Content: Front Cover
Easy Statistics for Food Science with R
Copyright Page
Dedication
Contents
Preface
1 Introduction
1.1 Why should multivariate analysis be studied?
1.2 Organization of Multivariate Data
1.3 Examples of Multivariate Data
1.4 Multivariate Normal Distribution
Further Reading
2 Introduction to R
2.1 Introduction to R Statistical Software
2.2 Installing R
2.2.1 R Documentation
2.2.2 Installing R Packages
2.3 The R Console
2.4 Expression and Assignment in R
2.5 Variables and Vectors in R
2.5.1 Matrix in R
2.6 Basic Definitions
2.7 Graphs in R
2.8 Installing RStudio. 2.8.1 Navigate RStudio2.9 Importing Data
Further Reading
3 Statistical Concepts
3.1 Introduction
3.2 Definition of Statistics
3.3 Basic Definitions
3.4 Data Collection
3.4.1 Methods of Data Collection
3.5 Sampling Techniques
3.5.1 Simple Random Sampling
3.5.2 Systematic Sampling
3.5.3 Stratified Sampling
3.5.4 Cluster Sampling
Further Reading
4 Measures of Location and Dispersion
4.1 Descriptive Statistics
4.2 Descriptive Statistics in R
4.3 Measures of Location
4.3.1 The Arithmetic Mean for Univariate
4.3.2 Multivariate (Mean Vector)
4.4 Measure of Dispersion (Variation). 4.4.1 Variance and Standard Deviation for Univariate4.5 Covariance
4.5.1 Covariance Matrices (Multivariate)
4.6 Correlation
4.6.1 Correlation Matrices
4.7 Scatter Plot
4.7.1 The Scatter-plot Matrix
4.8 Distance
Reference
Further Reading
5 Hypothesis Testing
5.1 What Is Hypothesis Testing?
5.2 Hypothesis Testing in R
5.3 General Procedure for Hypothesis Testing
5.3.1 Definitions
5.3.2 Definitions
5.4 Hypothesis Testing About a Mean Value
5.4.1 Inference About a Mean Value for One Sample (Univariate)
5.4.2 Inference About a Mean Vector for One Sample (Multivariate). 5.5 Comparing Two Population Means5.5.1 Comparing the Means of Two Populations (One Variable)
5.5.2 Comparing Two Multivariate Population Means
Further Reading
6 Comparing Several Population Means
6.1 Introduction
6.2 ANOVA and MANOVA in R
6.3 Analysis of Variance (ANOVA)
6.3.1 One-Way ANOVA
6.3.2 Two-Way ANOVA
6.3.2.1 Hypothesis Testing for a Two-Way ANOVA
6.4 Multivariate Analysis of Variance (MANOVA)
6.4.1 One-Way MANOVA
6.4.2 Two-Way MANOVA
Further Reading
7 Regression Models
7.1 Introduction
7.2 Regression Analysis in R
7.3 Simple Linear Regression. 7.3.1 Hypothesis Testing7.3.2 Interpretation of Regression Equation
7.3.3 Prediction Using a Regression Equation
7.3.4 Outliers and Influential Observations
7.3.5 Residuals
7.3.6 Explained and Unexplained Variation
7.3.7 Coefficient of Determination
7.4 Multiple Regression
7.5 Hypothesis Testing in Multiple Linear Regression
7.5.1 Test of Overall Significance of the Regression Model
7.5.2 Tests on Individual Regression Coefficients Regression Model
7.5.3 Tests on a Subset of the Regression Coefficients
7.6 Adjusted Coefficient of Determination.