IPS - Day 40

Today was our first day back from break. I had graded the mid-term exams and realized as I went through responses that the class was still shaky on differences in sampling techniques and with different biases that occur during sampling.

I assigned another portfolio problem related to sampling and bias. The assignment consists of students providing a definition or explanation of each sampling technique we covered: simple random, systematic, stratified, cluster, and multi-stage. In addition, students needed to explain poor sampling design as evidenced by convenience sampling and voluntary response. Finally, they needed to discuss different types of bias that can arise through sampling, specifically response versus non-response bias.

Starting today, we will proceed through a series of investigations that involve survey sampling, observational studies, and experimental design. Students will begin to develop hypotheses, use simulations to determine what random samples look like under their hypotheses, generate a data collection plan, collect data, and compare their actual data to what they expect data could result purely on a random basis. As we proceed and build upon these ideas, students will develop an understanding of a modern approach to statistical analysis.

The first problem is an investigation titled, "What Do Students Drive?" This investigation comes from Activities and Projects for Introductory Statistics Courses, by Millard and Turner. I begin this investigation by asking students to estimate the percentage of American, Asian, and European made cars in the student parking lot. I then have students run simulations in order to look at the distribution of percentages that may occur under random sampling. Once the simulations are completed, students create histograms to view the distribution.

I was pleased that students had very little trouble creating their hypothesized values, determining how to simulate their values, and running their simulations. The creation of appropriate histograms was a bit more problematic. Here, students wanted to generate averages and simply plot the three average they calculated, in essence creating a bar graph.

I anticipated that creating appropriate histograms could pose a problem. Since several groups had not got started on their histograms, I asked students to finish running their trials, if needed, calculate the appropriate percentages from each trial, and attempt to create their three histograms from their data.

Tomorrow, I'll have students share their histograms with the class in order to discuss the appropriateness of the graphs. Next, I'll pass out schematics of the parking lot that include numbered parking spots and ask each group to come up with a sampling plan that will generate a random sample of approximately 30 cars.

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