Correlation and regression are different, but not mutually exclusive, techniques. Roughly, regression is used for prediction (which does not extrapolate beyond the data used in the analysis) whereas correlation is used to determine the degree of association. There situations in which the x variable is not fixed or readily chosen by the experimenter, but instead is a random covariate to the y variable. This paper shows the relationships between the coefficient of determination, the multiple correlation coefficient, the covariance, the correlation coefficient and the coefficient of alienation, for the case of two related variables x and y. It discusses the uses of the correlation coefficient r, either as a way to infer correlation, or to test linearity. A number of graphical examples are provided as well as examples of actual chemical applications. The paper recommends the use of z Fisher transformation instead of r values because r is not normally distributed but z is (at least in approximation). For eithe...

The Correlation Coefficient: An Overview

Aqueous two phase system (ATPS) is a liquid – liquid extraction method which employs two aqueous phases having applications in the field of biotechnology for the separation and purification of biological materials such as proteins, enzymes, nucleic acids, virus, antibodies and cell organelles. This review discusses the basic principles of ATPS, the factors affecting partitioning, optimization by design of experiments and the recent applications like extractive fermentation, membrane supported liquid – liquid extraction and aqueous two phase floatation. A comparative study between ATPS and other conventional methods is also discussed. The emphasis is given to PEG/salt two-phase systems because of the low cost of the system.

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Aqueous Two Phase Systems for the Recovery of Biomolecules –A Review

A review of experiments in tourism and hospitality.

The life sciences are currently being transformed by an unprecedented wave of developments in molecular analysis, which include important advances in instrumental analysis as well as biocomputing. In light of the central role played by metabolism in nutrition, metabolomics is rapidly being established as a key analytical tool in human nutritional studies. Consequently, an increasing number of nutritionists integrate metabolomics into their study designs. Within this dynamic landscape, the potential of nutritional metabolomics (nutrimetabolomics) to be translated into a science, which can impact on health policies, still needs to be realized. A key element to reach this goal is the ability of the research community to join, to collectively make the best use of the potential offered by nutritional metabolomics. This article, therefore, provides a methodological description of nutritional metabolomics that reflects on the state-of-the-art techniques used in the laboratories of the Food Biomarker Alliance (funded by the European Joint Programming Initiative "A Healthy Diet for a Healthy Life" (JPI HDHL)) as well as points of reflections to harmonize this field. It is not intended to be exhaustive but rather to present a pragmatic guidance on metabolomic methodologies, providing readers with useful "tips and tricks" along the analytical workflow.

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Nutrimetabolomics: An Integrative Action for Metabolomic Analyses in Human Nutritional Studies

Structural reliability analysis for implicit performance function using radial basis function network

