Learning Statistics with R
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Contents
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Preface
I Background
Why do we learn statistics?
On the psychology of statistics
The cautionary tale of Simpson's paradox
Statistics in psychology
Statistics in everyday life
There's more to research methods than statistics
A brief introduction to research design
Introduction to psychological measurement
Scales of measurement
Assessing the reliability of a measurement
The ``role'' of variables: predictors and outcomes
Experimental and non-experimental research
Assessing the validity of a study
Confounds, artifacts and other threats to validity
Summary
II An introduction to R
Getting started with R
Installing R
Typing commands at the R console
Doing simple calculations with R
Storing a number as a variable
Using functions to do calculations
Letting Rstudio help you with your commands
Storing many numbers as a vector
Storing text data
Storing ``true or false'' data
Indexing vectors
Quitting R
Summary
Additional R concepts
Using comments
Installing and loading packages
Managing the workspace
Navigating the file system
Loading and saving data
Useful things to know about variables
Factors
Data frames
Lists
Formulas
Generic functions
Getting help
Summary
III Working with data
Descriptive statistics
Measures of central tendency
Measures of variability
Skew and kurtosis
Getting an overall summary of a variable
Descriptive statistics separately for each group
Standard scores
Correlations
Handling missing values
Summary
Drawing graphs
An overview of R graphics
An introduction to plotting
Histograms
Stem and leaf plots
Boxplots
Scatterplots
Bar graphs
Saving image files using R and Rstudio
Summary
Pragmatic matters
Tabulating and cross-tabulating data
Transforming and recoding a variable
A few more mathematical functions and operations
Extracting a subset of a vector
Extracting a subset of a data frame
Sorting, flipping and merging data
Reshaping a data frame
Working with text
Reading unusual data files
Coercing data from one class to another
Other useful data structures
Miscellaneous topics
Summary
Basic programming
Scripts
Loops
Conditional statements
Writing functions
Implicit loops
Summary
IV Statistical theory
Introduction to probability
How are probability and statistics different?
What does probability mean?
Basic probability theory
The binomial distribution
The normal distribution
Other useful distributions
Summary
Estimating unknown quantities from a sample
Samples, populations and sampling
The law of large numbers
Sampling distributions and the central limit theorem
Estimating population parameters
Estimating a confidence interval
Summary
Hypothesis testing
A menagerie of hypotheses
Two types of errors
Test statistics and sampling distributions
Making decisions
The p value of a test
Reporting the results of a hypothesis test
Running the hypothesis test in practice
Effect size, sample size and power
Some issues to consider
Summary
V Statistical tools
Categorical data analysis
The 2 goodness-of-fit test
The 2 test of independence (or association)
The continuity correction
Effect size
Assumptions of the test(s)
The most typical way to do chi-square tests in R
The Fisher exact test
The McNemar test
What's the difference between McNemar and independence?
Summary
Comparing two means
The one-sample z-test
The one-sample t-test
The independent samples t-test (Student test)
The independent samples t-test (Welch test)
The paired-samples t-test
One sided tests
Using the t.test() function
Effect size
Checking the normality of a sample
Testing non-normal data with Wilcoxon tests
Summary
Comparing several means (one-way ANOVA)
An illustrative data set
How ANOVA works
Running an ANOVA in R
Effect size
Multiple comparisons and post hoc tests
Assumptions of one-way ANOVA
Checking the homogeneity of variance assumption
Removing the homogeneity of variance assumption
Checking the normality assumption
Removing the normality assumption
On the relationship between ANOVA and the Student t test
Summary
Linear regression
What is a linear regression model?
Estimating a linear regression model
Multiple linear regression
Quantifying the fit of the regression model
Hypothesis tests for regression models
Testing the significance of a correlation
Regarding regression coefficients
Assumptions of regression
Model checking
Model selection
Summary
Factorial ANOVA
Factorial ANOVA 1: balanced designs, no interactions
Factorial ANOVA 2: balanced designs, interactions allowed
Effect size, estimated means, and confidence intervals
Assumption checking
The F test as a model comparison
ANOVA as a linear model
Different ways to specify contrasts
Post hoc tests
The method of planned comparisons
Factorial ANOVA 3: unbalanced designs
Summary
VI Endings, alternatives and prospects
Bayesian statistics
Probabilistic reasoning by rational agents
Bayesian hypothesis tests
Why be a Bayesian?
Bayesian analysis of contingency tables
Bayesian t-tests
Bayesian regression
Bayesian ANOVA
Summary
Epilogue
The undiscovered statistics
Learning the basics, and learning them in R
References
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