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.