Modern Statistics for Engineering and Quality Improvement

Introduction Statistics and Data Collection Beginnings of Statistically Planned Experiments Definitions and Preliminaries Purposes of Experimental Design Types of Experimental Designs Planning Experiments Performing the Experiments Use of R Software Completely Randomized Designs with One Factor Introduction Replication and Randomization A Historical Example Linear Model for Completely Randomized Design (CRD) Verifying Assumptions of the Linear Model Analysis Strategies When Assumptions Are Violated Determining the Number of Replicates Comparison of Treatments after the F-Test Factorial Designs Introduction Classical One at a Time versus Factorial Plans Interpreting Interactions Creating a Two-Factor Factorial Plan in R Analysis of a Two-Factor Factorial in R Factorial Designs with Multiple Factors-Completely Randomized Factorial Design (CRFD) Two-Level Factorials Verifying Assumptions of the Model Randomized Block Designs Introduction Creating a Randomized Complete Block (RCB) Design in R Model for RCB An Example of a RCB Determining the Number of Blocks Factorial Designs in Blocks Generalized Complete Block Design Two Block Factors Latin Square Design (LSD) Designs to Study Variances Introduction Random Sampling Experiments (RSE) One-Factor Sampling Designs Estimating Variance Components Two-Factor Sampling Designs-Factorial RSE Nested SE Staggered Nested SE Designs with Fixed and Random Factors Graphical Methods to Check Model Assumptions Fractional Factorial Designs Introduction to Completely Randomized Fractional Factorial (CRFF) Half Fractions of 2k Designs Quarter and Higher Fractions of 2k Designs Criteria for Choosing Generators for 2k-p Designs Augmenting Fractional Factorials Plackett-Burman (PB) Screening Designs Mixed-Level Fractional Factorials Orthogonal Array (OA) Definitive Screening Designs Incomplete and Confounded Block Designs Introduction Balanced Incomplete Block (BIB) Designs Analysis of Incomplete Block Designs Partially Balanced Incomplete Block (PBIB) Designs-Balanced Treatment Incomplete Block (BTIB) Row Column Designs Confounded 2k and 2k-p Designs Confounding 3 Level and p Level Factorial Designs Blocking Mixed-Level Factorials and OAs Partially CBF Split-Plot Designs Introduction Split-Plot Experiments with CRD in Whole Plots (CRSP) RCB in Whole Plots (RBSP) Analysis Unreplicated 2k Split-Plot Designs 2k-p Fractional Factorials in Split Plots (FFSP) Sample Size and Power Issues for Split-Plot Designs Crossover and Repeated Measures Designs Introduction Crossover Designs (COD) Simple AB, BA Crossover Designs for Two Treatments Crossover Designs for Multiple Treatments Repeated Measures Designs Univariate Analysis of Repeated Measures Design Response Surface Designs Introduction Fundamentals of Response Surface Methodology Standard Designs for Second-Order Models Creating Standard Response Surface Designs in R Non-Standard Response Surface Designs Fitting the Response Surface Model with R Determining Optimum Operating Conditions Blocked Response Surface (BRS) Designs Response Surface Split-Plot (RSSP) Designs Mixture Experiments Introduction Models and Designs for Mixture Experiments Creating Mixture Designs in R Analysis of Mixture Experiment Constrained Mixture Experiments Blocking Mixture Experiments Mixture Experiments with Process Variables Mixture Experiments in Split-Plot Arrangements Robust Parameter Design Experiments Introduction Noise Sources of Functional Variation Product Array Parameter Design Experiments Analysis of Product Array Experiments Single Array Parameter Design Experiments Joint Modeling of Mean and Dispersion Effects Experimental Strategies for Increasing Knowledge Introduction Sequential Experimentation One-Step Screening and Optimization An Example of Sequential Experimentation Evolutionary Operation Concluding Remarks Appendix: Brief Introduction to R Answers to Selected Exercises Bibliography Index A Review and Exercises appear at the end of each chapter.

