Alliance ClassFebruary 7, 2012

Discuss Poster Project

Analyzing Categorical Data

Constructing and using Two-Way tables

We will be able to do the following after completing this investigation:

Organize data collected into a two-way table

Analyze data in a two-way table

Construct and analyze a segmented bar graph

8.SP.4 Understand that patterns of association also can be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Categorical variables take a value that is one of several possible categories. As naturally measured, categorical variables have no numerical meaning. Examples: Hair color, gender, field of study, college attended, political affiliation, status of disease infection.

Statistical Question:How do those sitting in the front and back of

the room compare in their ability to roll their tongue?

Collect Data On post-it note indicate front or back of room and whether or not can roll your tongue.

Possibilities FrequencyFront – YesFront – NoBack – YesBack – No

Total

Front Back Total

Roll Yes a b

Roll No c d

Total

• How many teachers in this study?• How many teachers could roll their tongue• How many teachers sat in the back?• How many teachers sat in the front?

How many teachers who sat in the back could roll their tongue?

How many teachers who sat in the front could roll their tongue?

How many teachers who could roll their tongue sat in the front?

What percent of the teachers who sat in the front could roll their tongue?

What percent of teachers who sat in the back could roll their tongue?

What percent of teachers who could roll their tongue sat in the front?

Decide what variable will be represented on the horizontal axis.

Ex: Where a person sat

Calculate percents using the variable on the x axis as the denominator of the fraction.

What percent of those sitting in the front could roll their tongue?

What percent of those sitting in the back could roll their tongue?

How different are the percents?

Do the two stacked bars look very different?

If there is a distinct difference then we say there is an association between the two variables.

That is; if I know one variable does it help me predict the other variable – if yes then there is an association.

Recently my dog Fudge attended an obedience class. There were 50 dogs in the class. 30 of the dogs were classified as “large” and 20 were classified as “small”. At the end of the class the owners of 15 dogs received certificates indicating that their dogs had passed the class.

Questions:1.How many large dogs passed?2.How many small dogs passed?

Passed the Course

Did not pass Total

Large Dogs

Small Dogs

Total

Passed the Course

Did not pass Total

Large Dogs 30

Small Dogs 20

Total 15 35 50

Questions:What is the proportion of large dogs?What is the proportion of small dogs?What is the proportion of dogs that passed the course?

Passed the Course

Did not pass Total

Large Dogs 30

Small Dogs 20

Total 15 35 50

Questions:What is the largest number of large dogs that could have passed the course?What is the largest number of small dogs that could have passed the course?

Complete a two-way table for each scenario.

Passed the Course

Did not pass Total

Large Dogs 15 15 30

Small Dogs 0 20 20

Total 15 35 50

All large dogs passed

Questions:What proportion of large dogs passed?What proportion of small dogs passed?

If you knew the size of the dog would that help in deciding whether or not theDog passed the class in this scenario?

Is there an association between size of the dog and whether or not passed the class?

Construct a stacked bar graph with size of dog on the x axis.

All the small dogs failed

Passed the Course

Did not pass Total

Large Dogs 0 30 30

Small Dogs 15 5 20

Total 15 35 50

All small dogs passed

Questions:What proportion of large dogs passed?What proportion of small dogs passed?

If you knew the size of the dog would that help in deciding whether or not theDog passed the class in this scenario?

Is there an association between size of the dog and whether or not passed the class?

Stacked bar graph All the large dogs failed

Passed the Course

Did not pass Total

Large Dogs 9 21 30

Small Dogs 6 14 20

Total 15 35 50Questions:What is the proportion of dogs that passed the course?

What is the proportion of large dogs that passed?What is the proportion of small dogs that passed?

If you knew the size of the dog would that help in deciding whether or not theDog passed the class in this scenario?

Is there an association between size of the dog and whether or not passed the class?

Assume 9 large dogs passed

No association stacked bar graph

Students at a high school conducted a research study to investigate questions about asthma. One question was “do students who suffer from asthma come from a home with a smoker?”

The students received responses from 937 high school students. Of these students 182 suffered with asthma and 395 lived in a home with one or more smokers.

Complete a two-way table

Homes with Smokers

Without Smokers

Total

Asthmatic Students

182

Non-asthmatic 755

Total 395 542 937

Questions:What proportion of students at this high school have asthma?

What proportion of students live in a home with at least one smoker?

What proportion of asthmatic students are asthmatic live in a home witha least one smoker?

Homes with Smokers

Without Smokers

Total

Asthmatic Students

182

Non-asthmatic 755

Total 395 542 937

The study reported that 113 students lived in a home with at least one smoker.

Complete the table

Homes with Smokers

Without Smokers

Total

Asthmatic Students

113 69 182

Non-asthmatic 282 473 755

Total 395 542 937

Questions:What proportion of asthmatic students live in a home with a least one smoker?

Is there an association between being asthmatic and living in a homewith a smoker?

8.SP.4 Understand that patterns of association also can be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Student Statistical Questions

Extra handout on analyzing categorical data

Read “Progressions Measurement and Data K-5” (in binder)

Read article and answer reflection questions◦ Read Statistics in the Elementary Grades found at

ww.nctm.org back issue of Teaching Children Mathematics August 2008

Reflection a. Write a short summary of the articleb. Which of the 6th, 7th, 8th grade CCSS Statistics

Domain standards are evident in the activities discussed in this article.