## Intro Stats – Sampling Techniques Activity

During the first week of class I go over different sampling techniques – Convenience, Random, Systematic, Cluster, & Stratified. Even though most of our sampling during the semester will be convenience sampling, I think it’s important for students to understand the other types that are available. It gives me a chance to talk about what I feel is one of the major themes of statistics, the tradeoff between easy/less reliable and difficult/more reliable. Basically we are looking for a practical approach that yields quality results.

I use Mike Sullivan’s Intro Stats text, and yesterday I used one of his activities to show the different sampling techniques in action. I asked my students two questions. How much did you spend this semester on books and supplies? Do you own an iPhone? We had two variables, one quantitative and one qualitative. I told the students that through sampling techniques we would try to estimate the mean cost for students in this class as well as the percentage of students in this class that own an iPhone.

Random Sampling

I began by numbering the students from 1 through 44. I then used Microsoft Excel to select random numbers until we had a sample of 10 students, wrote the data for those students on the board, and we calculated the sample mean and proportion.

Systematic Sampling

Students struggle with systematic sampling in the homework because they are given an abstract situation, asked to calculate a step value, and give the number of the 47th individual selected. It is more effective to show systematic sampling by actually taking a sample. We had 44 students and I wanted a sample size of 10, so my students told me that a step size of 4 would work. (44/10) We randomly selected a starting value using Excel, and then sampled every 4 students from there. Students started to understand that this was pretty similar to the way we used to count off in gym class to pick teams. Once I had the data on the board, we calculated the sample mean and proportion.

Cluster Sampling

I have 6 rows of tables in my classroom, so we made each row a cluster. We selected a row at random (Excel) and sampled each individual in that row. In my experience students do pretty well with the idea that cluster sampling can be done by dividing the population geographically by location and sampling each individual in the selected clusters. Again, once the data was on the board we calculated the sample mean and proportion.

Stratified Sampling

I began by asking my students which strata we could use to categorize students, and they came up with gender pretty quickly. It is pretty easy to use gender as opposed to year in school, religious affiliation, … because it is information we already know. I took a sample of 6 female students and 3 male students, as my class roughly has a 2:1 ratio of females to males. We renumbered students within each group and used Excel to randomly select students. Once the data was on the board we calculated the sample mean and proportion.

Wrap Up

Once we were done sampling I collected all of the information for the entire class and calculated the population mean (~ \$315) and proportion (~38%). We then compared our sample statistics to the population parameters, and the students really got to see that individual samples vary. This is a really BIG idea as we head towards inferential statistics.

I feel that my students got a much better handle on sampling techniques and on sampling in general. Next week I will show them how to use StatCrunch to draw a random sample.

Do you have any sampling activities that you use and really like? Or any other activities that you’d like to share? Leave a comment or drop me a line – maybe we can arrange a guest blog!

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

• 1. shannonorr  |  September 18, 2014 at 12:41 pm

This is a great post. I teach graduate statistics/research methods and was looking for some hands on activities to teach sampling. Can’t wait to try these on Monday!

• 2. Calvin Climie  |  January 12, 2016 at 2:45 pm

Awesome!

• 3. Rayna Friendly  |  February 13, 2017 at 12:38 pm

I also look forward to trying these, thanks!