Design and Analysis of Experiments with R

Introduction Statistics and Data Collection Beginnings of Statistically Planned Experiments Definitions and Preliminaries Purposes of Experimental Design Types of Experimental Designs Planning Experiments Performing the Experiments Use of SAS Software Completely Randomized Designs with One Factor Introduction Replication and Randomization A Historical Example Linear Model for Completely Randomized Design (CRD) Verifying Assumptions of the Linear Model Analysis Strategies When Assumptions Are Violated Determining the Number of Replicates Comparison of Treatments after the F-Test Factorial Designs Introduction Classical One at a Time versus Factorial Plans Interpreting Interactions Creating a Two-Factor Factorial Plan in SAS Analysis of a Two-Factor Factorial in SAS Factorial Designs with Multiple Factors-Completely Randomized Factorial Design (CRFD) Two-Level Factorials Verifying Assumptions of the Model Randomized Block Designs Introduction Creating a Randomized Complete Block (RCB) Design in SAS Model for RCB An Example of a RCB Determining the Number of Blocks Factorial Designs in Blocks Generalized Complete Block Design Two Block Factors Latin Square Design (LSD) Designs to Study Variances Introduction Random Sampling Experiments (RSE) One-Factor Sampling Designs Estimating Variance Components Two-Factor Sampling Designs-Factorial RSE Nested SE Staggered Nested SE Designs with Fixed and Random Factors Graphical Methods to Check Model Assumptions Fractional Factorial Designs Introduction to Completely Randomized Fractional Factorial (CRFF) Half Fractions of 2k Designs Quarter and Higher Fractions of 2k Designs Criteria for Choosing Generators for 2k-p Designs Augmenting Fractional Factorials Plackett-Burman (PB) Screening Designs Mixed-Level Fractional Factorials Orthogonal Array (OA) Incomplete and Confounded Block Designs Introduction Balanced Incomplete Block (BIB) Designs Analysis of Incomplete Block Designs Partially Balanced Incomplete Block (PBIB) Designs-Balanced Treatment Incomplete Block (BTIB) Youden Square Designs (YSD) Confounded 2k and 2k-p Designs-Completely Confounded Blocked Factorial (CCBF) and Completely Confounded Blocked Fractional Factorial (CCBFF) Confounding 3 Level and p Level Factorial Designs Blocking Mixed Level Factorials and OAs Partial CBF Split-Plot Designs Introduction Split-Plot Experiments with CRD in Whole Plots (CRSP) RCB in Whole Plots (RBSP) Analysis Unreplicated 2k Split-Plot Designs 2k-p Fractional Factorials in Split Plots (FFSP) Sample Size and Power Issues for Split-Plot Designs Crossover and Repeated Measures Designs Introduction Crossover Designs (COD) Simple AB, BA Crossover Designs for Two Treatments Crossover Designs for Multiple Treatments Repeated Measures Designs Univariate Analysis of Repeated Measures Design Response Surface Designs Introduction Fundamentals of Response Surface Methodology Standard Designs for Second-Order Models-Completely Randomized Response Surface (CRRS) Designs Creating Standard Designs in SAS Non-Standard Response Surface Designs Fitting the Response Surface Model with SAS Determining Optimum Operating Conditions Response Surface Designs in Blocks (BRS) Response Surface Designs in Split-Plots (RSSP) Mixture Experiments Introduction Models and Designs for Mixture Experiments Creating Mixture Designs in SAS Analysis of Mixture Experiment Constrained Mixture Experiments Blocking Mixture Experiments Mixture Experiments with Process Variables Mixture Experiments in Split Plot Arrangements Robust Parameter Design Experiments Introduction Noise Sources of Functional Variation Product Array Parameter Design Experiments Analysis of Product Array Experiments Single Array Parameter Design Experiments Joint Modeling of Mean and Dispersion Effects Experimental Strategies for Increasing Knowledge Introduction Sequential Experimentation One-Step Screening and Optimization Evolutionary Operation Concluding Remarks Bibliography Index A Review and Exercises appear at the end of each chapter.

Design and Analysis of Experiments with SAS

Every technical investigation involving trial-and-error experimentation embodies a strategy for deciding what experiments to perform, when to quit, and how to interpret the data. This handbook presents several statistically derived strategies which are more efficient than any intuitive approach and will get the investigator to their goal with the fewest experiments, give the greatest degree of reliability to their conclusions, and keep the risk of overlooking something of practical importance to a minimum. 
Features:


Provides a comprehensive desk reference on experimental design that will be useful to practitioners without extensive statistical knowledge
Features a review of the necessary statistical prerequisites
Presents a set of tables that allow readers to quickly access various experimental designs
Includes a roadmap for where and when to use various experimental design strategies
Shows compelling examples of each method discussed
Illustrates how to reproduce results using several popular software packages on a companion web site

Following the outlines and examples in this book should quickly allow a working professional or student to select the appropriate experimental design for a research problem at hand, follow the design to conduct the experiments, and analyze and interpret the resulting data. 
John Lawson and John Erjavec have a combined 25 years of industrial experience and over 40 years of academic experience.　 They have taught this material to numerous practicing engineers and scientists as well as undergraduate and graduate students.

John Lawson

Papers

Modern Statistics for Engineering and Quality Improvement

Design and Analysis of Experiments with R

Design and Analysis of Experiments with SAS

Basic Experimental Strategies and Data Analysis for Science and Engineering

Basic Two-Level Factorial Experiments