Why Sampling Matters
We Can't Measure Everyone
We rarely have resources to measure entire populations. Sampling lets us learn about millions by studying thousands - but only if we sample correctly. Bad sampling = bad conclusions, no matter how sophisticated our analysis.
Sampling Bias
Actual: Roosevelt wins with 62%
Error: 19 percentage points!
Sampling bias occurs when some population members are more likely to be selected than others. The Literary Digest polled 2.4 million people but still got it wrong because their sample wasn't representative.
Population vs Sample
The population is everyone/everything you want to study. The sample is who/what you actually measure. Good sampling ensures the sample reflects the population.
Simple Random Sampling
Equal Probability Selection
Simple random sampling (SRS) gives every member of the population an equal chance of being selected. It's the gold standard that other methods are compared against.
Implementation
SRS requires a complete list of the population (sampling frame). Use a random number generator - not human 'random' selection which is biased toward certain patterns.
When to Use SRS
+ Unbiased by design
+ Easy to calculate SE
+ Foundation for other methods
- May miss small subgroups
- Can be expensive if spread out
- Not always most efficient
SRS is conceptually simple and mathematically elegant, but requires a complete sampling frame and may not efficiently capture important subgroups.
Stratified Sampling
Divide Then Sample
Stratified sampling divides the population into non-overlapping subgroups (strata) based on a characteristic, then takes a simple random sample from each stratum. This guarantees representation of all groups.
University Survey
| Year | Population | % | Sample |
|---|---|---|---|
| Freshmen | 5,000 | 25% | 100 |
| Sophomores | 4,000 | 20% | 80 |
| Juniors | 5,500 | 27.5% | 110 |
| Seniors | 5,500 | 27.5% | 110 |
| Total | 20,000 | 100% | 400 |
Proportionate stratified sampling: sample size in each stratum matches its population proportion. This guarantees freshman voice isn't drowned out even if they're less likely to respond.
Stratified vs SRS
+ Small subgroups need guaranteed representation
+ You want to compare subgroups
+ You know stratification variable for everyone
Stratified sampling reduces variance when the stratifying variable is related to the outcome. If men and women have very different opinions, stratifying by gender ensures both are heard and reduces overall sampling error.
Cluster Sampling
Sample Groups, Not Individuals
Cluster sampling randomly selects groups (clusters) rather than individuals. You then measure everyone in the selected clusters. It's practical when you can't list all individuals but can list groups.
Key Difference
| Stratified | Cluster | |
|---|---|---|
| Groups | Homogeneous within | Heterogeneous within |
| Selection | Sample FROM all groups | Sample SOME groups entirely |
| Goal | Precision (reduce variance) | Convenience (reduce cost) |
| Example | Sample from each grade | Sample some schools entirely |
Stratified: divide by characteristic, sample from EVERY group. Cluster: divide by convenience, sample SOME groups entirely. Ideal clusters are mini-populations (heterogeneous within).
Practical Applications
+ Population is geographically spread
+ Travel costs are high
+ Natural groupings exist (schools, hospitals, neighborhoods)
Cluster sampling is common in large-scale surveys where listing every individual is impossible. National health surveys often select counties, then households, then individuals (multi-stage cluster sampling).
Systematic Sampling
Every kth Unit
Systematic sampling selects every kth element after a random start. If you want n=100 from N=1000, k=10. Randomly pick a number 1-10 (say, 7), then select 7, 17, 27, 37, etc.
Periodicity Problem
If the list has periodicity matching your interval, systematic sampling is biased. Always check for patterns in how the list is ordered.
Choosing a Method
Method Comparison
| Method | Best For | Requires |
|---|---|---|
| Simple Random | Homogeneous populations | Complete list |
| Stratified | Comparing subgroups | Strata known for all |
| Cluster | Geographic spread | Natural groupings |
| Systematic | Ordered lists | No periodic patterns |
No single method is best for all situations. Consider: Do you have a complete list? Are there important subgroups? Is the population spread out? Are there natural clusters?
How to Choose
No → Consider Cluster Sampling
Yes → Consider Stratified Sampling
Yes → Systematic is simple and effective
Use Simple Random Sampling
Start with your constraints. What information do you have? What resources? What's the population structure? The 'best' method depends on your specific situation.
Real-World Examples
Apply your knowledge to practical scenarios
National Election Polling
A polling organization wants to estimate voter preferences for the upcoming presidential election. They need to survey 1,500 likely voters across the United States.
Key Insights
- Real-world sampling often combines multiple methods
- Weighting corrects for known biases in who responds
- Even sophisticated sampling can miss 'shy voters' or enthusiasm differences
Clinical Trial Recruitment
A hospital system wants to test a new diabetes treatment. They need 200 patients with Type 2 diabetes across their 15 hospitals.
Key Insights
- Budget constraints often dictate sampling method
- Volunteer bias is a major threat to clinical trial validity
- Stratification variables should relate to treatment response
Sampling Methods Quiz
Test your understanding • Passing score: 70%