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Lecture 9

Lecture 9, Mar 12.docx

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Department
Child and Youth Studies
Course Code
CHYS 3P15
Professor
Patricia Kirkpatrick

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3P15, Mar 12, Lecture 9
Chapter 12
Bivariate Statistics for Nominal Data
Introduction
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
Refrigerator 100
Change Channels 110
No Reaction 750
Total 1000
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
Respondent
Response of Respondent to
Television Commercial Female Male
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
relationship.
Is there a significant relationship between sex of respondent and reaction to pizza
commercial?
The Chi-Square Test of Significance
Introduced by Karl Pearson in 1900
Useful for determining whether a relationship exists
Suitable for all levels of measurement
Non-parametric (no assumptions about distribution)
Measures the discrepancy between observed and expected values
Cannot measure the direction or strength of the relationship
The co-ed soccer game example
How to Calculate Chi-Square
e
eo
f
ff
2
2
)(
Σ=
χ
2
χ
Where:
o
o
f
= chi-square
o = observed frequency of the cell
o
e
f
= expected frequency of the cell
Chi-Square: An Example
The co-ed soccer game
2 teams (A and B), 10 males + 12 females
Each team has the same number of people
What is the expected distribution of males and females?

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Description
3P15, Mar 12, Lecture 9 Chapter 12 Bivariate Statistics for Nominal Data Introduction • 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 Refrigerator Change Channels 110 No Reaction 750 Total 1000 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 Television Commercial Female Male 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 relationship. • Is there a significant relationship between sex of respondent and reaction to pizza commercial? The Chi-Square Test of Significance • Introduced by Karl Pearson in 1900 • Useful for determining whether a rel
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