 Free

# Learning Statistics with R

By Daniel Navarro
Free
Book Description
• 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
• Storing many numbers as a vector
• Storing text data
• Storing ``true or false'' data
• Indexing vectors
• Quitting R
• Summary
• Managing the workspace
• Navigating the file system
• 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
• 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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