Statistical tools univariate data

In addition to univariate statistical analysis, the data were also examined by means of multivariate statistical techniques. In particular, R-mode factor analysis was used, which is a very effective tool to interpret anomalies and to help identify their sources. Factor analysis allows grouping of anomalies by compatible geochemical associations from a geologic-mineralogical point of view, the presence of mineralizing processes, or processes connected to the surface environment. Based on this analysis, six meaningful chemical associations were identified (Fig. 15.8). 

Statistical methods provide tools for assessing univariate data (replicate measurements of a single parameter) resulting in measurements of i) accuracy, defined as the difference between an experimental value and the true value the latter is generally not known for a real-world analytical sample, so that accuracy must be estimated using a surrogate sample e.g., a blank matrix spiked with a known amount of analytical standard) ii) precision, such as the relative standard deviation (RSD, also known as the coefficient of variance, COV or CV) iii) methods for calculation of propagation of experimental error in calculations. 

In univariate statistics a key question discussed previously was to evaluate how close the values of p and m are for a certain population and an experimental m. The answer to this question is used as a model for significance tests. One main tool used to evaluate statistical data is the distribution function, which describes the distribution of measurements about their mean. In other words, the distribution function gives the... 

In the era of single-loop control systems in chemical processing plants, there was little infrastructure for monitoring multivariable processes by using multivariate statistical techniques. A limited number of process and quality variables were measured in most plants, and use of univariate SPM tools for monitoring critical process and quality variables seemed appropriate. The installation of computerized data acquisition and storage systems, the availability of inexpensive sensors for typical process variables such as temperature, flow rate, and pressure, and the development of advanced chemical analysis systems that can provide reliable information on quality variables at high frequencies increased the number of variables measured at... 

Since yMst is a random variable, SPM tools can be used to detect statistically significant changes. histXk) is highly autocorrelated. Use of traditional SPM charts for autocorrelated variables may yield erroneous results. An alternative SPM method for autocorrelated data is based on the development of a time series model, generation of the residuals between the values predicted by the model and the measured values, and monitoring of the residuals [1]. The residuals should be approximately normally and independently distributed with zero-mean and constant-variance if the time series model provides an accurate description of process behavior. Therefore, popular univariate SPM charts (such as x-chart, CUSUM, and EWMA charts) are applicable to the residuals. Residuals-based SPM is used to monitor lhist k). An AR model is used for representing st k) ... 

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