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Sampling Methods
How to Choose Your Sample
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Sampling methods are the techniques statisticians use to choose a subset of a population for study. Because measuring every individual is often too expensive, slow, or impossible, a well chosen sample lets us estimate population characteristics efficiently. The quality of the sample strongly affects how trustworthy the conclusions will be. Good sampling reduces bias and helps results represent the full population.
Different sampling methods are designed for different goals and real world constraints. Simple random sampling gives every member an equal chance, while stratified sampling ensures important subgroups are represented. Cluster and systematic sampling can save time and cost when populations are large or spread out. Choosing the right method means balancing practicality, randomness, and the need for accurate inference.
Key Facts
- Population = entire group of interest; sample = subset actually observed.
- A parameter describes a population, while a statistic describes a sample.
- Simple random sample: each possible sample of size n has an equal chance of being chosen.
- Systematic sampling uses a fixed interval k, often k = N/n, after a random starting point.
- Sampling error tends to decrease as sample size increases, roughly with 1/sqrt(n).
- Bias is a systematic error caused by poor sampling design, undercoverage, or nonresponse.
Vocabulary
- Population
- The full set of individuals, objects, or measurements that a study wants to describe.
- Sample
- A smaller group taken from the population and actually measured in the study.
- Simple random sampling
- A method where every member of the population has an equal chance of being selected.
- Stratified sampling
- A method that divides the population into groups and randomly samples from each group.
- Sampling bias
- A systematic problem in the sampling process that makes the sample unrepresentative of the population.
Common Mistakes to Avoid
- Using a convenience sample and calling it random, because choosing people who are easiest to reach does not give every population member an equal chance of selection.
- Ignoring important subgroups in the population, because if one category is underrepresented the sample statistic may not reflect the true population parameter.
- Using systematic sampling without a random start, because starting at a fixed predictable point can create hidden patterns and bias the sample.
- Assuming a larger sample always fixes bad design, because increasing n reduces random error but does not remove bias from a flawed sampling method.
Practice Questions
- 1 A school has 1200 students and wants a systematic sample of 100 students. What sampling interval k should be used?
- 2 A population has 300 people in Group A and 700 people in Group B. If a stratified sample of 100 people is taken proportionally, how many should be sampled from each group?
- 3 A researcher wants to study average commute time in a city and chooses one neighborhood at random, then surveys every household there. What sampling method is this, and what is one advantage and one possible drawback?