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Contents - Lessons & Practice

Math

Introductory Statistics 2e

OpenStax book

OpenStax

Introductory Statistics

13 lessons

One lesson for each chapter, from sampling through ANOVA. The algebra is the same algebra you just practiced.

  1. 1Sampling and dataA parameter describes the population. A statistic describes the sample.
  2. 2Descriptive statisticsPicture the sample before you infer anything, and let the median resist outliers.
  3. 3Probability topicsSubtract the overlap, and multiply only when the events are independent.
  4. 4Discrete random variablesA binomial count has mean np. The trials are independent, and the success probability stays put.
  5. 5Continuous random variablesProbability is area. A single exact value has no width, so its probability is 0.
  6. 6The normal distributionA z-score counts standard deviations from the mean.
  7. 7The central limit theoremA sample mean varies less than a single observation, and the drop is σ / √n.
  8. 8Confidence intervalsThe percent names the method, not the chance that this finished interval contains the parameter.
  9. 9Hypothesis testing with one sampleReject the null when the p-value is at most α. A large p-value is not proof that the null is true.
  10. 10Hypothesis testing with two samplesMatched pairs are analyzed as one sample of differences.
  11. 11The chi-square distributionCompare observed counts with expected counts. The test is right-tailed.
  12. 12Linear regression and correlationr measures a straight-line association. It does not, by itself, show cause.
  13. 13One-way ANOVACompare three or more means in one test. The null says they are all equal.