Explain the difference between a stratified sample and a cluster sample. (Select all that apply.)
In a cluster sample, every sample of size n has an equal chance of being included.
In a stratified sample, every sample of size n has an equal chance of being included.
In a stratified sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
In a cluster sample, random samples from each strata are included.
In a cluster sample, the only samples possible are those including every kth item from the random starting position.
In a stratified sample, random samples from each strata are included.
In a stratified sample, the only samples possible are those including every kth item from the random starting position.
The Correct Answer and Explanation is:
The correct answers are:
✅ In a stratified sample, random samples from each strata are included.
✅ In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
Explanation:
Understanding the difference between stratified sampling and cluster sampling is essential in statistics, particularly when selecting representative subsets from a larger population.
Stratified Sampling:
In a stratified sample, the population is divided into distinct subgroups known as strata. These strata are formed based on shared characteristics such as age, gender, income level, or education. Once the population is divided into strata, a random sample is taken from each stratum. The goal is to ensure that each subgroup is properly represented in the final sample.
- For example, if you’re conducting a survey on college students’ study habits, you might stratify by academic year (freshman, sophomore, junior, senior), and then randomly sample students from each year.
- This technique increases the precision of the results and reduces sampling bias, especially when population subgroups differ significantly.
✅ This is why the statement “In a stratified sample, random samples from each strata are included” is correct.
Cluster Sampling:
In a cluster sample, the population is divided into groups or clusters, often based on geographical location or naturally occurring groups (e.g., classrooms, zip codes). Then, entire clusters are randomly selected, and every member within those selected clusters is included in the sample.
- For example, if a school district wants to assess student performance, it might randomly select 10 schools (clusters) and test every student in those schools.
- This method is more cost-effective and practical when dealing with large, spread-out populations.
✅ That’s why the statement “In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included” is correct.
Incorrect Statements:
- Random sampling of individuals from each strata is not cluster sampling.
- Selecting every kth item refers to systematic sampling, not stratified or cluster.
- Not every sample of size n has an equal chance in either method.
Thus, stratified and cluster sampling differ mainly in how subgroups are formed and sampled: stratified sampling ensures representation across all strata, while cluster sampling involves whole groups selected randomly for analysis.
