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Interpreting Categorical Data

Interpreting Categorical Data. Alliance Class February 7, 2012. Agenda. Discuss Poster Project Analyzing Categorical Data Constructing and using Two-Way tables. WALT. We will be able to do the following after completing this investigation: Organize data collected into a two-way table

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Interpreting Categorical Data

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  1. Interpreting Categorical Data Alliance Class February 7, 2012

  2. Agenda • Discuss Poster Project • Analyzing Categorical Data • Constructing and using Two-Way tables

  3. WALT 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

  4. CCSS 8th Grade • 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.

  5. Qualitative or Categorical Variable • 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.

  6. Can you Roll your Tongue? 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.

  7. Build a Frequency Table Possibilities Frequency Front – Yes Front – No Back – Yes Back – No Total

  8. Construct a Two-Way Table

  9. Questions • 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?

  10. Questions • 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?

  11. Questions 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?

  12. Construct a stacked bar graph 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?

  13. Construct a Stacked Bar Graph

  14. Interpret the Results 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.

  15. My Dog Fudge 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: • How many large dogs passed? • How many small dogs passed?

  16. Organizing qualitative DataTwo-Way Table

  17. Organizing qualitative DataTwo-Way Table 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?

  18. Organizing qualitative DataTwo-Way Table 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.

  19. Organizing Qualitative DataTwo-Way Table 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 the Dog passed the class in this scenario? Is there an association between size of the dog and whether or not passed the class?

  20. Construct a stacked bar graph with size of dog on the x axis. All the small dogs failed

  21. Organizing qualitative DataTwo-Way Table 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 the Dog passed the class in this scenario? Is there an association between size of the dog and whether or not passed the class?

  22. Stacked bar graph All the large dogs failed

  23. Organizing qualitative DataTwo-Way Table Assume 9 large dogs passed Questions: 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 the Dog passed the class in this scenario? Is there an association between size of the dog and whether or not passed the class?

  24. No association stacked bar graph

  25. Is there a link between symptoms of asthma and cigarette smoke? 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

  26. Asthma data 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 with a least one smoker?

  27. Asthma data The study reported that 113 students lived in a home with at least one smoker. Complete the table

  28. Asthma data 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 home with a smoker?

  29. Association?

  30. CCSS 8th Grade • 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.

  31. Homework 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 article b. Which of the 6th, 7th, 8th grade CCSS Statistics Domain standards are evident in the activities discussed in this article.

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