Statistical analysis with historical data

In this chapter, several types of control charts for the analysis of historical data are discussed. Explanations of the use of x and R charts, for both two or more measurements per batch and only one measurement per batch, are give, along with explanations of modified control charts and cusum charts. Starting with a brief exposition on the calculation of simple statistics, the construction and graphic analysis of x and R charts are demonstrated. The concepts of under control and out of control, as well as their relationship to test specifications, are included. The chapter concludes with consideration of the question of robustness of x and R charts. 

The multivariate statistical data analysis, using principal component analysis (PCA), of this historical data revealed three main contamination profiles. A first contamination profile was identified as mostly loaded with PAHs. A samples group which includes sampling sites R1 (Ebro river in Miranda de Ebro, La Rioja), T3 (Zadorra river in Villodas, Alava) and T9 (Arga river in Puente la Reina, Navarra), all located in the upper Ebro river basin and close to Pamplona and Vitoria cities,... 

For example, a single estimate for total PCB s has been historically collected in the NHATS program. Current advances in chemical analysis protocols now allow for the determination of isomer specific resolution of PCB s. Given the 209 PCB s that are now possible to detect, an adequate evaluation of the data without the use of pattern recognition techniques seems impossible. From a QA/QC perspective, these methods can facilitate the detection of outliers and aid in the interpretation of human chemical residue data. The application of statistical analysis must keep abreast with these advances made in chemisty. To handle the complexity and quantity of such data, the use of more sophisticated statistical analyses is needed. 

Continued analysis of Sasanian silver objects will be directed towards (1) a detailed statistical study of the data, (2) analysis of Sasanian and Umayyad coins, (3) determination of isotope ratios of lead extracted from the silver, (4) correlation between the analytical data and stylistic information obtained from an art historical and archaeological study and with information on methods of manufacture, toolmark, etc. 

A study is considered valid if the results obtained with positive and negative controls are consistent with the laboratory s historical data and with the literature. Statistical analysis is usually applied to compare treated and negative control groups. Both pairwise and linear trend tests can be used. Because of the low background and Poisson distribution, data transformation (e.g., log transformation) is sometimes needed before using tests applicable to normally distributed data. Otherwise, nonparametric analyses should be preferred. 

New techniques for data analysis abound in statistical literature. GAM is a powerful tool technique, and a full historical account of GAM with ample references can be found in the research monograph of Hastie and Tibshirani (15). GAM is closer to a reparameterization of the model than a reexpression of the response. Once an additive model is fitted to the data, one can plot their p coordinate functions separately to examine the roles of predictors in modeling response. With the GAM approach the dependence of a parameter (P) on covariates (predictors) Xi,..., Xp are modeled. Usually, the multiple linear regression (MLR) approach is the method of choice for this type of problem. The MLR model is expressed in the following form ... 

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