MAX 201
Quantitative Methods for the
Social Sciences
Controlling for a Third Variable;
Developing a Research Topic
Univariate, bivariate, and
multivariate analysis

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Most basic data description: statistics
applied to one variable: mean, median,
percentages.
Bivariate analysis uses contingency tables
to look at two variables at a time.
Introducing a third variable is called
controlling or specifying the original
relationship.
Controlling for a third variable:
sex and auto accidents

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Men have more accidents than women
(gender is related to accident
involvement)
Introduce a third variable: miles driven
per year

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Gender is related to miles driven (men drive
more)
Miles driven is related to accidents (the more
you drive, the more likely you are to have an
accident).
Sex & accidents: spurious
relationship

SEX

MILES driven

ACCIDENT Frequency

SEX

ACCIDENT Frequency
Control Variable as an
Intervening Variable
Ind.
Var.
Control
Variable
Dep.
Var.
Caffeine and Heart Attacks
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One study linked caffeine consumption with an
increased of heart disease.
Study did not control for a third variable:
whether patients in the smoked.
Heavy caffeine consumers also smoke.
Further study revealed that smoking not caffeine
was the cause of the heart disease.
Source: Ian Ayres, Super Crunchers. NY:
Bantam: 2007: pp 90-91.
Wealthier is Healthier
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For countries, a graph of mortality against
income reveals that populations of richer
countries live longer.
For individuals within a country, higherincome individuals live longer than lowerincome individuals.
The relationships are much more complex,
however.
Wealthier is Healthier

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For countries, public health –sanitation and removal of
waste – plays an important role. Big Medicine –
vaccination and antibiotics – play a role. Individual care
plays a larger role as income grows.
In poor countries, mosquitoes, AIDS, unsafe drinking
water and other public health issues play a large role in
mortality.
Insecticide will work to some degree on mosquitoes, but
eventually mosquitoes develop a resistance. Need to
remove open, stagnant pools where mosquitoes breed.
Wealthier is Healthier
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
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For individuals, the relationship between health
and income is more complex.
Better utilization of knowledge about health
(smoking) and more education may cause
health, rather than income directly causing
health.
Certain groups experience more stress from
discrimination, low-income and that harms
health.
Source: David Cutler, Angus Deaton, Adriana Lleras-Muney. “”The
Determinants of Mortality.” Journal of Economic Perspectives. 20 (3) 2006:
97-120.
Controlling for a third variable:
health care and party id

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Controlling for a third variable discussed in
the chapter from the Cole book, “Sorting
Out Relationships”
Work through that example:
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original relationship is support of health care
and party identification (10.1)
control variable is income
different possibilities are considered
Party ID and Health Care Reform
Support Health
Care Reform
Republican
Democrat
Totals
No
73
37
110
Yes
67
123
190
Totals
140
167
300
Gamma = 0.57 Democrats in general support health care reform; republicans
show no discernable (statistical) pattern of support or opposition.
Party ID and Health Care Reform
Income: Low
Income: High
Support
Health
Care
R
D
Totals
R
D
Totals
No
33
27
60
40
10
50
Yes
27
113
140
40
10
50
Totals
60
140
200
80
20
100
Gamma = 0.67
Gamma = 0.00
Low-income democrats support health care reform more than lower-income
republicans do; high-income democrats and republicans show no relationship
between party affiliation and support for health care reform.
Interpreting the controls
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Controlling for a third variable can help
you understand the bivariate relationship
you’re interested in
Controlling for a third variable can tell you
that the original relationship
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Is spurious
Is maintained
Differs within categories of the 3rd variable
GSS data and 3-variable
relationships
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May find spurious relationships
More likely to find specified relationships
Very likely to look at joint impact of two
independent variables on a dependent
variable
Example
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Hypothesis: People with more children will
have more conservative or traditional
views on childrearing.
These views may differ by gender.
# of children * Child Suffers if Mom Works Crosstabulation
# of children
0-2
3 or more
Total
Child Suffers if Mom
Works
Agree
Disagree
294
315
48.3%
51.7%
147
108
57.6%
42.4%
441
423
51.0%
49.0%
Total
609
100.0%
255
100.0%
864
100.0%
RESPONDENTS SEX * Child Suffers if Mom Works Crosstabulation
RESPONDENTS
SEX
MALE
FEMALE
Total
Child Suffers if Mom
Works
Agree
Disagree
218
146
59.9%
40.1%
224
277
44.7%
55.3%
442
423
51.1%
48.9%
Total
364
100.0%
501
100.0%
865
100.0%
# of children * Child Suffers if Mom Works * RESPONDENTS SEX
Crosstabulation
MALE
# of children
0-2
3 or more
Total
FEMALE
# of children
0-2
3 or more
Total
Child Suffers if Mom
Works
Agree
Disagree
158
113
58.3%
41.7%
59
33
64.1%
35.9%
217
146
59.8%
40.2%
136
202
40.2%
59.8%
88
75
54.0%
46.0%
224
277
44.7%
55.3%
Total
271
100.0%
92
100.0%
363
100.0%
338
100.0%
163
100.0%
501
100.0%
Assignment 8
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Control for third
variable and interpret
Find and summarize
an article related to
your topic
Briefly describe your
projected research
project.
Citations of Scholarly Articles
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Research-based papers very important
In “Refereed” or Peer-reviewed journals
Other sources (Newsweek, Washington Post,
NYT, blogs, on-line informational sites) may be
used as supplements, but be careful here. Blogs
and wikpedia might be simply uninformed
opinion. Do they belong in your paper?
Library data bases (e-journals)