# Module 5 Survey Sampling Methods

by Patrick Boily; influenced by Patrick Farrell’s STAT 4502 course at Carleton University

Simply put, data analysis requires data. In pedagogical settings, we take for granted that the data at our disposal is “perfect” (or “ideal”): it either consists of the totality of potentially available data, or it is a representative subset thereof. In practice, either of these can be difficult to achieve; it can prove costly (and sometimes impractical) to collect data from which we can infer population trends and characteristics.

While web scraping (and automated methods) are sometimes used to facilitate the data collection process (see Module 17), the samples that they provide often fail to be representative enough to be of use in practice.

In this module, we discuss the principles that underlie statistical sampling methods, and show how to obtain estimates for various sampling plans.

### Contents

5.1 Background
5.1.1 Survey Sampling Generalities
5.1.2 Survey Frames
5.1.3 Fundamental Sampling Concepts
5.1.4 Data Collection Basics
5.1.5 Types of Sampling Methods

5.2 Questionnaire Design
5.2.1 Basic Concepts
5.2.2 Question Types
5.2.3 Design Considerations
5.2.4 Question Order

5.3 Simple Random Sampling
5.3.1 Basic Notions
5.3.2 Estimators and Confidence Intervals
5.3.3 Sample Size

5.4 Stratified Random Sampling
5.4.1 Estimators and Confidence Intervals
5.4.2 Sample Size and Allocation
5.4.3 Comparison Between SRS and StS

5.5 Ratio, Regression, Difference
5.5.1 Ratio Estimation
5.5.2 Regression Estimation
5.5.3 Difference Estimation
5.5.4 Comparisons

5.6 Cluster Sampling
5.6.1 Estimators and Confidence Intervals
5.6.2 Sample Size
5.6.3 Comparison Between SRS and CLS

5.7 Special Topics
5.7.1 Systematic Sampling
5.7.2 Sampling with Prob. Proportional to Size
5.7.3 Multi-Stage Sampling
5.7.4 Multi-Phase Sampling
5.7.5 Miscellaneous

5.8 Exercises