POSC 202A: Lecture 2
Homework #1: 1.2, 1.44, 1.54, 1.62,1.74, 3.2,
3.6, 3.52, 3.54, 3.60, 3.67, 3.70
Today: Research Designs, Mean, Variance
Research Design
Research DesignA strategy for evaluating the truth of a
proposition
Research Design
Two related issues:
1. Finding evidence that one thing causes
another. We observe a relationship.
2. Finding evidence that alternative
explanations do not cause the observed
relationship.
Research Design
How do we find evidence that alternative
explanations do not cause the observed
relationship?
We try to compare cases in which the
relationship occurs (and does not) occur
to varying degrees.
Research Design
So comparison is done through case
selection.
9 factors characterize “goodness” in case
selection.
By maximizing particular characteristics in
the cases we select we gain confidence
about our inference.
Research Design: 9 Criteria
1.
2.
3.
4.
5.
Plenitude
Boundedness
Comparability
Independence
Representativeness
6. Variation
7. Replicability
8. Mechanism
9. Causal comparison
Research design is governed by tradeoffs among these
different criteria rather than by fixed rules
Research Design: 9 Criteria
PlenitudeThe accumulation of comparative reference
points constitutes evidence. The more
cases, the more evidence.
Research Design: 9 Criteria
BoundednessA proposition should cover cases that are
fundamentally similar, comparable or
relevant.
Sometimes increasing the N might require
inclusion of inappropriate cases.
Research Design: 9 Criteria
Comparability-
Research Design: 9 Criteria
ComparabilityCases must be similar to one another in
some important respect(s). Refers to the
internal properties of the sample.
Research Design: 9 Criteria
Independence-
Research Design: 9 Criteria
IndependenceThe selection of a case for examination
should not be related to, or affect the
likelihood of selecting another case that is
being examined.
Research Design: 9 Criteria
IndependenceExamples:
1. Selection of a card from a deck changes the
likelihood of the next card being selected.
2. But if we put the card back in the deck, shuffle
them, and select again, the draws are
independent.
Research Design: 9 Criteria
Representativeness-
Research Design: 9 Criteria
RepresentativenessThe degree to which the sample an accurate
description of the characteristics of the
population.
Research Design: 9 Criteria
RepresentativenessExample: Experiments of the effect of drug use on
rats may not be generalizable to humans
because rats are different in some important
ways.
But note that the rats themselves are comparable
with one another (i.e. they are similar).
Research Design: 9 Criteria
VariationThe range of values registered for a given
explanatory (x) or outcome (y) variable.
Important because causation occurs when
two things vary together.
Research Design: 9 Criteria
ReplicabilityA good research design produces reliable
results that do not vary across iteration.
The results are repeatable.
Research Design: 9 Criteria
MechanismExplains the link between cause and effect.
We remain skeptical of a causal
relationship until two factors can be linked.
Example: Time of Day is negatively
associated with light (as it gets later it gets
darker) but lacks a mechanism for causing
it.
Research Design: 9 Criteria
Causal ComparisonWe must evaluate rival explanations to
provide evidence for a particular cause.
An argument is verified when evidence
indicates that one causal story is superior
to others that explain the same event.
Review: Research Design
By maximizing particular characteristics in
the cases we select, we gain confidence
about our inferences.
Research Design: Methods
3 general types of methods:
1. Case Study (N=1)
2. Small or Medium “N”
3. Large “N”
Exhibit the 9 criteria to varying degrees
Research Design: Methods
Case StudyThe study of a single unit.
Research Design: Methods
Case Study
The study of a single unit.
It allows us to understand the mechanisms
that connect a particular X with a
particular y.
Research Design: Methods
Case Study Types:
Extreme Case
Crucial-Case
Typical-Case
Research Design: Methods
Extreme CaseSelection of a case that exhibits a high (extreme)
level of the thing we wish to study.
Example: A campaign that is highly competitive.
This allows us to examine what factors are
associated with competition.
Research Design: Methods
Typical CaseSelection of a case that is most
representative or typical of the thing we
want to study.
Example: A campaign that is not very
competitive(!).
Research Design: Methods
Crucial CaseA case in which alternative explanations for
the same phenomena predict different
outcomes.
These are often hard to find
But you want to find examples that fit all
case-types, and the poles
Research Design: Methods
Case Study
It allows us to understand the mechanisms that
connect a particular X with a particular y.
BUT
It lacks plenitude (i.e., case size is small) so it may
be hard to tell whether the mechanism is
systematic across cases or unique to the case
being examined.
Research Design: Methods
Small or Medium “N” Studies
Analyses that employ small or medium sized
samples and generally focus on variation
across the primary unit of analysis.
Research Design: Methods
Small or Medium “N” Study Types
1. Most Similar
2. Most Different
Research Design: Methods
Most SimilarLooks for a few cases that are as similar as
possible in all respects except for the
outcome of interest which is expected to
vary.
Research Design: Methods
Most SimilarCountry A
Country B
GDP Per Capita = $50K
GDP Per Capita = $50K
European
European
10% Foreign Born
9% Foreign Born
Foreign Born: Mexico
Foreign Born: Algeria
Policy: Keep Head Scarves
Policy: Ban Head Scarves
Research Design: Methods
Most DifferentLook for a few cases that are as different as
possible in all respects except for the
outcome of interest which is expected to
be the same.
Research Design: Methods
Most DifferentBUT
these are more useful for eliminating
possible causes than providing proof for a
cause.
Research Design: Methods
Large “N”
Methods that draw on large numbers of
cases or examples.
Research Design: Methods
Large “N”
1. Experimental
2. Statistical
Research Design: Methods
Large N studies maximize the largest
number of the criteria for research design
Research Design: Methods
Statistical Experimental Typical
Case
Plenitude
+
+
Boundedness
+
+
Comparability
+
Independence
Yes/No
+
Representativeness
+
+
Variation
+
+
Mechanism
+
+
Reliability
+
+
Causal Comparison
+
Describing Data
VariableA thing or quantity that varies across
individuals, or objects
(which are usually referred to as observations)
Describing Data
Distributions:
Tell us what value a variable takes
and how frequently they take them.
Describing Data
The most famous is the Normal
distribution.
What is it?
Describing Data
Measures of central tendency
mean, median, mode
Measures of dispersion (spread)
IQR, standard deviation, variance
Describing Data
Nth Percentile
The percentage of observations in a
distribution that fall to the left of point n.
20th percentile
20
80
Describing Data
Quartile
A range containing 25% of the observations
in a distribution.
Describing Data
5 number summary:
Minimum, 1st quartile, median, 3rd quartile
and maximum
Describing Data
5 number summary:
Minimum, 1st quartile, median, 3rd quartile
and maximum
1st Quartile
Median
3rd Quartile
Describing Data
Inter-quartile range:
The distance between the first and third
quartiles.
1st Quartile
3rd Quartile
Describing Data
Variance:
A number that summarizes how far all of the
observations are from the average of the
distribution.
Describing Data
Variance:
Describing Data
Standard Deviation:
Think of this as how far away from the mean is the
typical observation.
It is the square root of the variance.