3P15, Mar 12, Lecture 9
Bivariate Statistics for Nominal Data
• Social scientists are interested in uncovering the associations or relationships
between several variables.
• To simultaneously analyze two variables that cannot be ranked or ordered, you need to
use bivariate analysis for nominal variables.
Some Sample Research Questions
• Are members of particular visible minority groups more susceptible to certain diseases?
• Are men more likely than women to gamble?
• Are Torontonians more likely than Edmontonians to be homeowners?
• Does this differ for men and women?
What You Need to Begin Answering these Questions
• A representative sample
• A knowledge of the level of measurement of each variable
• A knowledge of bivariate statistics and measures of association
Analysis with Two Nominal Variables
• The first step for performing bivariate analysis is organizing the data so that patterns can
be easily discerned.
• It is useful to create a frequency table, with the information organized into two columns
(e.g., Table 12.1).
• The variable that we think is modifying the outcome is an independent variable.
• The outcome of interest is the dependent variable.
• *Note that these will not always be clear*
Effectiveness of a Pizza Commercial on Television
Response of Respondent
to Television Commercial f
Order a Pizza 40
Grab Food from the 100
Change Channels 110
No Reaction 750
Bivariate Statistics: Visualizing a Relationship
• Need to make data intelligible to identify the existence of relationships
• Often convenient to use a cross-tabulation or contingency table
• Put independent variable (IV) in columns, dependent variable (DV) in rows (if known)
A Bivariate Contingency Table Sex of
Response of Respondent to Respondent
Order a Pizza 10 30
Grab Food from the Refrigerator 60 40
Change Channels 60 50
No Reaction 490 260
Total 620 380
Measures of Association
• It is always useful to able to see relationships in bivariate tables.
• It is also useful, however, to have a single number to indicate the significance of the
• Is there a significant relationship between sex of respondent and reaction to pizza
The Chi-Square Test of Significance
• Introduced by Karl Pearson in 1900
• Useful for determining whether a rel