A random sample uses chance to choose who is in the sample, so the sample tends to represent the population. Here is a school of 100 students in 10 homerooms. Each student's grade is shown by color, and older students tend to sleep less. Estimate the school's mean hours of sleep with four sampling methods and compare how well each one works.
Pick a method, take one sample to see who gets chosen, then take hundreds of samples to see how much the estimates vary.
The SD of the sample means measures how much estimates vary from sample to sample. Smaller is more precise.
Every group of n individuals has the same chance to be the sample. Label every individual, then use a random number generator (or names from a hat) to pick n different labels.
Split the population into strata of similar individuals (like grade level), then take an SRS within each stratum. When the strata differ on the variable, this gives more precise estimates than an SRS of the same size.
Split the population into clusters, usually by location (like homerooms), randomly choose some clusters, and include everyone in them. It is cheaper and easier. It works best when each cluster is a mini-version of the population.
From an ordered list, pick a random starting point from the first k, then take every kth individual after it. It is easy, but it can go wrong if the list has a repeating pattern.
Strata are alike within and different between; you sample some from every stratum. Clusters are mixed within and similar between; you sample all from some clusters.
A census measures every individual. It gives the parameter exactly but is often too slow, costly, or impossible for a large population.
A full description names the labels, the random device, and how repeats are handled.
| Method | Sample procedure for 20 of the 100 students | Best when |
|---|---|---|
| SRS | Label students 1–100. Use a random number generator to pick integers from 1 to 100, ignoring repeats, until 20 different students are chosen. | You have a full list and no useful groups |
| Stratified | Separate students by grade (25 per grade). Within each grade, label 1–25 and randomly choose 5 different students. Combine for 20. | Groups differ on the variable (sleep differs by grade) |
| Cluster | Label homerooms 1–10. Randomly choose 2 different homerooms and survey every student in them. | Groups are mixed and easy to reach together |
| Systematic | List students 1–100. Randomly choose a start from 1 to 5, then take every 5th student after it. | The list has no pattern related to the variable |
| Census | Survey all 100 students. | The population is small and reachable |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 1.11. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.