IPS - Day 31

Today we explored sampling and bias. To start things off we reviewed a couple of the sampling plans that students created. This allowed for a discussion of how to introduce randomization into the designs and to discuss whether or not the sample would be representative.

The discussion brought up issues that included the topic or objective of the sample. For instance, students wondered whether or not sampling from attendees of a dance would generate a representative sample. If the topic of the survey were about the quality of the DJ this would be an acceptable sample space. However, if you are trying to determine the next dance's venue, this would not be a representative sample of students as you are missing those students who did not attend the dance because they did not like the current venue.

One student then said it sounded as if there were never a perfect sample. This is true. You can only hope to create as representative sample as you can with as little bias as you can. It won't be perfect but by following good sampling procedures and techniques it will get you closer to the population that you are interested in studying.

We then looked at an example of a biased sample compared to a simple random sample. To do this I followed the Random Rectangles investigation. There are many versions of this activity available. I used the one from NCTM's Navigating Through Data Analysis Grades 9-12.

Students could see clearly that their subjectively selected rectangles had a dispersed, almost uniform distribution. The simple random sample generated a much more compact, unimodal distribution that was roughly symmetric. The mean area for the subjective rectangles was approximately 2 square units larger than the simple random sample's mean.

Next, students compared a simple random sample of 5 rectangles to a simple random sample of 10 rectangles. In this case, the sample size of 10 generated a unimodal, roughly symmetric distribution that had approximately the same mean but was even more tightly compressed around the mean.

Students seemed to understand how to generate a simple random sample. They also readily recognized that the simple random sample was generating a more representative sample.

Next class we'll compare simple random samples to cluster and stratified samples.

Visit the class summary for a student's perspective and to view the lesson slides.