacokinetic and most statistical software packages use these heteroscedastic-consistent standard error estimators. 

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. 

Cluster analysis is justifiably a popular and common technique for exploratory data analysis. Most commercial multivariate statistical software packages offer several algorithms, along with a wide range of graphical display facilities to aid the user in identifying patterns in data. Having indicated that... 

For terrain generation, student experiments, and possible inclusion in statistical software packages, I have found the transformation given by... 

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. 

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