## Saturday, June 23, 2018

### Fake Data

This year my math department focused on student engagement in our professional development meetings. My AP Statistics colleagues (Doug Shuman and Alexandra Brennan) and I developed this activity for the 𝜒² unit as a result and the three of us implemented it in our classrooms. Here's a little information about this two-part activity. Even though our students faked their data, it was a real success!

As I said, the intent of this activity was to provide a formative assessment for the chi-square unit (which we teach fairly early with statistical inference). In past years, I have felt this unit was lacking a bit of cohesion. We wanted something that would be truly collaborative but allows flexibility, encourages creativity, and fosters success for a broad range of abilities. In addition, we wanted the activity to generate student work that they could in turn peer review.

In groups, students must create a scenario with a statistical question, generate tabular data, and conduct a 𝜒² test that meets as many of the following conditions as possible.
1. The data are discrete.
2. The topic is related to [your topic goes here].
3. There is only one categorical variable.
4. The data are analyzed using a χ² test of independence/association.
5. The total sample size is between 150 and 250.
6. The result is not statistically significant at α = 0.05.
7. One χ² component is between 4 and 5 times the size of all the others.
8. One expected value is between 10 and 11.
9. The degrees of freedom are between 3 and 5.
10. The χ² statistic is between 12 and 15.
In regards to the second condition above, we used the topic of our school community this first time we did it, but the topic could be anything... current events, social justice, sports, etc.

 My students faking their data like champs
Spoiler alert: You might notice that it is not possible to meet all of the above conditions. Shh, don't tell the students. That's part of the fun of this activity.

Groups submit their work along with an activity sheet that indicates which of the above conditions they believe they have satisfied. Another group will peer assess their scenario, the met conditions, and the statistical test using a rubric and give constructive feedback. Finally, I assess the groups both for their work on the task as well as peer-reviewers.

There were lots of reasons I felt this group activity was successful beyond just being fun. The groups I chose were fairly homogenous in terms of content ability in this unit which allowed student conversations to focus on their specific needs. I loved watching students discover how the 𝜒² statistic and related values could change based on data changes. I also loved having students peer assess with this activity so they had to apply the same skills they had just used to new scenario. Lastly, because each group's product was unique there was no way to cheat (or, maybe, because I let them cheat) and I was more accurately able to assess their strengths and weaknesses with the content. Overall, I think my students felt much more confident with the 𝜒² distribution and tests once they did this activity.

Here are the two activity sheets, one used by the groups as "fakers" and one they use when they peer review. Rubrics for both parts of the assessment are included.

Fake Data (two-part 𝜒² activity with grading rubrics)

Alexandra and I presented this activity at the 2018 AP Statistics reading. You can find the presentation slides for all the Best Practices presentations, including ours, on Bob Lochel's blog: AP Statistics Reading.

I hope your students enjoy faking their data as much as mine did.