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Sampling & Study Design

How data is generated and collected: defining populations and variables, choosing a sampling method, and designing studies that support the intended conclusions. Topics: Populations, Variables & Statistical Questions, Sampling Methods, Sources of Bias in Data Collection, Observational Studies & Experimental Design.

Descriptive Statistics

Summarizing and displaying a single variable's distribution with graphs, measures of center and spread, and comparing distributions including relationships shown in two-way tables. Topics: Displaying Distributions, Numerical Summaries, Comparing Distributions & Two-Way Tables.

Probability & Random Variables

A compact toolkit of probability rules and discrete random variables needed for inference: interpreting probability, combining events, conditioning, and the binomial model. Topics: Probability Rules, Discrete Random Variables & the Binomial Model, Continuous Random Variables.

Normal & Sampling Distributions

Using the normal model to find probabilities and percentiles, and understanding how sample statistics vary from sample to sample, culminating in the Central Limit Theorem. Topics: The Normal Model, Sampling Distributions.

Confidence Intervals

Building and interpreting confidence intervals for a mean and a proportion, including the logic of margin of error, the conditions that justify each procedure, and how to plan sample size. Topics: Confidence Interval Foundations, Confidence Intervals for a Mean, Confidence Intervals for a Proportion.

Hypothesis Testing

The logic of testing a claim about a population using sample data, and carrying out the standard one- and two-sample tests for means and proportions, plus the reasoning needed to interpret results responsibly. Topics: Testing Logic & One-Sample Tests, Two-Sample Tests, Interpreting and Using Test Results.

Chi-Square Tests and ANOVA

Testing categorical data against a model or across groups with the chi-square distribution, and comparing means across several groups with one-way ANOVA and the F distribution. Topics: Chi-Square Foundations & Tests, One-Way ANOVA.

Correlation and Regression

Describing and modeling the linear relationship between two quantitative variables, using the model for prediction, checking it with residuals, and recognizing its diagnostic and causal limits. Topics: Describing Association, Building and Using the Regression Model, Regression Diagnostics and Inference.