independent variable

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Today's topics
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Causal thinking, theories, hypotheses
Independent and dependent variables; forms of
relationships
Formulating hypothesis; hypothesis testing by
comparisons
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Causal structure; Isolating causal effects
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The empirical research process
Causation
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Social scientists systematically observe social life to
identify and understand patterns
Understanding facilitated by theoretical causal
explanations, statements about the underlying causal
structure giving rise to observed data. Plausible stories.
Other important factors for causation: empirical
correlation (not sufficient), temporal ordering, no
confounding
Deterministic vs. probabilistic causation:
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Women more likely to favor gun control
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Not every woman favors gun control.
Theories and Hypotheses
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Theories help us make sense of observed data, and
guide us in designing future research
Not all theories are “good”
A “good” theory is not only logically plausible, but
suggests testable hypotheses about the empirical
relationship between variables representing causes
and effects
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e.g. Gender and gun control
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e.g. People with more education are more likely to vote
than people with less education (more education, better
informed, higher sense of efficacy).
Variables
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“Education”, “turnout”,”gender”, and “gun control
opinion” are variables.
A variable is a measured concept that takes
varying values for different subjects.
We distinguish between dependent variable
(conventionally denoted by Y) and independent
variable (conventionally denoted by X)
Dependent variables represent effects,
independent variables causes.
Dependent and Independent Variables:
Example (State Data)
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Dependent variable
(Y): % voting for Bush
in 2004
Independent variable
(X): % of the public
who were Republican
Independent and dependent
Variables: More Examples
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Gender and Candidate Preference
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Education and Income
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Party ID and gun control attitude
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Regime Type and Economic Development (this
one is hard!)
Independent and dependent
Variables: forms of relationships
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A relationship can be positive or negative
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A relationship can be linear or nonlinear
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Linear: effect size constant wherever you look
See figures 3-1 to 3-6, pp. 60-66
Hypothesis
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General template: (Pollock p.50)
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In a comparison of [units of analysis], those having
[one value on the independent variable] will be
more likely to have [one value on the dependent
variable] than will those having [a different value on
the independent variable]
e.g. People with more education are more likely to
vote than people with less education
Examples of bad hypotheses: p.52. Pollock
Hypothesis
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A hypothesis suggests a comparison, which is the
basis of hypothesis testing
Cross tabulation if x and y both categorical
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Mean comparison if y quantitative
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e.g. Table 3-1, p.55
e.g. Table 3-3, p.59
correlation/regression
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e.g., the scatter plot we've see
Causal Structures
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If there were no rival causal explanations,
testing hypothesis would be easy
But that's not generally the case
e.g. May observe correlation between Turnout
and Education, Income, Party Identification
Questions is whether any of the correlation
might be “spurious” that can be “explained
away”?
Causal Structures
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Education
Income
Turnout
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Party ID
In this hypothetical causal
structure, the relationship
between income and turnout
is spurious, explained away
by the common cause of
Education
Controlling for Education, the
effect of income on turnout is
no more.
Causal Structures
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Education
Efficacy
Turnout
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Party ID
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In this hypothetical causal
structure, the relationship
between education and
turnout is mediated by
Efficacy, an “intervening
variable”.
Intervening variables help
explain how the independent
variable causes the
dependent variable.
What happens if you control
for the intervening variable?
Causal Structures
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Gender
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Gun control
Partisanship
In this hypothetical causal
structure, the relationship
between partisanship and
gun control opinion is
spurious.
Controlling for “gender” --e.g., only look at data on
women---you'd see that
partisanship no longer
matters.
Causal Structures
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Gender
Gun control
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Partisanship
In this hypothetical causal
structure, the effects of
Gender and Partisanship is
“additive” .
Figure 4-4, p.85, Pollock.
Each of the two X's adds to
the explanation.
Causal Structures
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Gender
Gun control
Partisanship
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In this hypothetical causal
structure, the effect of
partisanship is interactive,
and depends on the value of
“gender”
Figure 4-6, 4-7, pp.87,88.
Pollock.
We'll get to the math
modeling of this later on
Isolating Causal Effects
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We usually don't know the true causal structure
To test whether some X has a causal effect on
Y, ideally we conduct randomized experiments,
with a control group and treatment group that
are identical (in a statistical sense, same
distribution) on everything except the value of
that X (we will return to this)
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(e.g. Medical experiment, effects of a new drug)
Isolating Causal Effects
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Natural experiments may see some differences
in the (self selected) treatment and control
groups that must be adjusted.
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e.g. Different modes of instruction. Students
sign up for two different versions of the
course, one emphasizes the Internet more
than the other. But same instructor, same
books, etc.
Isolating Causal Effects
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Most often, social scientists must rely on observational
data, such as survey data on turnout and other
variables. The challenge then is to control for the
“right” set of confounding variables, so that the
resulting “marginal effect” would represent causal
effect.
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e.g. Suppose education is the only confounder for
the relationship between income and turnout. We
ask: among people with the same level of
education, is there still a relationship between
income and turnout, and how strong?
The Empirical Research Process
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Identify the general topic of interest. (e.g. do drug prevention
programs work?)
Identify units of analysis (study who? Individuals? Schools?)
Conduct literature review: what has been said on this? What
would be your contributions?
Develop theory (e.g. social influence), and formulate testable
hypothesis (e.g. % of students smoking is decreased in the
treatment group)
Nominal and operational definitions, measurement
Data collection (primary or secondary, experimental or
observational..)
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Methods/models; data analysis
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Writing up.
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