Free

# Learning Statistics with R

By Daniel Navarro

Free

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Book Description

Table of Contents

- 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

- Why do we learn statistics?
- 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

- Getting started with R
- 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

- Descriptive statistics
- 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

- Introduction to probability
- 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

- Categorical data analysis
- 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

- Bayesian statistics

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