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4 Tutorials that teach Two-Way Tables/Contingency Tables
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Two-Way Tables/Contingency Tables
Common Core: 8.SP.4 S.CP.4 S.ID.5

Two-Way Tables/Contingency Tables

Author: Ryan Backman
Description:

Calculate the probability of an event from a contingency table.

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Tutorial

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Hi. This tutorial covers two-way tables, which are also known as contingency tables. Let's just start with an example here. So I'm in charge of picking up lunch on Friday at work. This week, I'd like to order from the local burrito shop. To make the order gathering easier, I set up this chart

OK. So basically, what I have here are two variables, burrito type and drink type. Each of these would be considered qualitative variables or categorical variables. And each variable has three categories, so burrito type has chicken, steak, vegetarian, has the three categories, drink type has cola, diet cola, and water.

So I set it up this way so that way each person only needs to make one mark, and that will tell me which type of both burrito and drink they would like. So if somebody put a tally mark down there, I would know to get them a burrito, a steak burrito and a diet coke to drink, or a diet cola to drink. OK, so that would tell me that I would need two steak burritos and two diet colas. So what that table is called is a two-way table, also known as a contingency table, and it's a way to organize qualitative data with two variables.

OK, so let's actually take a look now at the orders I collected. OK, so if we go through here, basically what this tells me now is that if there's a 3 here, I know that three people wanted a chicken burrito and a regular cola. OK, the one here means that one person wanted a vegetarian burrito and a water, OK. Now what's helpful on this is you can calculate what are called the marginal totals.

So what a marginal total is is really just either a row total or a column total, OK. So we can see that if we add up this row, we end up with getting 6, 3 plus 2 plus 1 means 6, so that means that when I place the order, I'll need to get six colas. The diet colas, that will end up being 10, OK. Water will be 6. So again, these are marginal totals, which tell me how many of the different types of colas I would need here.

I could also do the marginal totals for the burritos. So 3, 3, and 2 is 8, 2, 2, and 3 is 7, 1, 5, 1, is 7, OK. So again, these are called marginal totals, and they give me-- so this 8 would tell me how many chicken burritos I'd need, the 7 would mean how many steak burritos I would need. So eventually these two-way tables are going to be really helpful to the study of probability, because these marginal totals compared to kind of the totals broken down into the two categories are going to be pretty important.

Just as a quick example of that, what I can do is if I look at the 3 here, and the 6 here. So what that means is that 3 out of 6 or 50% of the Cola drinkers ordered a chicken burrito, OK. So that's the sort of information that you'll be able to do with these two-way tables as you can continue this study of probability. So that has been your tutorial on the two-way table, also known as the contingency table. Thanks for watching.

Terms to Know
Two-Way Table/Contingency Table

A way of presenting data such that we can see the relationships between two categorical variables.