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References for Sampling Distributions

Curated resources to deepen your understanding of sampling variability, sampling distributions, the Central Limit Theorem, and the foundations of statistical inference.

Wikipedia Articles

  1. Sampling Distribution - Wikipedia - Explains how sample statistics vary across repeated samples, covering the sampling distribution of the mean and proportion with visual diagrams and mathematical foundations.

  2. Central Limit Theorem - Wikipedia - Comprehensive coverage of this fundamental theorem, explaining why sampling distributions become normal regardless of population shape, with historical context and mathematical proofs.

  3. Standard Error - Wikipedia - Defines standard error as the standard deviation of a sampling distribution, distinguishing it from standard deviation and showing how sample size affects precision.

Textbooks

  1. The Practice of Statistics by Daren S. Starnes and Josh Tabor - W.H. Freeman (2018) - Features excellent coverage of sampling distributions with clear explanations of the formulas for sample means and proportions, plus the conditions for normal approximation.

  2. Introduction to the Practice of Statistics by David S. Moore and George P. McCabe - W.H. Freeman (2017) - Provides intuitive explanations of the Central Limit Theorem with numerous examples and exercises that build understanding of sampling variability.

Online Resources

  1. Seeing Theory: Basic Probability - Brown University - Interactive visualizations that let students explore sampling distributions by drawing repeated samples and watching distributions emerge, bringing the Central Limit Theorem to life.

  2. Khan Academy: Sampling Distributions - Khan Academy - Video lessons covering the sampling distribution of sample means and proportions, with step-by-step calculations of standard error and normal approximation conditions.

  3. Rice Virtual Lab in Statistics: Sampling Distributions - Rice University - Java-based simulations demonstrating how sample statistics vary across samples and how the CLT transforms non-normal populations into normal sampling distributions.

  4. AP Classroom: Sampling Distributions Unit - College Board - Official AP Statistics resources including practice questions, progress checks, and personal progress reports aligned with the Unit 5 learning objectives.

  5. StatKey: Sampling Distribution Demos - Lock5 - Bootstrap and randomization-based tools for exploring sampling distributions, allowing students to create empirical sampling distributions from real or simulated data.