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Intro Statistics

Statistics is the study of variability: how to describe it, how to model it, and how to draw a conclusion from a sample without fooling yourself. Twelve chapters, in the order AP Statistics and a first college course take them — the outline is here in full, and the lessons follow chapter by chapter.

  • Chapter 1Outline

    Exploring Data

    • Categorical and quantitative variables, and the displays for each: bar charts, dot plots, stem-and-leaf plots, histograms.
    • Describing a distribution: shape, centre, spread, and outliers.
    • Mean and median, and when they disagree.
    • Standard deviation, the five-number summary, and the interquartile range.
    • Box plots and the 1.5 × IQR rule for outliers.
    • Comparing distributions between groups.
  • Chapter 2Outline

    Modeling Distributions of Data

    • Percentiles and cumulative relative frequency graphs.
    • z-scores: measuring position in standard deviations.
    • Transforming data by adding and multiplying, and what happens to the summaries.
    • Density curves as models for a distribution.
    • The normal distribution and the 68–95–99.7 rule.
    • Standard normal calculations, and judging whether data are approximately normal.
  • Chapter 3Outline

    Describing Relationships

    • Scatterplots: direction, form, strength, and unusual points.
    • Correlation, and what r does and does not measure.
    • Least-squares regression lines: slope, intercept, and prediction.
    • Residuals and residual plots.
    • r² and the standard deviation of the residuals.
    • Outliers, influential points, extrapolation, and why correlation is not causation.
  • Chapter 4Outline

    Designing Studies

    • Populations, samples, and why a convenience sample misleads.
    • Simple random, stratified, cluster and systematic sampling.
    • Bias: undercoverage, nonresponse, and the wording of a question.
    • Observational studies versus experiments, and confounding.
    • Randomised comparative experiments: control, random assignment, replication.
    • Blocking, matched pairs, blinding, and placebos.
    • Scope of inference: what a study can say about a population, and about cause.
  • Chapter 5Outline

    Probability

    • Randomness, the law of large numbers, and simulation.
    • Sample spaces, events, and the basic probability rules.
    • Two-way tables and Venn diagrams.
    • The general addition rule.
    • Conditional probability and independence.
    • Tree diagrams and the general multiplication rule.
  • Chapter 6Outline

    Random Variables

    • Discrete and continuous random variables.
    • The mean and standard deviation of a random variable.
    • Transforming and combining random variables.
    • Binomial distributions: conditions, probabilities, mean and standard deviation.
    • Geometric distributions.
    • The normal approximation to the binomial.
  • Chapter 7Outline

    Sampling Distributions

    • Parameters versus statistics.
    • Sampling variability, and the sampling distribution of a statistic.
    • Bias and variability of an estimator.
    • The sampling distribution of a sample proportion.
    • The sampling distribution of a sample mean.
    • The central limit theorem.
  • Chapter 8Outline

    Estimating with Confidence

    • Confidence intervals: the idea, and how to interpret one correctly.
    • Conditions for inference: random, normal, independent.
    • A confidence interval for a population proportion.
    • The t distribution, and a confidence interval for a population mean.
    • Choosing a sample size for a given margin of error.
  • Chapter 9Outline

    Testing a Claim

    • Null and alternative hypotheses.
    • p-values, and what a p-value is not.
    • Significance levels and statistical significance.
    • Type I and Type II errors, and power.
    • The one-sample z test for a proportion.
    • The one-sample t test for a mean.
  • Chapter 10Outline

    Comparing Two Populations

    • The sampling distribution of a difference.
    • Two-sample z procedures for a difference in proportions.
    • Two-sample t procedures for a difference in means.
    • Paired data, and why it is a one-sample problem.
    • Choosing between paired and two-sample designs.
  • Chapter 11Outline

    Chi-Square Tests

    • Expected counts and the chi-square statistic.
    • The chi-square distributions and degrees of freedom.
    • Goodness-of-fit tests.
    • Tests for homogeneity across groups.
    • Tests for independence in a two-way table.
  • Chapter 12Outline

    Inference for Regression

    • The sampling distribution of the slope.
    • Conditions for regression inference.
    • A confidence interval for the slope.
    • A significance test for the slope.
    • Transforming to achieve linearity: logarithms and powers.

12 chapters · 69 topics · outlines now, lessons to come