Sampling Techniques: Methods, Errors & Applications

TAKEAWAYS:

• Sampling error is the difference between sample statistics and population parameters, minimized by larger samples and proper techniques.
• Probability sampling (random, systematic, stratified, cluster) ensures every unit has a known chance of selection, while non-probability sampling (convenience, purposive, snowball) is faster but less generalizable.
• Stratified sampling divides populations into homogenous subgroups (e.g., age groups in a Kathmandu traffic study) for precise estimates.
• Quota sampling (used in NTC customer satisfaction surveys) fills predefined quotas (e.g., 30% youth, 50% adults) but risks bias if quotas are poorly defined.
• Sampling frame is the list of all population units (e.g., NEPSE’s listed companies for a stock market study), and its accuracy directly affects sample validity.
• Pilot studies (Unit 9) often use convenience sampling to test data collection methods before full-scale research.

1. What is Sampling? Why Does It Matter?

Sampling is the process of selecting a subset (sample) from a larger group (population) to study, analyze, or make inferences about the whole. It’s essential in business research because:

• Cost-effective: Surveying 1,000 Nepali shoppers (sample) is cheaper than studying all 30 million consumers.
• Time-saving: Daraz can’t wait months to analyze every order; they sample customer reviews weekly.
• Practical: Some populations (e.g., all microfinance borrowers in Nepal) are too large or dispersed to study entirely.

Key Terms:

• Population: The entire group of interest (e.g., all Pathao riders in Kathmandu).
• Sample: The subset selected for study (e.g., 500 Pathao riders surveyed via app).
• Sampling unit: The individual element (e.g., one rider’s feedback).
• Sampling frame: The list of all sampling units (e.g., Pathao’s rider database).

mindmap
  root((Sampling))
    Why Sample?
      Cost
      Time
      Feasibility
    Key Terms
      Population
      Sample
      Sampling Unit
      Sampling Frame
    Types
      Probability
        Random
        Systematic
        Stratified
        Cluster
      Non-Probability
        Convenience
        Purposive
        Snowball
        Quota

2. Sampling Error: The Gap Between Sample and Reality

Definition: Sampling error is the difference between a sample statistic (e.g., average income of 500 sampled households) and the true population parameter (e.g., average income of all Nepali households). It’s not a mistake—it’s inherent due to random variation.

How to Calculate Sampling Error (Simplified)

For a proportion (e.g., % of Ncell users who upgrade plans): $$\text{Sampling Error}=z\times \sqrt{\frac{p(1-p)}{n}}$$ Where:

• $z$ = confidence level (1.96 for 95% confidence),
• $p$ = sample proportion (e.g., 30% upgrade rate),
• $n$ = sample size.

Worked Example: NEPSE Stock Study

• Population: 200 listed companies.
• Sample: 50 companies (25%).
• Sample mean return: 12% (vs. true population mean of 10%).
• Sampling error: $12\%-10\%=2\%$ (absolute error).

How to Reduce Sampling Error:

1. Increase sample size: Larger samples (e.g., 200 vs. 50 companies) narrow the error margin.
2. Use probability sampling: Random selection reduces bias.
3. Stratify the sample: Ensure subgroups (e.g., small vs. large-cap stocks) are represented.

3. Probability Sampling: Fair and Random Selection

Probability sampling gives every unit a known chance of being selected. It’s gold standard for generalizable results (e.g., national polls, clinical trials).

A. Simple Random Sampling

• How it works: Every unit has an equal chance of selection (e.g., lottery system).
• Example: Ncell selects 1,000 subscribers randomly from its 5 million users via a computer-generated list.
• Advantages:
  • Unbiased, representative.
  • Easy to calculate sampling error.
• Disadvantages:
  • Expensive (requires full sampling frame).
  • Hard to implement for large populations (e.g., all Daraz sellers).

Worked Example: Kathmandu Metro Feedback

• Population: 50,000 daily commuters.
• Sample: 500 selected via random number generator from a passenger list.
• Result: 65% satisfaction rate (margin of error: ±4%).

B. Systematic Sampling

• How it works: Select every k-th unit from a list.
  • Step 1: $k=\frac{\text{Population size}}{\text{Sample size}}$ (e.g., $k=50$ for 5,000 users and 100 samples).
  • Step 2: Start at a random point (1–50), then pick every 50th user.
• Example: NTC audits every 100th electricity bill in a stack of 10,000.
• Advantages:
  • Simpler than random sampling.
  • Even coverage if the list is random.
• Disadvantages:
  • Risk of periodicity bias (e.g., if bills are ordered by usage, high users may cluster).

C. Stratified Sampling

• How it works: Divide the population into homogenous subgroups (strata), then sample from each stratum.
• Example: Studying customer loyalty at Himalayan Java:
  • Strata:
    • Regulars (visit >10x/month),
    • Occasional (3–9 visits),
    • First-timers.
  • Sample: 100 from each stratum (total 300).
• Advantages:
  • More precise estimates for subgroups.
  • Reduces sampling error for small strata.
• Disadvantages:
  • Requires prior knowledge of strata.
  • More complex than random sampling.

Visual: Stratified Sampling for a Bank Loan Study

D. Cluster Sampling

• How it works: Divide population into heterogenous clusters, randomly select clusters, then sample all units in those clusters.
• Example: Studying rural vs. urban internet usage in Nepal:
  • Clusters: 77 districts.
  • Sample: Randomly pick 10 districts, then survey all households in those districts.
• Advantages:
  • Cost-effective (no full sampling frame needed).
  • Useful for geographically dispersed populations.
• Disadvantages:
  • Higher sampling error if clusters are homogenous.
  • Less precise than stratified sampling.

