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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
â€¢Social scientists are interested in uncovering the associations or relationships
between several variables.
â€¢To simultaneously analyze two variables that cannot be ranked or ordered, you need to
use bivariate analysis for nominal variables.
Some Sample Research Questions
â€¢Are members of particular visible minority groups more susceptible to certain diseases?
â€¢Are men more likely than women to gamble?
â€¢Are Torontonians more likely than Edmontonians to be homeowners?
â€¢Does this differ for men and women?
What You Need to Begin Answering these Questions
â€¢A representative sample
â€¢A knowledge of the level of measurement of each variable
â€¢A knowledge of bivariate statistics and measures of association
Analysis with Two Nominal Variables
â€¢The first step for performing bivariate analysis is organizing the data so that patterns can
be easily discerned.
â€¢It is useful to create a frequency table, with the information organized into two columns
(e.g., Table 12.1).
â€¢The variable that we think is modifying the outcome is an independent variable.
â€¢The outcome of interest is the dependent variable.
â€¢*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
â€¢Need to make data intelligible to identify the existence of relationships
â€¢Often convenient to use a cross-tabulation or contingency table
â€¢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
â€¢It is always useful to able to see relationships in bivariate tables.
â€¢It is also useful, however, to have a single number to indicate the significance of the
relationship.
â€¢Is there a significant relationship between sex of respondent and reaction to pizza
commercial?
The Chi-Square Test of Significance
â€¢Introduced by Karl Pearson in 1900
â€¢Useful for determining whether a relationship exists
â€¢Suitable for all levels of measurement
â€¢Non-parametric (no assumptions about distribution)
â€¢Measures the discrepancy between observed and expected values
â€¢Cannot measure the direction or strength of the relationship
â€¢The co-ed soccer game example
How to Calculate Chi-Square
e
eo
f
ff
2
2
)( âˆ’
Î£=
Ï‡
â€¢
2
Ï‡
Where:
o
o
f
= chi-square
o = observed frequency of the cell
o
e
f
= expected frequency of the cell
Chi-Square: An Example
â€¢The co-ed soccer game
â€¢2 teams (A and B), 10 males + 12 females
â€¢Each team has the same number of people
â€¢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 â€¢ Social scientists are interested in uncovering the associations or relationships between several variables. â€¢ To simultaneously analyze two variables that cannot be ranked or ordered, you need to use bivariate analysis for nominal variables. Some Sample Research Questions â€¢ Are members of particular visible minority groups more susceptible to certain diseases? â€¢ Are men more likely than women to gamble? â€¢ Are Torontonians more likely than Edmontonians to be homeowners? â€¢ Does this differ for men and women? What You Need to Begin Answering these Questions â€¢ A representative sample â€¢ A knowledge of the level of measurement of each variable â€¢ A knowledge of bivariate statistics and measures of association Analysis with Two Nominal Variables â€¢ The first step for performing bivariate analysis is organizing the data so that patterns can be easily discerned. â€¢ It is useful to create a frequency table, with the information organized into two columns (e.g., Table 12.1). â€¢ The variable that we think is modifying the outcome is an independent variable. â€¢ The outcome of interest is the dependent variable. â€¢ *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 â€¢ Need to make data intelligible to identify the existence of relationships â€¢ Often convenient to use a cross-tabulation or contingency table â€¢ 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 â€¢ It is always useful to able to see relationships in bivariate tables. â€¢ It is also useful, however, to have a single number to indicate the significance of the relationship. â€¢ Is there a significant relationship between sex of respondent and reaction to pizza commercial? The Chi-Square Test of Significance â€¢ Introduced by Karl Pearson in 1900 â€¢ Useful for determining whether a rel
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