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Understanding Relationships in Qualitative Data: Frequency and Conditional Distributions

This lecture focuses on analyzing relationships between two qualitative variables by using frequency tables and marginal distributions. It explains the importance of assessing whether a relationship exists through graphical representation and numerical measures like percentages and frequency counts. Key concepts include constructing contingency tables, exploring marginal distributions, and calculating conditional distributions to analyze dependencies between variables such as academic performance and nutritional status. Exercises are included for practical application.

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Understanding Relationships in Qualitative Data: Frequency and Conditional Distributions

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Presentation Transcript

  1. Displaying Distributions – Qualitative Variables – Part 2 Lecture 16 Sec. 4.3.3 Wed, Feb 11, 2004

  2. Studies with Two Qualitative Variables • Typically, the purpose of studying two variables is to see whether there is a relationship between them. • Also, when working with qualitative data, percentages are the numerical measure of choice. • The next-most-common measure is frequency (or count).

  3. Relationships between Two Qualitative Variables • Frequency table – A table where • The rows represent values of one variable, • The columns represent values of the other variable, • And the cells show the frequency of the row-column combinations of values. • A frequency table is also called a contingency table.

  4. Example • Let the row variable be the student’s year in college. • Let the column variable be whether the student is from Virginia or is from out of state. • This will be a 4 x 2 frequency table.

  5. Example

  6. Frequency Tables • If there is a relationship between the variables, then perhaps it will be apparent from the table. • Perhaps not. • Do we see any relationship between year in college and state of residence?

  7. Example

  8. Example • See example on page 199.

  9. Example • Is there any apparent relationship between academic performance and nutritional status? • It is hard to say (in my opinion). • A possible relationship is that students with better nutrition perform better academically.

  10. Excel Bar Graph

  11. Excel Bar Graph

  12. The Marginal Distribution • Each variable has a marginal distribution. • To find the marginal distribution of a variable, find the total frequency of the cells for each value of that variable. • Then express each total frequency as a percentage of the grand total for all cells.

  13. The Marginal Distribution of Nutritional Status

  14. Example • The grand total of frequencies is 1000. • The marginal distribution for nutritional status is

  15. The Marginal Distribution of Academic Performance

  16. Example • The marginal distribution for academic performance is

  17. The Marginal Distribution • The marginal distribution shows us the distribution of one variable independently of the other variable.

  18. Conditional Distributions • In the example, • What percentage of all students are below average academically and have poor nutrition? • What percentage of students who are below average academically have poor nutrition? • What percentage of students who have poor nutrition are below average academically?

  19. Conditional Distributions • The answers are • 70/1000 = 7% • 70/200 = 35% • 70/290 = 24%

  20. Conditional Distributions • To get the conditional distribution of academic performance given nutritional status, • For each category of nutritional status (i.e., for each column), divide the various frequencies in that category by the total for that category.

  21. Conditional Distributions • The conditional distribution of academic performance given nutritional status is

  22. Conditional Distributions • The conditional distribution of nutritional status given academic performance is

  23. Let's Do It! • Let's do it! 4.8, p. 203 – Beer Tastes. • Let’s do it! 4.9, p. 205 – About Your Class. • Use the data concerning year in college vs. whether in or out of state.

  24. Assignment • Page 206: Exercises 12 – 17. • Page 249: Exercises 62 – 66.

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