Cluster sampling and stratified sampling are two ways to collect data when studying an entire population is too expensive or slow. Both methods divide the population into groups, but they use those groups in very different ways. Understanding the difference matters because the sampling method affects cost, accuracy, and how well the sample represents the population.
A good design helps researchers avoid bias and make stronger conclusions from limited data.
In cluster sampling, the population is divided into natural groups called clusters, such as classrooms, city blocks, or hospitals, and a researcher randomly selects some entire clusters to study. In stratified sampling, the population is divided into meaningful subgroups called strata, such as grade level, age group, or income level, and a researcher samples from every stratum. Cluster sampling is often efficient when people are already grouped geographically or organizationally.
Stratified sampling is often more precise when important differences between subgroups must be represented.
Key Facts
- Cluster sampling: randomly select whole groups, then study all members or a sample within those selected groups.
- Stratified sampling: divide the population into strata, then randomly sample from each stratum.
- Cluster sampling is usually used to reduce travel time, cost, or data collection effort.
- Stratified sampling is usually used to improve representation of important subgroups.
- Proportional stratified sample size: n_h = (N_h / N) n, where N_h is stratum size, N is population size, and n is total sample size.
- Sampling error generally decreases when strata are internally similar and increases when selected clusters differ greatly from one another.
Vocabulary
- Population
- The entire group of individuals or items that a researcher wants to study.
- Sample
- A smaller group selected from the population to collect data and make conclusions.
- Cluster
- A natural group within a population, often based on location or organization, that may contain a mix of different types of individuals.
- Stratum
- A subgroup formed by a shared characteristic that is important to the study, such as age, grade, or income level.
- Sampling bias
- A systematic error that occurs when some members of the population are more likely to be selected than others in a way that affects results.
Common Mistakes to Avoid
- Calling any grouped sample a cluster sample. This is wrong because cluster sampling selects entire natural groups, while stratified sampling samples from every important subgroup.
- Using stratified sampling but forgetting to sample from one stratum. This is wrong because the main purpose of stratification is to ensure all key subgroups are represented.
- Choosing clusters that are convenient instead of randomly selected. This is wrong because convenience selection can introduce bias and make the sample unrepresentative.
- Assuming cluster sampling is always more accurate than stratified sampling. This is wrong because cluster sampling can have higher sampling error if clusters are very different from each other.
Practice Questions
- 1 A school district has 20 schools with about 500 students each. A researcher randomly selects 4 schools and surveys every student in those schools. What sampling method is being used, and about how many students are surveyed?
- 2 A population has 600 freshmen, 900 sophomores, and 500 juniors. A researcher wants a proportional stratified sample of 100 students. How many students should be selected from each grade level?
- 3 A city health researcher wants to estimate average household water use. Explain whether cluster sampling or stratified sampling would be better if neighborhoods vary greatly by income and water use patterns, and justify your choice.