Sampling Methods

Introduction

Sampling methods: procedures to select subsets from populations. Purpose: obtain representative data efficiently. Importance: enables inference without full population study. Categories: probability and non-probability sampling. Applications: surveys, experiments, observational studies.

"Sampling is the process of selecting units from a population of interest so that by studying the sample we may fairly generalize our results back to the population from which they were chosen." -- W.G. Cochran

Probability Sampling

Definition

Sampling method where every unit in population has known, non-zero chance of selection. Basis for statistical inference. Ensures representativeness and unbiased estimates.

Advantages

Enables calculation of sampling error. Facilitates generalization. Reduces selection bias.

Types

Includes simple random, systematic, stratified, cluster, and multi-stage sampling.

Simple Random Sampling

Mechanism

Every unit has equal probability of selection. Selection performed by random number generators or tables.

Procedure

Define sampling frame, assign numbers, select using random method.

Pros and Cons

Pros: unbiased, easy to analyze. Cons: requires complete frame, may not be efficient for heterogeneous populations.

Systematic Sampling

Definition

Sampling every kth unit after a random start. k = population size/sample size.

Steps

Order population, select random start between 1 and k, select every kth unit thereafter.

Benefits and Limitations

Efficient, simpler than random sampling. Risk: periodicity bias if population is ordered cyclically.

Stratified Sampling

Principle

Population divided into homogeneous strata. Random samples drawn from each stratum. Improves precision by reducing variance within strata.

Types

Proportional stratified sampling: sample size proportional to stratum size. Disproportional: fixed sample size per stratum.

Applications

Used when population is heterogeneous but strata are homogeneous. Ensures representation of all subgroups.

Cluster Sampling

Concept

Population divided into clusters (usually naturally occurring groups). Random selection of entire clusters. Data collected from all units within selected clusters.

Advantages

Cost-effective, practical for widespread populations. Reduces travel and administrative costs.

Disadvantages

Higher sampling error compared to simple random sampling. Clusters may not be homogeneous.

Multi-Stage Sampling

Definition

Combination of sampling methods applied in stages. Commonly clusters selected first, then random sampling within clusters.

Procedure

Stage 1: select clusters. Stage 2: select units within clusters. Further stages possible.

Use Cases

Large-scale surveys, national censuses, complex populations.

Stage 1: Select 10 clusters randomly from 50 totalStage 2: Within each cluster, select 5 units via simple random samplingFinal sample size = 10 clusters × 5 units = 50 units

Non-Probability Sampling

Definition

Sampling methods where units have unknown or zero probability of selection. No randomization involved. Often used when probability sampling is impractical.

Consequences

Cannot calculate sampling error. Risk of selection bias. Limited generalizability.

Common Methods

Convenience, quota, purposive sampling.

Convenience Sampling

Description

Sampling units easiest to reach or access. No random selection.

Applications

Preliminary studies, pilot testing, exploratory research.

Limitations

High risk of bias. Poor representativeness. Results not generalizable.

Quota Sampling

Mechanism

Population divided into strata. Predetermined quotas set for each stratum. Units selected non-randomly until quotas filled.

Advantages

Ensures representation of subgroups. Easier than stratified random sampling.

Disadvantages

Potential selection bias. Non-random units may not represent strata accurately.

Purposive Sampling

Definition

Sample selected based on researcher judgment about units’ relevance.

Uses

Specialized populations, expert interviews, case studies.

Limitations

Subjectivity risk. Limited external validity.

Sampling Errors and Bias

Sampling Error

Difference between sample statistic and true population parameter due to chance. Decreases with larger sample size.

Sampling Bias

Systematic error from non-random sampling or non-response. Leads to unrepresentative samples.

Mitigation Strategies

Use probability sampling, increase sample size, ensure sampling frame completeness.

Sampling Error (SE) = σ / √nWhere:σ = population standard deviationn = sample size

References

• Cochran, W.G. Sampling Techniques, 3rd ed., Wiley, 1977, pp. 1-428.
• Kish, L. Survey Sampling, Wiley, 1965, pp. 1-643.
• Lohr, S.L. Sampling: Design and Analysis, 2nd ed., Brooks/Cole, 2009, pp. 1-456.
• Kalton, G. Introduction to Survey Sampling, Sage Publications, 1983, pp. 1-88.
• Thompson, S.K. Sampling, 3rd ed., Wiley, 2012, pp. 1-369.