Displaying Distributions – Qualitative Variables – Part 2

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Displaying Distributions – Qualitative Variables – Part 2. Lecture 16 Sec. 4.3.3 Wed, Feb 11, 2004. Studies with Two Qualitative Variables. Typically, the purpose of studying two variables is to see whether there is a relationship between them.

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### Displaying Distributions – Qualitative Variables – Part 2

Lecture 16

Sec. 4.3.3

Wed, Feb 11, 2004

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).
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.
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.
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?
Example
• See example on page 199.
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.
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.
Example
• The grand total of frequencies is 1000.
• The marginal distribution for nutritional status is
Example
• The marginal distribution for academic performance is
The Marginal Distribution
• The marginal distribution shows us the distribution of one variable independently of the other variable.
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?
Conditional Distributions
• 70/1000 = 7%
• 70/200 = 35%
• 70/290 = 24%
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.
Conditional Distributions
• The conditional distribution of academic performance given nutritional status is
Conditional Distributions
• The conditional distribution of nutritional status given academic performance is
Let's Do It!
• Let's do it! 4.8, p. 203 – Beer Tastes.
• Use the data concerning year in college vs. whether in or out of state.
Assignment
• Page 206: Exercises 12 – 17.
• Page 249: Exercises 62 – 66.