For many years, I have been left wondering whether or not I should spend time teaching students about the systematic random sample. It was not officially included in the old Topic Outline, but there was that one multiple choice question where it was used as a distractor (2002 MC #15). Well now it's official. The College Board released the new Course and Exam Description (CED) and guess what is included?
There are two important ideas for students to understand when it comes to systematic random samples:
There must be a randomly selected starting point.
The remainder of the sample must be selected using a fixed, periodic interval.
So what is the best way to teach this to students? Give them the definition and then have them try a few practice problems? Of course not! Here is a great opportunity to have students Experience First, Formalize Later (EFFL).
We decided to create a Day 2 of the Justin Timberlake activity (and do a refresh of the original). In these activities, students will be trying to predict the average enjoyment level for fans at the Justin Timberlake concert.
Justin Timberlake Activity - Day 1 (Updated!)
Students compare estimates made using a simple random sample, a stratified random sample using rows, and a stratified random sample using columns (yes this is the same as the River Problem or the Sunflower Problem). In the end, students discover that a stratified sample using rows as strata is the best sampling method, because it guarantees some super fans like Luke and Lindsey (front row) and some wannabes (back row) and some in between. Additionally, the distribution of the estimates when stratifying by row shows much lower variability than the other two sampling methods.
Justin Timberlake Activity - Day 2
For Day 2, students compare estimates made using a simple random sample, a cluster sample, and a systematic random sample. Students discover that the cluster and systematic random sampling methods both produce estimates with lower variability than estimates made using an SRS. You can now use the Justin Timberlake context to help students understand the difference between stratified and cluster samples.