Contents:

• 1 Introduction to data
  • 1.1 Case study
  • 1.2 Data basics
    • 1.2.1 Observations, variables, and data matrices
    • 1.2.2 Types of variables
    • 1.2.3 Relationships between variables
  • 1.3 Overview of data collection principles
    • 1.3.1 Populations and samples
    • 1.3.2 Anecdotal evidence
    • 1.3.3 Sampling from a population
    • 1.3.4 Explanatory and response variables
    • 1.3.5 Introducing observational studies and experiments
  • 1.4 Observational studies
  • 1.5 Experiments
    • 1.5.1 Principles of experimental design
    • 1.5.2 Reducing bias in human experiments
  • 1.6 Examining numerical data
    • 1.6.1 Scatterplots for paired data
    • 1.6.2 Dot plots and the mean
    • 1.6.3 Histograms and shape
    • 1.6.4 Variance and standard deviation
    • 1.6.5 Box plots, quartiles, and the median
    • 1.6.6 Robust statistics
    • 1.6.7 Transforming data
    • 1.6.8 Mapping data
  • 1.7 Considering categorical data
    • 1.7.1 Contingency tables and bar plots
    • 1.7.2 Row and column proportions
    • 1.7.3 Segmented bar and mosaic plots
    • 1.7.4 The only pie chart you will see in this course
    • 1.7.5 Comparing numerical data across groups
  • 1.8 Case study: gender discrimination
    • 1.8.1 Variability within data
    • 1.8.2 Simulating the study
    • 1.8.3 Checking for independence
• 2 Distributions and Inference
  • 2.1 Review of Discrete random variables
    • 2.1.1 Binomial Distribution
    • 2.1.2 Geometric Distribution
    • 2.1.3 Poisson Distribution
  • 2.2 Review of Continuous random variables
    • 2.2.1 Uniform Distribution
    • 2.2.2 Exponential Distribution
  • 2.3 Normal distribution
    • 2.3.1 Normal distribution model
    • 2.3.2 Standardizing with Z scores
    • 2.3.3 Calculating Normal Probabilities
    • 2.3.4 Normal probability examples
    • 2.3.5 68-95-99.7 rule
  • 2.4 Fitting Distributions to Data
    • 2.4.1 Method of Moments
  • 2.5 Assessing the fit of a distribution
    • 2.5.1 Q-Q plot
  • 2.6 Foundations for inference
  • 2.7 Variability in estimates
    • 2.7.1 Point estimates
    • 2.7.2 Point estimates are not exact
    • 2.7.3 Standard error of the mean
    • 2.7.4 Basic properties of point estimates
  • 2.8 Confidence intervals
    • 2.8.1 Capturing the population parameter
    • 2.8.2 An approximate 95% confidence interval
    • 2.8.3 A sampling distribution for the mean
    • 2.8.4 Changing the confidence level
    • 2.8.5 Interpreting confidence intervals
  • 2.9 Hypothesis testing
    • 2.9.1 Hypothesis testing framework
    • 2.9.2 Testing hypotheses using confidence intervals
    • 2.9.3 Decision errors
    • 2.9.4 Formal testing using p-values
    • 2.9.5 Two-sided hypothesis testing with p-values
    • 2.9.6 Choosing a significance level
  • 2.10 Examining the Central Limit Theorem
  • 2.11 Inference for other estimators
    • 2.11.1 Confidence intervals for nearly normal point estimates
    • 2.11.2 Hypothesis testing for nearly normal point estimates
    • 2.11.3 Non-normal point estimates
    • 2.11.4 When to retreat
    • 2.11.5 Statistical significance versus practical significance
• 3 Inference for numerical data
  • 3.1 Paired data
    • 3.1.1 Paired observations and samples
    • 3.1.2 Inference for paired data
  • 3.2 Difference of two means
    • 3.2.1 Point estimates and standard errors for differences of means
    • 3.2.2 Confidence interval for the difference
    • 3.2.3 Hypothesis tests based on a difference in means
    • 3.2.4 Summary for inference of the difference of two means
    • 3.2.5 Examining the standard error formula
  • 3.3 One-sample means with the $t$ distribution
    • 3.3.1 The normality condition
    • 3.3.2 Introducing the $t$ distribution
    • 3.3.3 The $t$ distribution as a solution to the standard error problem
    • 3.3.4 One sample $t$ confidence intervals
    • 3.3.5 One sample $t$ tests
  • 3.4 The $t$ distribution for the difference of two means
    • 3.4.1 Sampling distributions for the difference in two means
    • 3.4.2 Two sample $t$ test
• 4 Inference for categorical data
  • 4.1 Inference for a single proportion
    • 4.1.1 Identifying when the sample proportion is nearly normal
    • 4.1.2 Confidence intervals for a proportion
    • 4.1.3 Hypothesis testing for a proportion
  • 4.2 Difference of two proportions
    • 4.2.1 Sample distribution of the difference of two proportions
    • 4.2.2 Intervals and tests for $p_1-p_2$
    • 4.2.3 Hypothesis testing when $H_0:p_1=p_2$