Theoretical / proof-based
Statistical inference · Undergraduate · Math
Learning objectives from the Statistical inference syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Statistical inference — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Estimation
- Point estimators: method of moments — Point estimators: method of moments
- Maximum likelihood (intro) — Maximum likelihood (intro)
- Properties of estimators: bias, variance, and MSE — Properties of estimators: bias, variance, and MSE
- Confidence intervals: pivot methods — Confidence intervals: pivot methods
- Large-sample confidence intervals — Large-sample confidence intervals
- Bootstrap confidence intervals (introduction) — Bootstrap confidence intervals (introduction)
Hypothesis testing
- Null and alternative hypotheses; test statistics — Null and alternative hypotheses; test statistics
- P-values and significance levels — P-values and significance levels
- Tests for means and proportions — Tests for means and proportions
- Variances — Variances
- Likelihood ratio tests (introduction) — Likelihood ratio tests (introduction)
- Multiple testing overview: family-wise error — Multiple testing overview: family-wise error
- Power and sample size (introduction) — Power and sample size (introduction)
Advanced inference topics
- Sufficient statistics — Sufficient statistics
- The factorization theorem (statement) — The factorization theorem (statement)
- Rao–Blackwell — Rao–Blackwell
- Cramér–Rao lower bound (statement) — Cramér–Rao lower bound (statement)
- Bayesian credible intervals (preview) — Bayesian credible intervals (preview)
- Nonparametric tests preview: sign — Nonparametric tests preview: sign
- Wilcoxon — Wilcoxon
Learning objectives
Click an objective for study materials.
Estimation
- Point estimators: method of moments — Point estimators: method of moments
- Maximum likelihood (intro) — Maximum likelihood (intro)
- Properties of estimators: bias, variance, and MSE — Properties of estimators: bias, variance, and MSE
- Confidence intervals: pivot methods — Confidence intervals: pivot methods
- Large-sample confidence intervals — Large-sample confidence intervals
- Bootstrap confidence intervals (introduction) — Bootstrap confidence intervals (introduction)
Hypothesis testing
- Null and alternative hypotheses — Null and alternative hypotheses; test statistics
- P-values and significance levels — P-values and significance levels
- Tests for means and proportions — Tests for means and proportions
- Variances — Variances
- Likelihood ratio tests (introduction) — Likelihood ratio tests (introduction)
- Multiple testing overview: family-wise error — Multiple testing overview: family-wise error
- Power and sample size (introduction) — Power and sample size (introduction)
Advanced inference topics
- Sufficient statistics — Sufficient statistics
- The factorization theorem (statement) — The factorization theorem (statement)
- Rao–Blackwell — Rao–Blackwell
- Cramér–Rao lower bound (statement) — Cramér–Rao lower bound (statement)
- Bayesian credible intervals (preview) — Bayesian credible intervals (preview)
- Nonparametric tests preview: sign — Nonparametric tests preview: sign
- Wilcoxon — Wilcoxon
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Estimation
Point estimators: method of moments
Coming soon - Hypothesis testing
Null and alternative hypotheses; test statistics
Coming soon - Advanced inference topics
Sufficient statistics
Coming soon
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$1,162 · Statistical inference · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.