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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 Design-
A 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. Plenitude
2. Boundedness
3. Comparability
4. Independence
5. 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
Plenitude-
The accumulation of comparative reference points constitutes evidence. The more
cases, the more evidence.
Research Design: 9 Criteria
Boundedness-
A 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
Comparability-
Cases 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
Independence-
The 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
Independence-
Examples:
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
Representativeness-
The degree to which the sample an accurate description of the characteristics of the
population.
Research Design: 9 Criteria
Representativeness-
Example: 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
Variation-
The 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
Replicability-
A good research design produces reliable results that do not vary across iteration.
The results are repeatable.
Research Design: 9 Criteria
Mechanism-
Explains 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 Comparison-
We 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 Study-
The 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 Case-
Selection 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 Case-
Selection 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 Case-
A 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.
BUTIt 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 Similar-
Looks 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 Similar-
Country 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 Different-
Look 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 Different-
BUT
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: MethodsStatistical Experimental Typical
Case
Plenitude + + -
Boundedness + +
Comparability +
Independence Yes/No +
Representativeness + - +
Variation + +
Mechanism - + +
Reliability + +
Causal Comparison +
Describing Data
Variable-
A 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.
20 80
20th percentile
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
3rd Quartile1st Quartile
Median
Describing Data
Inter-quartile range:
The distance between the first and third quartiles.
3rd Quartile1st 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 DataStandard Deviation:
Think of this as how far away from the mean is the typical observation.
It is the square root of the variance.
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