Real-World Tie-In: NTC’s Electricity Consumption Survey

• Population: All households in Nepal.
• Clusters: 7 provinces.
• Sample: Survey all households in 3 randomly selected provinces.
• Result: Estimates national consumption patterns without surveying every home.

4. Non-Probability Sampling: Fast but Biased

Used when probability sampling is impractical (e.g., pilot studies, exploratory research). Results cannot be generalized but are useful for insights.

A. Convenience Sampling

• How it works: Select the easiest-to-reach units.
• Example: Daraz asks the first 200 shoppers who visit their booth at a trade fair.
• Advantages:
  • Cheap and quick.
  • No sampling frame needed.
• Disadvantages:
  • High bias (e.g., trade fair visitors may not represent all online shoppers).
  • Not generalizable.

Worked Example: Pathao Driver Feedback

• Method: Survey drivers waiting at a single pickup spot in Thapathali.
• Problem: These drivers may be more stressed (high traffic area), skewing results.

B. Purposive (Judgmental) Sampling

• How it works: Select units based on specific criteria.
• Example: Studying successful microfinance borrowers in Nepal:
  • Criteria: Repayment rate >90%, loan duration >2 years.
  • Sample: 50 borrowers meeting these criteria from a bank’s records.
• Advantages:
  • Targets specific subgroups.
  • Useful for rare populations (e.g., CEO interviews).
• Disadvantages:
  • Researcher bias in selection.
  • Not representative.

C. Snowball Sampling

• How it works: Start with a few units, then ask them to refer others who fit the criteria.
• Example: Studying underground gig workers (e.g., freelance delivery riders not registered with Pathao):
  • Start with 5 riders, ask them to refer 5 more, and so on.
• Advantages:
  • Useful for hidden populations (e.g., informal workers).
• Disadvantages:
  • Severe bias (referrals may share similar traits).
  • Non-random, hard to estimate sampling error.

D. Quota Sampling

• How it works: Fill predefined quotas based on key characteristics (e.g., age, gender).
• Example: NTC wants to survey 1,000 households with quotas:
  • 40% urban, 60% rural.
  • 50% male, 50% female.
  • Interviewers stop once quotas are met.
• Advantages:
  • Ensures representation on key variables.
  • Faster than probability sampling.
• Disadvantages:
  • Selection bias (interviewers may pick easiest respondents).
  • No way to calculate sampling error.

Comparison Table: Probability vs. Non-Probability Sampling

5. Real-World Applications in Nepali Businesses

Case Study 1: Ncell’s Customer Retention Study

• Problem: Ncell wants to know why 20% of customers churn annually.
• Method: Stratified random sampling of 5,000 customers:
  • Strata: Prepaid vs. postpaid, urban vs. rural, age groups.
  • Result: Found that rural postpaid users churn most due to poor network coverage.
• Action: Targeted infrastructure upgrades in rural areas.

Case Study 2: Daraz’s Order Fulfillment Efficiency

• Problem: Daraz wants to reduce delivery delays.
• Method: Cluster sampling of 50 warehouses out of 200 nationwide.
  • Findings: 60% of delays came from 3 clusters (Kathmandu, Pokhara, Biratnagar).
• Action: Redesigned logistics routes for these clusters.

Case Study 3: NTC’s Electricity Theft Detection

• Problem: NTC suspects 15% of connections are tampered for theft.
• Method: Systematic sampling of every 50th connection in a district.
  • Result: Confirmed 20% theft rate in high-density areas.
• Action: Deployed smart meters in those areas.

6. How to Choose the Right Sampling Method

Use this decision flowchart to pick the best technique:

Exam Tip: How to Score Full Marks

1. Define clearly: Always start with definitions (e.g., “Sampling error is the difference between...”).
2. Use real examples: Link methods to Nepali businesses (e.g., “Ncell uses stratified sampling to...”).
3. Compare methods: Tables or flowcharts (like above) show understanding of trade-offs.
4. Calculate sampling error: For numerical questions, show the formula and steps (even if simplified).
5. Critique methods: For essay questions, discuss advantages/disadvantages of each technique in context.
   • Example: “While quota sampling is cost-effective for NTC’s surveys, its reliance on interviewer judgment introduces bias, limiting its validity for policy decisions.”
6. Avoid vague answers: Instead of “random sampling is good,” say “Simple random sampling ensures every Pathao rider has an equal chance of selection, minimizing selection bias in customer satisfaction studies.”

Practice Questions (Exam-Style)

1. Short Answer:

   • Define sampling frame and explain why it’s critical in NEPSE’s annual stock performance study.
   • List two disadvantages of convenience sampling and suggest an alternative for a market research study on Himalayan Java’s coffee drinkers.

2. Numerical:

   • A survey of 400 Kathmandu shoppers finds 60% prefer online shopping. Calculate the sampling error at 95% confidence.

3. Essay:

   • “Probability sampling is always better than non-probability sampling.” Discuss this statement with reference to Ncell’s customer survey and a pilot study for a new Daraz feature.

Key Formulas to Memorize

Final Visual Summary

mindmap
  root((Sampling Techniques))
    Probability Sampling
      Simple Random: Equal chance, unbiased
      Systematic: Every k-th unit, risk of periodicity
      Stratified: Subgroups, precise estimates
      Cluster: Groups, cost-effective
    Non-Probability Sampling
      Convenience: Easy but biased
      Purposive: Targeted criteria
      Snowball: Hidden populations
      Quota: Fill categories, fast but flawed
    Real-World Examples
      Ncell: Stratified for customer retention
      Daraz: Cluster for warehouse efficiency
      NTC: Systematic for theft detection
    Exam Tips
      Define > Example > Compare > Calculate