Sampling Methods Course

Lesson 1 • Populations, Samples, and Parameters

Defines population, sample, parameter, and statistic with concrete examples. Establishes the vocabulary used throughout the entire course.

Lesson 2 • Core Concepts of Statistical Inference

Introduces estimation, bias, variance, and the sampling distribution concept. Provides the inferential framework that underpins all sampling methods.

Lesson 3 • Why Sampling Is Necessary

Examines cost, time, and feasibility constraints that make full enumeration impractical. Connects practical limitations to the logic of inference.

Lesson 4 • Overview of Sampling Design Types

Surveys probability and non-probability design families at a high level. Orients students to the course roadmap before detailed methods are introduced.

Lesson 1 • Variance Estimation and Standard Errors

Presents variance formulas for SRS estimators and the finite population correction. Students apply these formulas to quantify estimation precision.

Lesson 2 • Sample Size Determination for SRS

Derives sample size formulas based on desired margin of error and confidence level. Enables students to plan studies with specified precision requirements.

Lesson 3 • Principles of Simple Random Sampling

Defines SRS with and without replacement and explains equal-probability selection. Establishes the baseline design against which all other methods are compared.

Lesson 4 • Confidence Intervals Under SRS

Constructs confidence intervals for means, totals, and proportions using SRS variance estimates. Reinforces the link between standard errors and interval width.

Lesson 1 • Allocation Methods Across Strata

Covers proportional, equal, and optimal (Neyman) allocation strategies. Students select allocation methods based on cost and variance objectives.

Lesson 2 • Stratified Estimators for Means and Totals

Derives the stratified mean and total estimators as weighted combinations of stratum estimates. Demonstrates unbiasedness and connects to SRS estimators.

Lesson 3 • Stratum Boundary Determination

Introduces cumulative square root frequency and other boundary-setting methods. Connects stratum construction to the efficiency of the final design.

Lesson 4 • Variance of Stratified Estimators

Presents variance formulas for stratified estimators and the finite population correction per stratum. Students quantify precision gains relative to SRS.

Lesson 1 • Estimation in One-Stage Cluster Sampling

Derives unbiased estimators for cluster means and totals under equal and unequal cluster sizes. Applies variance formulas to measure design efficiency.

Lesson 2 • Introduction to Cluster Sampling

Defines clusters, primary sampling units, and the one-stage cluster design. Contrasts cluster sampling with stratification in terms of within-group homogeneity.

Lesson 3 • Two-Stage Cluster Sampling

Extends one-stage clusters by subsampling within selected clusters. Students derive two-stage estimators and understand the variance decomposition.

Lesson 4 • Systematic Sampling Mechanics

Defines the skip interval, random start, and selection procedure for systematic sampling. Builds on SRS to show how systematic sampling simplifies field operations.

Lesson 1 • Horvitz-Thompson Estimator

Derives the Horvitz-Thompson (HT) estimator and its variance using inclusion probabilities. Establishes HT as the general unbiased estimator for any probability design.

Lesson 2 • Rationale for Unequal Probability Sampling

Explains why equal-probability designs are inefficient when unit sizes vary widely. Motivates PPS as a variance-reduction strategy for skewed populations.

Lesson 3 • PPS Selection Procedures

Covers cumulative total, Lahiri, and systematic PPS selection methods. Students implement each procedure and verify inclusion probabilities.

Lesson 4 • Design Effect and Efficiency Comparisons

Quantifies efficiency gains of PPS over SRS using the design effect (DEFF). Students interpret DEFF values to justify design choices.

Lesson 1 • Weighting in Complex Surveys

Derives base weights from inclusion probabilities and adjusts for nonresponse and calibration. Students construct and apply final analysis weights.

Lesson 2 • Replication Variance Methods

Covers balanced repeated replication, jackknife, and bootstrap for complex survey variance. Students select and apply replication methods to real survey structures.

Lesson 3 • Linearization Variance Estimation

Applies Taylor series linearization to estimate variance for nonlinear statistics in complex designs. Connects to the HT variance framework from Chapter 5.

Lesson 4 • Architecture of Multi-Stage Designs

Describes how stratification, clustering, and PPS are layered across sampling stages. Builds directly on Chapters 3, 4, and 5 to integrate all prior design elements.

Lesson 1 • Snowball and Network Sampling

Covers chain-referral methods for hard-to-reach populations. Students understand recruitment bias and conditions under which network sampling is appropriate.

Lesson 2 • Bias Assessment in Non-Probability Samples

Introduces methods for detecting and adjusting selection bias in non-probability data. Connects to weighting concepts from Chapter 6 for potential bias correction.

Lesson 3 • Foundations of Non-Probability Sampling

Defines non-probability sampling and contrasts it with probability-based inference. Establishes when non-probability designs are acceptable and their inferential limits.

Lesson 4 • Respondent-Driven Sampling

Presents RDS as a structured network method with probability-based estimation adjustments. Students apply RDS estimators and assess convergence assumptions.

Lesson 1 • Total Survey Error Framework

Integrates all error sources into the total survey error (TSE) model for quality evaluation. Students apply TSE to audit a complete survey design.

Lesson 2 • Weighting Adjustments for Nonresponse

Covers response propensity weighting and cell-based nonresponse adjustments. Builds on Chapter 6 weighting to extend adjustments for missing data.

Lesson 3 • Imputation Methods for Item Nonresponse

Presents hot-deck, mean, regression, and multiple imputation techniques. Students select and apply imputation methods appropriate to data structure.

Lesson 4 • Calibration Estimation

Derives calibration estimators that align survey weights to known population benchmarks. Students implement raking and generalized regression (GREG) calibration.