Sampling Methods
- Distinguish a population from a sample and a parameter from a statistic
- Describe simple random, stratified, cluster, and systematic sampling
- Explain why random sampling supports generalization to a population
Population, sample, parameter, statistic
A population is the entire group we want to learn about; a sample is the subset we actually collect data from. A parameter is a fixed number describing the population (like the true proportion of all voters who approve), while a statistic is computed from the sample and estimates it. We use statistics to infer parameters because measuring the whole population is usually impossible.
Four random sampling designs
In a simple random sample (SRS) every group of n individuals is equally likely to be chosen. In a stratified sample we split the population into similar groups (strata) and take an SRS within each — good when strata differ (e.g., sampling each grade level). In a cluster sample we split into groups (clusters) and randomly pick whole clusters to measure everyone in them — convenient when clusters are scattered (e.g., choosing whole classrooms). A systematic sample picks every kth individual from a random start.
Why randomize the selection
Random selection is what lets us generalize from the sample to the population. It avoids the bias a human chooser would introduce and makes the sample representative on average. Without random selection you may have a convenience or voluntary response sample, which cannot be trusted to reflect the population no matter how large it is.
Distinguish stratified from cluster by a simple test: strata are made homogeneous on purpose and you sample within each one; clusters should each resemble the whole population and you sample some entire clusters. Stratifying by grade, then sampling from every grade, is stratified; picking a few whole homerooms is cluster.
A principal wants student opinions and worries that freshmen, sophomores, juniors, and seniors feel differently. She randomly selects 25 students from each grade. Name and justify the sampling method.
- 1.Identify the groups: the four grade levels, formed because they are expected to differ in opinion.
- 2.Note that a random sample is taken within every one of these groups (25 from each grade).
- 3.Sampling within groups that are formed to be internally similar is the definition of stratified sampling.
A quality inspector selects every 50th item coming off an assembly line, starting from a randomly chosen one of the first 50. This is an example of:
The true proportion in the population is a parameter; the proportion you calculate from your sample is a statistic. Keep the labels straight: parameters are fixed and usually unknown, statistics vary from sample to sample and are what you actually compute.
A news website posts an online poll and reports results from the 8,000 readers who chose to answer. Why might this large sample still be untrustworthy?
Answer the 2 checkpoints as you read.
Sign in to save your progress