Statistical Data Analysis: A Practical Guide

Woodhead Publishing Ltd, May 2011, Pages: 800

Over the past decade, computer supported data analysis by statistical methods has been one of the fastest growth areas in chemometrics, biometrics and other related branches of natural, technical and social sciences. This has been strongly supported by the development of exploratory data analysis, testing assumptions about data, model and statistical methods and computer intensive techniques. This book presents a combination of individual topics with solved problems and a collection of experimental tasks. Methods suitable for extreme or small and large datasets are described.

Key features:

- presents a combination of individual topics in one complete volume featuring statistical analysis of univariate and multivariate data
- interspersed throughout with solved problems and experimental tasks suitable for extreme or small and large datasets
- features the interpretation of results based on the comprehensive information about data behaviour and validity of used assumptions

Errors in instrumental measurements
- Types of measurement error
- The precision and accuracy of instrumental measurements
- Models of measuremants
- Quantiles estimates of measurement errors
- Summation of the quantile estimates od measurement errors
- Moment estimates of measurement errors
- Error propagation
- Summary: the determination of measurement errors
- References

The exploratory and confirmatory analysis of univariate data
- Sampling, sorting and ranking
- Order statistics, Quantiles and letter values
- Plots and displays in exploratory data analysis
- Examining sample distribution by EDA
- Data transformation
- The rs-expression of statistics for transformation data
- The confirmatory analysis of assumptions about data
- Summary of the procedure for the EDA and CDA of univariate data

Statistical analysis of univariate data
- Point estimates of location, spread and shape
- Interval of location and spread
- Point and interval estimators for selected distributions
- Robust eliments of location and spread
- Statistical hypothesis testing
- Summary of univariate data analysis
- References

Statistical Analysis of Multivariate Data (MDA)
- Objectives of multivariate data matrix
- Descriptive statistics
- Exploratory analysis of multivariate structure
- Principle components analysis (PCA)
- Factor analysis (FA)
- Canonical correlation analysis (CCA)
- Discriminant analysis (DA)
- Logistic regression (LR)
- Cluster analysis (CLU)
- Multidimensional scaling (MDS)
- Correspondence analysis (CA)
- References

Analysis of variance (ANOVA)
- Objectives of analysis of variance
- One-way ANOVA
- Two-way ANOVA
- Summary
- References

Linear regression models
- Formulation of the linear regression model
- Condition for the least-squares method
- Statistical properties of the least-squares method
- Numerical problems in the computer calculation of linear regression
- Regression diagnostics
- Procedures when conditions for least-squares are violated
- Calibration
- Procedure for linear regression analysis
- References

Correlation
- Correlation models
- Correlation coefficients
- Procedure for correlation analysis
- References

Nonlinear regression models
- Formulation of a nonlinear regression model
- Models of measurement errors
- Formulation of the regression criterion
- Geometry of nonlinear regression
- Numerical procedure for parameter estimation
- Statistical analysis of nonlinear regression
- Procedure for the building and testing a nonlinear model
- References

Milan Meloun is Professor of Chemometrics at Department of Analytical Chemistry, Faculty of Chemical Technology, Technical University of Liberec, Czech Republic.

J Militky, Professor, Department of Textile Materials, Faculty of Textile Engineering, Technical University of Liberec, Czech Republic.

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