displaying distributions qualitative variables part 2 n.
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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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studies with two qualitative variables
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
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
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
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?
example3
Example
  • See example on page 199.
example4
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
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.
example5
Example
  • The grand total of frequencies is 1000.
  • The marginal distribution for nutritional status is
example6
Example
  • The marginal distribution for academic performance is
the marginal distribution1
The Marginal Distribution
  • The marginal distribution shows us the distribution of one variable independently of the other variable.
conditional distributions
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 distributions1
Conditional Distributions
  • The answers are
    • 70/1000 = 7%
    • 70/200 = 35%
    • 70/290 = 24%
conditional distributions2
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 distributions3
Conditional Distributions
  • The conditional distribution of academic performance given nutritional status is
conditional distributions4
Conditional Distributions
  • The conditional distribution of nutritional status given academic performance is
let s do it
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.
assignment
Assignment
  • Page 206: Exercises 12 – 17.
  • Page 249: Exercises 62 – 66.