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Mathematical Sets Elements Intersections Unions Cardinality Types of Subsets (Infinite Finite Equal Empty)Categorical Propositions Subject Predicate Equivalent Infinite Sets What is a Two-Way Table

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What is a Two-Way Table

Do you believe in Martians? Do you watch football on television? A Two-Way Table or Contingency Table is a great way to show the results of all kinds of survey questions. In this lesson, we will learn how to read a two-way table.

What is a Two-Way Table

Two-Way Table

Do you believe in Martians? Here is a survey of 100 college students asking that very question: Do you believe in Martians?

This type of table is called a two-way or contingency table.

A two-way or contingency table is a statistical table that shows the observed number or frequency for two variables, the rows indicating one category and the columns indicating the other category. The row category in this example is gender - male or female. The column category is their choice, yes or no.

There is a lot of information we can learn from this small table. Let's look at a couple questions you could see on a test.

How many males were asked? Let's look across the male row. Ten said 'yes' and 32 said 'no.' That would be a total of 42 males.

How many college students believe in Martians? Look down the Yes column. Ten males and 38 females said 'yes.' That would be a total of 48 college students.

Example No 2

A recent survey of 100 college students asked if they prefer to drink tea, coffee, or an energy drink during finals week. Here is the table created from that survey.

Let's look at a couple questions you could see on a test.

How many college students drink tea given that they are a female? In this question, we're looking for tea drinkers that are female. Let's look at the female row and tea column. The answer is 18.

How many students drink tea or are male? In this question, we're looking for all tea drinkers united with all males. To figure out the answer, let's highlight the Tea column and Male row. We do have an overlap at Tea and Male, so be sure not to add that twice. So our answer is Total Tea drinkers 20 plus Total Males 56 minus the overlap of 2. 20 + 56 - 2 = 74. There are 74 students that are tea drinkers or male.

How many coffee or tea drinkers are not female? Let's look at each part. Let's highlight the coffee and tea columns. Now, let's highlight the male row. Remember, the question asks for drinkers that are not female, so they have to be male.

So our answer will unite the coffee and tea drinkers with the contingency that they are males. Males that drink tea are 2, males that drink coffee, 15. 2 + 15 = 17. There are 17 males that drink coffee or tea.

Lesson Summary

A Two-Way or contingency table is a statistical table that shows the observed number or frequency for two variables. The rows indicate one category and the columns indicate the other category.

Here are some tips for you when you are doing a two-way or a contingency table:

Highlight the column or row that is in the question. This will keep you focused on the question and not all of the extra stuff in the table. Also, beware of highlights that are overlapped. Don't count anything twice!
Read the question carefully. Tests try to trick students using words such as 'not' and 'or'. As in our example, if you are not female, you have to be male, and, drink tea or coffee.

We need to count all of the tea and coffee drinkers.