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•
• About the picture on the cover
• 1. Introduction
• Before beginning
• Statistical inference defined
• Summary notes
• The goals of inference
• The tools of the trade
• Exercises
• 2. Probability
• Where to get a more thorough treatment of probability
• Kolmogorov’s Three Rules
• Consequences of The Three Rules
• Random variables
• Probability mass functions
• Probability density functions
• CDF and survival function
• Quantiles
• Exercises
• 3. Conditional probability
• Conditional probability, motivation
• Conditional probability, definition
• Bayes’ rule
• Diagnostic Likelihood Ratios
• Independence
• IID random variables
• Exercises
• 4. Expected values
• The population mean for discrete random variables
• The sample mean
• Continuous random variables
• Simulation experiments
• Summary notes
• Exercises
• 5. Variation
• The variance
• The sample variance
• Simulation experiments
• The standard error of the mean
• Data example
• Summary notes
• Exercises
• 6. Some common distributions
• The Bernoulli distribution
• Binomial trials
• The normal distribution
• The Poisson distribution
• Exercises
• 7. Asymptopia
• Asymptotics
• Limits of random variables
• The Central Limit Theorem
• CLT simulation experiments
• Confidence intervals
• Simulation of confidence intervals
• Poisson interval
• Summary notes
• Exercises
• 8. t Confidence intervals
• Small sample confidence intervals
• Gosset’s t distribution
• The data
• Independent group t confidence intervals
• Confidence interval
• Mistakenly treating the sleep data as grouped
• Unequal variances
• Summary notes
• Exercises
• 9. Hypothesis testing
• Hypothesis testing
• Types of errors in hypothesis testing
• Discussion relative to court cases
• Building up a standard of evidence
• General rules
• Two sided tests
• T test in R
• Connections with confidence intervals
• Two group intervals
• Exact binomial test
• Exercises
• 10. P-values
• Introduction to P-values
• What is a P-value?
• The attained significance level
• Binomial P-value example
• Poisson example
• Exercises
• 11. Power
• Power
• Question
• Notes
• T-test power
• Exercises
• 12. The bootstrap and resampling
• The bootstrap
• The bootstrap principle
• Group comparisons via permutation tests
• Permutation tests
• Variations on permutation testing
• Permutation test B v C
• Exercises

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