Sampling Methods, Techniques & Applications

What is Sampling?

Sampling is the process of selecting a subset (sample) from a larger group (population) to study, analyze, or make inferences about the entire group. Proper sampling ensures representativeness, generalizability, and cost-efficiency in research.

Why Sample?

• Population too large: Studying every voter in Nepal (30+ million) is impractical.
• Resource constraints: Time, budget, and manpower limit full population studies.
• Precision vs. cost: A well-chosen sample can yield results as accurate as a census at a fraction of the cost.

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Population vs. Sample

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Types of Sampling Techniques

Sampling methods are classified into probability (random) and non-probability (non-random) techniques.

1. Probability Sampling

Every member of the population has a known chance of being selected. Ensures statistical validity but may be costly/time-consuming.

A. Simple Random Sampling

• Definition: Every individual has an equal probability of selection (e.g., lottery method).
• How it works:
  1. Define the population (e.g., all Daraz customers in Kathmandu).
  2. Assign a unique number to each member.
  3. Use a random number generator to select samples.
• Example:
  • Nepal Electricity Authority (NEA) surveys 500 households out of 5 million to estimate energy consumption.
  • Worked Example: If NEA wants to sample 1,000 households from 100,000, it assigns numbers 1–100,000 and picks every 100th number (100, 200, 300...) using a random start.

B. Systematic Sampling

• Definition: Selects every k-th individual from a list (e.g., every 50th student in a register).
• Steps:
  1. Determine sampling interval: $k=\frac{\text{Population size}}{\text{Sample size}}$.
  2. Randomly select a starting point between 1 and k.
  3. Select every k-th individual thereafter.
• Example:
  • Pathao surveys every 200th ride out of 50,000 daily rides to assess driver satisfaction.
  • Worked Example: For a population of 5,000 students and a sample of 200, $k=25$. If the random start is 7, the sample includes students numbered: 7, 32, 57, 82, ...

C. Stratified Sampling

• Definition: Population divided into homogeneous subgroups (strata), then samples are taken from each stratum.
• When to use: When subgroups vary significantly (e.g., age, income, region).
• Example:
  • Nepal Rastra Bank (NRB) studies inflation by sampling:
    • Urban households (stratum 1: 30% sample)
    • Rural households (stratum 2: 50% sample)
    • Semi-urban (stratum 3: 20% sample)
  • Worked Example: A study on smartphone usage among PU students divides students into:

    Stratum	Size (N)	Sample Size (n)	Sampling Method
    1st Year	10,000	200	Simple Random
    2nd Year	12,000	240	Systematic (k=50)
    3rd Year	8,000	160	Stratified Random
    4th Year	5,000	100	Convenience (if limited)

D. Cluster Sampling

• Definition: Population divided into heterogeneous clusters, then entire clusters are randomly selected.
• When to use: When population is geographically dispersed (e.g., nationwide surveys).
• Example:
  • NTC (Nepal Telecom) surveys internet usage by randomly selecting 10 districts out of 77, then surveying all households in those districts.
  • Worked Example: A study on electric vehicle adoption in Nepal:
    1. Divide Nepal into 7 provinces.
    2. Randomly select 3 provinces (e.g., Province 3, 5, 7).
    3. Survey all vehicle owners in those provinces.

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2. Non-Probability Sampling

Selection is not random; used when probability methods are impractical. Less generalizable but faster/cheaper.

A. Convenience Sampling

• Definition: Samples are chosen based on accessibility (e.g., students in a class).
• Example:
  • A PU professor surveys 50 students in their class about online learning tools.
  • Risk: May not represent all PU students (e.g., only tech-savvy students respond).

B. Purposive Sampling

• Definition: Researcher intentionally selects individuals with specific traits.
• Example:
  • Studying cybersecurity threats in Nepal, a researcher targets IT professionals at Ncell or NTC.
  • Worked Example: A study on elderly health in Kathmandu targets only residents of senior citizen homes.

C. Snowball Sampling

• Definition: Initial samples refer others with similar traits (used for hard-to-reach populations).
• Example:
  • Studying undocumented migrant workers in Nepal: Start with 5 workers, who refer 10 more, and so on.
  • Risk: Sample may be homogeneous (e.g., only friends of initial respondents).

D. Quota Sampling

• Definition: Population divided into strata, then non-randomly fill quotas per stratum.
• Example:
  • A market research firm for Daraz sets quotas:
    • 40% urban, 30% semi-urban, 30% rural.
    • Interviewers stop once quotas are met (no random selection within strata).

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Sampling Errors & Biases

1. Sampling Errors

Occur when the sample does not represent the population due to random variation.

• Types:
  • Random error: Natural variation (e.g., a sample of 500 may overrepresent young voters).
  • Systematic error: Flawed method (e.g., surveying only daytime shoppers at Daraz).

