Sampling Methods

Sampling Fundamentals - The Who & Why

• Population (N): Entire group of interest.
• Sample (n): Subset of N, chosen for study.
• Sampling Frame: List of all units in N for sample selection.
• Parameter: Population characteristic (e.g., $\mu$).
• Statistic: Sample characteristic (e.g., $\bar{x}$), estimates parameter.
• Purpose: Feasibility (cost, time); make inferences about N.
• Errors:
  • Sampling Error: Sample-population discrepancy; ↓ with ↑ n.
  • Non-Sampling Error: Due to measurement/processing flaws.

⭐ The primary goal of sampling is to draw inferences about a larger population based on a smaller, representative subset, balancing precision with practicality.

Probability Sampling - Everyman's Chance

• Core principle: Every member has a known, non-zero selection chance. Allows generalization to the population.
• Types:
  • Simple Random Sampling (SRS):
    • Each unit has an equal and independent chance of selection.
    • Methods: Lottery, random number tables/generator.
    • 
  • Systematic Sampling:
    • Select units at regular intervals (e.g., every $k^{th}$ unit).
    • Sampling interval $k = N/n$ (N=population size, n=sample size).
    • Requires a random start; can be biased if there's periodicity in the list.
  • Stratified Sampling:
    • Population divided into homogeneous subgroups (strata) based on specific characteristics (e.g., age, sex).
    • SRS or systematic sampling is then done within each stratum.
    • Ensures representation of key subgroups; increases precision.

    ⭐ Stratified sampling is preferred when the population is heterogeneous, and specific subgroups need to be proportionally represented to increase precision and reduce sampling error for subgroup estimates.

  • Cluster Sampling:
    • Population divided into clusters (often geographic, e.g., villages, schools).
    • Randomly select clusters; sample all units or a sample of units within selected clusters.
    • Cost-effective for large, dispersed populations; may ↑ sampling error (design effect).
  • Multistage Sampling:
    • Complex form involving sampling in multiple stages (e.g., states → districts → villages → households).

Non-Probability Sampling - Quick Picks & Quirks

• Subject selection is non-random, based on convenience or researcher judgment.
• Major Drawback: Findings not generalizable; high selection bias risk.
• Common in exploratory research or when random sampling is impractical.
• Methods:
  • Convenience: Easiest to reach subjects. Fast, cheap; high bias.
  • Purposive (Judgmental): Researcher selects based on specific traits/expertise.
  • Quota: Non-random selection to fill subgroup quotas (e.g., age, gender).
  • Snowball: Initial subjects refer subsequent ones.

    ⭐ Snowball sampling is particularly useful for accessing hidden, hard-to-reach, or socially networked populations (e.g., drug users, rare disease patients).

Sampling Errors & Bias - Data Tripwires

• Sampling Error (Random Error):
  • Difference between sample statistic & true population parameter due to chance.
  • Unavoidable; inherent to sampling.
  • Magnitude ↓ with ↑ sample size ($n$).
  • Quantified by Standard Error (SE): $SE = \frac{\sigma}{\sqrt{n}}$.
• Non-Sampling Error (Bias/Systematic Error):
  • Systematic deviation from the true value; not due to chance.
  • Leads to inaccurate (invalid) results; not reduced by ↑ $n$.
  • Major Types:
    • Selection Bias: Sample not representative of the target population.
      • Examples: Sampling bias (faulty technique), volunteer bias, non-response bias, Berkson's bias (hospital-based studies), Neyman bias (incidence-prevalence bias; e.g., missing fatal/mild cases). 📌 Neyman: No early/mild/dead.
    • Information Bias (Measurement/Observation Bias): Errors in data collection or measurement.
      • Examples: Recall bias, interviewer bias, observer bias, misclassification bias.

⭐ Selection bias, where the sample is not representative of the population due to systematic differences in choosing participants, is a critical flaw that can invalidate study conclusions.

High‑Yield Points - ⚡ Biggest Takeaways

• Simple Random Sampling (SRS): Equal chance of selection for all units; best for homogeneous populations.
• Stratified Sampling: Divides population into homogeneous strata; SRS within each. ↑Precision, ↓error.
• Systematic Sampling: Selects units at regular intervals (k-th unit). Easy, but risk of periodicity bias.
• Cluster Sampling: Randomly selects intact groups (clusters). Cost-effective for dispersed populations; ↑sampling error vs SRS.
• Sampling Error: Inversely proportional to the square root of the sample size; ↑sample size, ↓error.
• Non-probability methods (e.g., convenience, quota) are biased; results not generalizable.