Aim: How do we analyze data with a two-way table?

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Aim How do we analyze data with a two-way table?

• HW Read chapter 2.5 page 142-148
• Complete last slide

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Studying Relationships between 2 variables

• Always ask whether each variable is quantitative
  or categorical
• 2 quantitative variables, we use a scatterplot to
  examine the relationship and fit a line to the
  data if the relationship is approximately linear
• If 1 variable is qauntitative and the other
  categorical, we can use boxplot, frequencies
  histogram, bar graphs, stemplot or pie charts
  (chapter 1)

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Categorical Data

• Variables such as gender, race, and occupation
• Categorical variables are also created by
  grouping values of a quantitative variable into
  classes
• Use the counts (frequency) or percents (relative
  frequency) of individuals that fall into various
  categories
• Example frequency of drinking

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What is the two-way table?

• The key idea in studying relationships between
  two variables is that both variables must be
  measured on the same individual or case
• When both variables are categorical, the raw data
  are summarized in a two-way table that gives
  counts of observations for each combination of
  values of the two categorical variables

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Example of two-way table

• Alcohol abuse has been described by college
  presidents as the number one problem on campus
  and it is an important cause of death in young
  adults. How common is it? A survey of 17,096
  students in U.S. four-year colleges collected
  information on drinking behavior and
  alcohol-related problems. The researchers defined
  frequent binge drinking as having five or more
  drinks in a row three or more times in the past
  two weeks.

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Example of two-way table

• Here is the two-way table classifying students by
  gender and whether or not they are frequent binge
  drinkers
• Two variables frequent binge drinking and gender

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Setting Up Two-Way Table

• Row Variable (dependent variable) each
  horizontal row in the table describes the
  drinking behavior
• Column Variable (independent variable) each
  vertical column describes one gender group
• Cell combination of the two groups
• Because there are only 2 rows and 2 columns, this
  table is called a 2 x 2 table

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Describing relationships between categorical data

• Need to compute different types of percents
  therefore, the two-way table needs a total column
• Table shows you total number of men, woman,
  participants and total number of each grouping
  variable

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Joint Distribution

• Joint Distributions the collection of these
  proportions of the two categorical variables
• To find proportions between two categorical
  variables you must divide the proportion you are
  looking at and the total
• Example The proportion of males who are frequent
  binge drinkers is found by simply dividing 1630
  by sample size 17,096 equally 0.095 ? estimate
  that 9.5 of college students are male frequent
  binge drinkers

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Joint Distribution
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Marginal Distribution

• Marginal Distribution used when examining the
  distribution of a single variable in a two-way
  table

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Marginal Distribution for this example

• We have two variables in this example, so there
  is to marginal distributions to calculate
• Marginal Distribution of GENDER found by
  dividing the total amount of males (7180) and
  females (9916) by the total sample size (17,096).

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Marginal Distribution for this example

• For marginal distribution, percents are usually
  preferred
• Marginal Distribution of BINGE DRINKING divide
  the total yes (3314) and the total no (13,782) by
  the sample size (17,096)

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Homework

• Full-time and part-time college students. The
  Census Bureau provides estimates of numbers of
  people in the United States classified in various
  ways. Let's look at college students. The
  following table gives us data to examine the
  relation between age and full-time or part-time
  status. The numbers in the table are expressed as
  thousands of U.S. college students.
• a) What is the U.S. Census Bureau estimate of
  the number of full-time college students aged 15
  to 19?
• (b) Give the joint distribution of age and status
  for this table.
• (c) What is the marginal distribution of age?
  Display the results graphically.
• (d) What is the marginal distribution of status?
  Display the results graphically.