AP Statistics: Relations Between Categorical Data

I was rehashing some of my old files and planning a lesson to introduce two way tables to my students.  I’ve always had trouble getting them to buy into the meaning/purpose/importance of two way tables.  And looking back through my old lessons, I figured out why:  I was focused solely on the two way tables…not the relationship between two categorical variables.  I decided to change that this year.

4.3 Relations in Categorical Data_1

This was my students’ warm up when they walked into the room.  There was not an explanation given…just for them to take 60 seconds to fill this out.  Then I went into story mode:

4.3 Relations in Categorical Data_2

We discussed the beginnings of why boys “like” blue and girls “like” pink and why the idea switched from the original boys should like pink and girls should like blue.  It’s an interesting story and my students had good insights from their history classes.

So I told my students to look at the relationship between their gender and their favorite color.  There wasn’t any other direction given.  So they decided to collect their data:

4.3 Relations in Categorical Data_3

I asked them to discuss any trends that they saw.  There was a bunch of statements that didn’t say a whole lot.  “Some males like blue” or “One girl likes green.”  Nothing of consequence.  Finally, someone said that they had a better way to organize the data:

4.3 Relations in Categorical Data_4

Now we were getting somewhere…unfortunately, today was PSAT/Blood Drive/Some Chorus Thing day and I was missing a lot of students.  They weren’t seeing any useful trends.

So, we looked at data I knew had some trends:

4.3 Relations in Categorical Data_5

Students gathered some great insights into how society views education through their look at marginal and conditional distributions.  Some interesting discussion ensued.

Most importantly, the two way table served to enhance our look at relationships between categorical variables.  We actually talked about the nature of statistics (I don’t know if that’s a real term…if it isn’t, I’m coining it now).  I’m curious to see if this approach pays off with two way tables.


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