intermediate 18 minutes

Sampling Methods

Learn different sampling techniques: random, stratified, cluster, and systematic sampling for effective data collection.

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Why Sampling Matters

Key Terms

TermDefinition
PopulationThe entire group we want to study
SampleA subset of the population we actually collect data from
ParameterA number describing the population (μ, σ, p)
StatisticA number calculated from sample data (x̄, s, p̂)
Sampling frameList of all individuals in the population

Probability vs Non-Probability Sampling

Probability SamplingNon-Probability Sampling
Every member has known chance of selectionNo known selection probabilities
Results generalizable to populationCannot generalize statistically
More expensive, time-consumingCheaper, faster
Examples: SRS, stratified, clusterExamples: convenience, voluntary

Simple Random Sampling (SRS)

In a simple random sample, every member of the population has an equal chance of being selected, and every possible sample of size n is equally likely.

Simple Random Sample

Population: 1000 employees at a company

Method:

  1. Assign each employee a number (1-1000)
  2. Use random number generator to select 50 numbers
  3. Survey those 50 employees

Result: SRS of size 50

Advantages

  • Eliminates selection bias
  • Simple to understand
  • Easy to calculate sampling error

Disadvantages

  • Requires complete sampling frame
  • May miss small subgroups
  • Can be impractical for large populations

Stratified Sampling

Divide the population into strata (groups), then take a random sample from each stratum.

Stratified Sample

Population: University students Strata: Year (Freshman, Sophomore, Junior, Senior)

Method:

  1. Separate students by year
  2. Take SRS from each year
  3. Combine into final sample
YearPopulationSample (10%)
Freshman3000300
Sophomore2500250
Junior2200220
Senior2300230
Total100001000

When to Use Stratified Sampling

  • Subgroups are important to study
  • Subgroups differ from each other
  • Want to ensure representation of all groups
  • Subgroups vary greatly in size

Advantages

  • Ensures representation of all strata
  • Often more precise than SRS
  • Can analyze subgroups separately

Disadvantages

  • Requires knowledge of strata membership
  • More complex to implement
  • Need to identify relevant strata

Cluster Sampling

Divide the population into clusters (natural groups), randomly select some clusters, then sample everyone (or many) within selected clusters.

Cluster Sample

Population: All high school students in a state Clusters: Individual schools

Method:

  1. List all high schools in state (clusters)
  2. Randomly select 20 schools
  3. Survey all students in those 20 schools

Advantage: Don’t need list of all students—just schools!

Stratified vs Cluster

StratifiedCluster
Sample from ALL strataSample from SOME clusters
Strata are different from each otherClusters are similar to each other
Small sample from each stratumAll (or many) from selected clusters
Increases precisionDecreases cost

Advantages

  • Cost-effective for geographically spread populations
  • Don’t need complete sampling frame
  • Practical for field research

Disadvantages

  • Less precise than SRS or stratified
  • Clusters may not be representative
  • Larger sampling error

Systematic Sampling

Select every kth individual from the sampling frame after a random start.

Systematic Sampling

Sampling interval: k=Nnk = \frac{N}{n}

Where N = population size, n = desired sample size

Systematic Sample

Population: 5000 customers Desired sample: 100

Method:

  1. k = 5000/100 = 50
  2. Randomly select start between 1-50 (say, 23)
  3. Select customers: 23, 73, 123, 173, …

Every 50th customer starting from #23.

Advantages

  • Simple to implement
  • Ensures spread across population
  • No need for random numbers for each selection

Disadvantages

  • Can miss patterns if population has periodicity
  • Not truly random if starting point biased

Non-Probability Sampling Methods

Convenience Sampling

Select whoever is readily available.

Convenience Sample
  • Survey people at a mall
  • Poll students in your class
  • Use your social media followers

Problem: Those available may differ from those not available.

Voluntary Response Sampling

People choose to participate on their own.

Voluntary Response
  • Online reviews
  • Call-in polls
  • Surveys with opt-in response

Problem: Those with strong opinions are more likely to respond.

Snowball Sampling

Ask participants to recruit others.

Snowball Sample

Useful for: Hard-to-reach populations

  • People with rare diseases
  • Underground communities
  • Specialized professionals

Sampling Errors and Bias

Sampling Error

Random variation between sample statistic and population parameter. Always present; decreases with larger n.

Sampling Bias

Systematic tendency to favor certain outcomes. Does NOT decrease with larger samples!

TypeExamplePrevention
Selection biasSurveying only daytime shoppersRandom selection
Nonresponse biasOnly 30% respond to surveyFollow-up, incentives
Response biasLeading questionsCareful wording
UndercoverageMissing homeless in censusImprove sampling frame

Choosing a Sampling Method


Summary

In this lesson, you learned:

  • Simple Random Sample (SRS): Every individual has equal chance
  • Stratified sampling: Divide into groups, sample from each
  • Cluster sampling: Select groups, sample within them
  • Systematic sampling: Every kth individual from random start
  • Non-probability methods (convenience, voluntary) cannot support statistical inference
  • Sampling error is random; sampling bias is systematic
  • Different methods suit different research needs and constraints

Practice Problems

1. A researcher wants to study eating habits of college students. She surveys everyone in her 9 AM class. What type of sampling is this? What’s the problem?

2. To study employee satisfaction at a large company with 4 departments, you randomly select 25 employees from each department. What sampling method is this?

3. A polling organization randomly selects 15 cities, then surveys all adults in those cities. What type of sampling is this?

4. You want a sample of 200 from a list of 10,000 customers. Describe how to implement systematic sampling.

Click to see answers

1. Convenience sampling (whoever was available)

Problems:

  • Cannot generalize to all college students
  • 9 AM students may differ from others (morning people, certain majors)
  • Only one class from one school
  • Results cannot support statistical inference

2. Stratified sampling

Departments are the strata, and a random sample is taken from each stratum.

3. Cluster sampling

Cities are the clusters. Some clusters are randomly selected, and then everyone (or many) within those clusters is sampled.

4. Systematic sampling procedure:

  1. Calculate interval: k = 10,000/200 = 50
  2. Randomly select a starting number between 1-50 (e.g., 17)
  3. Select customers: 17, 67, 117, 167, 217, …
  4. Continue selecting every 50th customer until you have 200
  5. Final sample: customers #17, 67, 117, 167, …, 9967

Next Steps

Continue learning about statistical inference:

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