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Preface
Contents
About the Author
1
Introduction to R and RStudio
1.1
The R Language
1.1.1
Why R?
1.1.2
Statistical analysis software for data modeling
1.2
Install R
1.3
Install RStudio
1.4
Use RStudio
1.4.1
Basic operations
1.4.2
Data types in R
1.4.3
Data structures in R
1.4.4
R packages
1.4.5
RStudio projects
1.4.6
Import and export Data
2
Review of Basic Statistics
2.1
Calculating Variance and Covariance
2.1.1
Covariance
2.1.2
Correlation
2.1.3
Using Matrix Algebra
2.2
Use R for Basic Statistics
2.2.1
Import and export data
2.2.2
Several functions for basic data management
2.2.3
Some descriptive statistics
2.2.4
Check normality
2.2.5
Check linearity
2.2.6
Pearson’s product moment correlation
2.3
Use R for Graphing Data
2.3.1
Use
plot()
2.3.2
Use
ggplot2
package
2.4
Use R to Graph a Correlation Matrix
2.4.1
Use
plot()
2.4.2
Use
ggplot()
2.5
Use R to Generate Random Data
2.5.1
Sampling distribution
2.5.2
Simulate data from a model
3
Correlation
3.1
Variance and Covariance
3.2
Pearson Product-Moment Correlation (Pearson Correlation)
3.2.1
Test that the population correlation equals zero
3.2.2
Check normality
3.2.3
Check for linearity with scatterplot
3.2.4
Factors that affect the Pearson Correlation
3.2.5
Test that the population correlation equals a certain value
3.2.6
Test that two population correlations are equal
3.3
Variations of the Pearson Product-Moment Correlation
3.3.1
Point Biserial Correlation
3.3.2
Biserial Correlation
3.3.3
Spearman’s Rank/Spearman’s Correlation/Spearman’s rho
3.3.4
Phi Coefficient
3.3.5
Tetrachoric Correlation
3.3.6
Polychoric Correlation
3.3.7
Chi-Square
3.3.8
Summary of measures of association
3.4
An Example
4
Simple Linear Regression
4.1
Plot the Data
4.1.1
Using
plot()
4.1.2
Using
ggplot()
4.2
The Regression Equation
4.2.1
Variance explained
4.2.2
Relationship with Pearson correlation
4.2.3
Coefficient of Determination (
R
2
R
2
)
4.2.4
R Syntax
4.3
Test of Significance and Confidence Interval
4.3.1
Testing the regression of Y on X
4.3.2
Testing the regression coefficient (slope) and the confidence interval
4.3.3
R Syntax
4.4
Summary of Important Statistics
4.5
Confidence Intervals, Hypothesis Testing, and Prediction Intervals
4.5.1
Prediction Intervals for New Observations
4.5.2
R Syntax
4.6
A Complete Example
5
Multiple Regression Analysis
5.1
F Test and Partial F Test
5.1.1
Overall test (F Test)
5.1.2
Partial F test for additional variable(s)
5.2
Testing the Partial Regression Coefficients
5.3
Partial and Semi-paritial (Part) Correlations
5.3.1
R Syntax
5.3.2
Sum up
5.4
A Complete Example
5.5
Types of Multiple Regression
5.5.1
Regression model selection based on statistics
5.6
(A Few) Assumptions in Regression
5.6.1
Linearity
5.6.2
Homoscedasticity (Constant Variance Assumption)
5.6.3
Normality
5.6.4
Independence of Residuals
5.6.5
Multicollinearity
5.7
Multiple Regression and Patterns of Association
5.7.1
Complete independence
5.7.2
Partial redundancy
5.7.3
Complete redundancy
5.7.4
Suppression in multiple regression
5.7.5
Summary of patterns of association
5.7.6
Statistical paradoxes
5.8
Regression Diagnostics
5.8.1
Leverage
5.8.2
Discrepancy
5.8.3
Influence
5.8.4
Sources of Outliers and Remedies
5.9
Curvilinear Regression
5.9.1
Polynomial regression
5.10
Useful Functions and Symbols Commonly Used in R When Fitting Linear Models
5.11
Interactions in Regression
5.11.1
An example
5.12
Categorical Independent Variables
5.12.1
Binary independent variables
5.12.2
Categorical independent variables with more than two categories
5.12.3
An example
5.13
Interactions Between Categorical and Continuous Variables
5.14
An Open Book on Regression
5.15
Create APA Tables with
apaTables
Package
6
Binary Logistic Regression
6.1
Some Definitions
6.2
Logarithm Rules
6.3
Logistic Regression Equation
6.4
Run Logistic Regression
6.5
Logistic Regression Coefficients
6.6
Similarities and Differences Between Binary Logistic Regression and OLS Regression
6.7
Empirical Example
6.7.1
Assess the model - model chi-square
6.7.2
Assess the model -
R
2
R
2
6.7.3
Diagnostics
6.7.4
Assumptions - Linearity
6.7.5
Assumptions - Independence of errors
6.7.6
Use more predictors
6.7.7
Check Multicollinearity Among IVs
6.7.8
Interprete results
7
Analysis of Variance
7.1
Historical Background
7.2
The General Linear Model (GLM)
7.3
One-Way ANOVA (for Single Factor Designs)
7.3.1
Statistical hypotheses
7.3.2
Basic idea of ANOVA
7.3.3
Empirical example
7.3.4
Pairwise comparisons
7.3.5
Planned comparisons
7.3.6
Post-hoc pairwise comparisons
7.4
ANOVA Assumptions
7.4.1
Robustness
7.5
One-way ANOVA Using GLM approach
7.6
Factorial Analysis of Variance (Factorial ANOVA)
7.6.1
Numerical calcuations for two-way ANOVA
7.6.2
Partitioning the total sum of squares
7.6.3
Empirical example - Two-way ANOVA
7.6.4
Assumptions for factorial ANOVA (see @ref(anova-assumptions))
7.6.5
Contrasts using the
multcomp
package
7.7
Factorial ANOVA as Multiple Regression
7.8
A Blog on ANOVA in R
8
Analysis of Covariance
8.1
Purposes of ANCOVA
8.2
Choice of covariates to use
8.3
Statistical Model for ANCOVA
8.4
ANCOVA Assumptions
8.5
Empirical Example
8.5.1
Assumptions - Normality
8.5.2
Assumptions - Homogeneity of Variance
8.5.3
Assumptions - Independence of the covariate and the independent variable
8.5.4
Assumptions - Homogeneity of regression slopes
8.6
Post-hoc Tests using the
multcomp
package
8.7
ANCOVA as a GLM
9
Repeated Measures ANOVA and Mixed Designs
9.1
Repeated-Measures ANOVA
9.1.1
Advantages of repeated-measures design
9.1.2
Disadvantages of repeated-measures design
9.1.3
Variance partitioning in one-way repeated measures design
9.1.4
Assumptions in repeated measures analysis
9.1.5
Alternative Specification of the Variance-Covariance Matrix
9.1.6
Empirical example
9.2
Mixed Designs
9.2.1
One between and one within factor design
9.2.2
A few online resources
10
Power Analysis
10.1
Components of Power Analysis
10.2
Effect Sizes
10.3
Types of Power Analysis
10.3.1
A priori power analysis
10.3.2
Post-hoc power analysis
10.4
a Two-Tailed
t Test
for Independent Samples Power Example
10.5
Software
References
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Quantitative Foundations in Educational Research
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