UNIVARIATE procedure

Note that for box and survival plots, PROC GPLOT is listed as an alternative. Although PROC BOXPLOT and PROC LIFETEST produce excellent graphs by themselves, sometimes it is necessary to make modifications to the output in a way that these procedures cannot handle directly. When modifications are needed, PROC GPLOT is an excellent choice. Also note that PROC REG and PROC UNIVARIATE are listed as options for scatter plots and box plots, respectively, as they can be useful in producing lower-resolution graphics for statistical appendices. 

PROC MEANS, PROC SUMMARY, and PROC TABULATE are other SAS procedures that you can use to get descriptive statistics and place them into output data sets. However, those procedures do not offer any descriptive statistical variables that you cannot get from PROC FREQ or PROC UNIVARIATE. 

A more subjective approach to the multiresponse optimization of conventional experimental designs was outlined by Derringer and Suich (22). This sequential generation technique weights the responses by means of desirability factors to reduce the multivariate problem to a univariate one which could then be solved by iterative optimization techniques. The use of desirability factors permits the formulator to input the range of property values considered acceptable for each response. The optimization procedure then attempts to determine an optimal point within the acceptable limits of all responses. 

If the heat capacity functions of the various terms in the reaction are known and their molar enthalpy, molar entropy, and molar volume at the 2) and i). of reference (and their isobaric thermal expansion and isothermal compressibility) are also all known, it is possible to calculate AG%x at the various T and P conditions of interest, applying to each term in the reaction the procedures outlined in section 2.10, and thus defining the equilibrium constant (and hence the activity product of terms in reactions cf eq. 5.272 and 5.273) or the locus of the P-T points of univariant equilibrium (eq. 5.274). If the thermodynamic data are fragmentary or incomplete—as, for instance, when thermal expansion and compressibility data are missing (which is often the case)—we may assume, as a first approximation, that the molar volume of the reaction is independent of the P and T intensive variables. Adopting as standard state for all terms the state of pure component at the P and T of interest and applying... 

The initial multivariate analysis consisted of a principal component analysis on the raw data to determine if any obvious relationships were overlooked by univariate statistical analysis. The data base was reviewed and records containing missing data elements were deleted. The data was run through the Statistical Analysis System (SAS) procedure PRINCOMP and the results were evaluated. 

The relative ease at which non-statisticians can make use of a sophisticated technique such as Principal Component Analysis speaks to its power in the hands of more accomplished practitioners or chemometricians. Simple univariate analyses are not sufficient to adequately check the large volume of data coming from state-of-the-art chemical analytical procedures. 

The crucial step in the univariate search procedure is undoubtedly minimizing along the line ei. In situations where the gradient of the function along the line is not readily available, direct search procedures along the given line (i.e. one-dimensional direct search procedures) must be employed to find the minimum. Many such procedures are available (see, e.g. Cooper and Steinberg6 pp. 136-151), but one of the more efficient procedures seems to be quadratic interpolation. This may briefly be described as follows. 

The chemometric procedures that are currently applied in empirical investigations have been notably improved in recent years with the assistance of computer science. Researchers have passed from initial application of univariate analyses to extensive use of multivariate procedures in less than one decade. This qualitative step has been possible because, first, the new sophisticated analytical instruments are now able to analyse dozens of chemical compounds in hundreds of samples daily, and, second, due to personal computers that can work with a great diversity of software packages. 

The great majority of statistical procedures are based on the assumption of normality of variables, and it is well known that the central limit theorem protects against failures of normality of the univariate algorithms. Univariate normality does not guarantee multivariate normality, though the latter is increased if all the variables have normal distributions in any case, it avoids the deleterious consequences of skewness and outliers upon the robustness of many statistical procedures. Numerous transformations are also able to reduce skewness or the influence of outlying objects. 

Koscielniak, P., Kozak, J. Review and classification of the univariate interpolative calibration procedures in flow analysis. Crit. Rev. Anal. Chem. 34, 25-37 (2004)... 

As the procedure consists in the evaluation of the quality of all the models with one variable (i.e. p univariate models), of all the models with two variables [i.e. p X (p - 1) bivariate models], up to all the possible models with k variables, the greatest disadvantage of this method is the extraordinary increase in the required computer time when p and k are quite large. In fact, the total number t of models is given by the relationship ... 

The least-squares procedure just described is an example of a univariate calibration procedure because only one response is used per sample. The process of relating multiple instrument responses to an analyte or a mixture of analytes is known as multivariate calibration. Multivariate calibration methods have become quite popular in recent years as new instruments become available that produce multidimensional responses (absorbance of several samples at multiple wavelengths, mass spectrum of chromatographically separated components, and so forth). Multivariate calibration methods are very powerful. They can be used to determine multiple components in mixtures simultaneously and can provide redundancy in measurements to improve precision. Recall that repeating a measurement N times provides a Vn improvement in the precision of the mean value. These methods can also be used to detect the presence of interferences that would not be identified in a univariate calibration. 

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