2. Non-Sampling Errors

Due to data collection issues (not sample selection).

• Examples:
  • Response bias: People lie or avoid sensitive questions (e.g., income in surveys).
  • Non-response bias: Only certain groups respond (e.g., wealthy users of eSewa vs. poor).
  • Measurement error: Poorly worded questions (e.g., "Do you use WhatsApp daily?" may exclude light users).

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How to Choose the Right Sampling Method?

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In the Real World

1. eSewa & Khalti (Digital Payments)

   • Method: Stratified sampling by income groups.
   • How: eSewa surveys users segmented into:
     • Low-income (<Rs. 20,000/month)
     • Middle-income (Rs. 20,000–100,000)
     • High-income (>Rs. 100,000)
   • Why: Ensures feedback from all user segments, not just frequent high-value users.

2. Pathao (Ride-Hailing App)

   • Method: Systematic sampling of ride data.
   • How: Pathao logs every 500th ride in Kathmandu to analyze peak hours and driver earnings.
   • Real Example:
     • If Pathao has 200,000 rides/day, it samples 400 rides (every 500th ride) to estimate average fare (Rs. 120 vs. actual Rs. 118).

3. Nepal Stock Exchange (NEPSE)

   • Method: Cluster sampling of listed companies.
   • How: NEPSE divides companies into sectors (banking, hydropower, FMCG) and randomly selects 20% of companies in each sector for regulatory audits.
   • Why: Ensures all sectors are represented without surveying all 250+ listed companies.

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Worked Example: Traffic Congestion Study in Kathmandu

Problem: Estimate average daily traffic delay in Kathmandu’s Thapathali–Kageshwori route. Population: All vehicles (cars, buses, motorcycles) on the route. Sample Size: 500 vehicles (due to budget constraints). Method: Stratified Systematic Sampling

Steps:

1. Divide into strata (vehicle types):
   • Cars (40% of traffic)
   • Buses (20%)
   • Motorcycles (30%)
   • Others (10%)
2. Calculate sample per stratum:
   • Cars: $500\times 0.4=200$
   • Buses: $500\times 0.2=100$
   • Motorcycles: $500\times 0.3=150$
   • Others: $500\times 0.1=50$
3. Systematic selection:
   • For cars: List all cars passing a checkpoint, pick every 50th car (if 10,000 cars pass daily, sample 200).
   • Repeat for other strata.
4. Measure delay for each sampled vehicle using GPS timestamps.

Result: Average delay = 18 minutes (vs. census estimate of 17.5 minutes).

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Advantages & Disadvantages of Sampling Methods

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Sampling Size Determination

The sample size (n) depends on:

1. Population size (N): Larger populations need larger samples.
2. Confidence level: Higher confidence (e.g., 95%) requires larger n.
3. Margin of error (e): Smaller error needs larger n.
4. Population variability (σ): More variation → larger n.

Formula:

For large populations (N > 10,000): $$n=\frac{Z^2\times {\sigma }^2}{e^2}$$

• $Z$: Z-score (1.96 for 95% confidence)
• $\sigma$: Standard deviation (use pilot data or 0.5 if unknown)
• $e$: Margin of error (e.g., 5% = 0.05)

Example:

• Study: PU student satisfaction with online exams.
• Population (N): 50,000 students.
• Confidence level: 95% ($Z=1.96$)
• Margin of error (e): 5% (0.05)
• Variability (σ): Assume 0.5 (moderate variation).

$$n=\frac{(1.96{)}^2\times (0.5{)}^2}{(0.05{)}^2}=\frac{3.8416\times 0.25}{0.0025}=384.16\approx 385$$

Conclusion: Survey 385 students for reliable results.

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Exam Tip

What Examiners Look For

1. Definitions: Clearly distinguish between probability vs. non-probability sampling.
2. Applications: Link methods to real-world scenarios (e.g., "How would NTC use cluster sampling?").
3. Worked Examples: Show step-by-step calculations for sample size or stratified sampling.
4. Bias Awareness: Identify sampling errors in flawed studies (e.g., "Why is convenience sampling risky?").
5. Visuals: Draw comparison tables or flowcharts to explain methods.

Common Pitfalls

• Confusing stratified vs. cluster sampling:
  • Stratified: Subgroups are homogeneous (e.g., age groups).
  • Cluster: Subgroups are heterogeneous (e.g., districts).
• Ignoring non-response bias: Always mention how to minimize it (e.g., follow-ups, incentives).
• Overlooking sample size: Examiners may ask you to calculate n given parameters.

Model Answer Structure

For a 5-mark question on sampling methods:

1. Define the method (1 mark).
2. Explain how it works (1 mark).
3. Give a real-world example (e.g., "Nepal Rastra Bank uses stratified sampling...") (1 mark).
4. Discuss advantages/disadvantages (1 mark).
5. Compare with another method (1 mark).

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