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Probability, Statistics and the Logic of Scientific CausalityPowerPoint Presentation

Probability, Statistics and the Logic of Scientific Causality

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### Measurement Causality

### Measurement Causality

### Probability Causality

### Causal Theory Causality

Probability, Statistics and the Logic of Scientific Causality

An Introduction to Social Science Data Analysis

Logic of Scientific Inquiry Causality Subjective Standards

- Inter-subjective Standards
- Mathematics
- Logic

- Religion
- Normative philosophy

What is the job of a social scientist? Causality

- To try to use whatever tools we have at our disposal to prove ourselves wrong about our causal theory.
- Tools:
- Logic
- Empirical observation

- Try to disprove our theory as much as possible
- Unfortunately, we cannot prove anything

- Tools:
- Always estimate the level of uncertainty in any claim

Approaches to Political Science Causality

- Interpretavism – if we describe the phenomenon, what does it mean
- Behavioralism – the underlying roots of our attitudes and behaviors
- Neo-institutionalism – the relationships among attitudes and behaviors depend on rules and other constraints
- Rational Choice
- Assume preferences
- Deduce outcomes

The Research Question: CausalityWhy does ‘y’ vary?

- Why do some people vote for Democrats and others for Republicans?
- Why do some ethnic conflicts get resolved and other end in holocausts?
- Why do some democracies remain stable and others fall apart?
- Why are some economies successful and others are not?
- Why do some civil conflicts result in revolution and others do not?
- What causes some people to support the civil liberties of political enemies?
- What causes some people to trust one another and others not to trust?
- What causes some people to participate in their government?
- What causes some people to bring litigation against their government?

Measurement Causality

- Inter-subjective Measures
- Inches
- Degrees Fahrenheit
- Dollars

- Continuous v. Discrete

Concepts that are difficult to measure inter-subjectively Causality

- Democracy
- Self-Esteem
- Ideology

Face Validity: Political Tolerance Causality

If your worst political enemy (i.e. Nazi’s, KKK) came to your town, would you support their right to march downtown?

Not support at all

Not really support

Somewhat support

Strongly support

4

1

2

3

Reliability Causality

Repeat Study: the same people who got a 1 would get about a 1 again and so on.

Multiple questions at the same time.

High Variance Causality

Mean

Low Variance Causality

Mean

Variance Causality

- Total Variance:
- Sum of squared distance of each point to the mean/number of observations.

(4)2=16

(3)2=9

(0)2=0

(2)2=4

(1)2=1

(1)2=1

(1)2=1

Mean

No error

Total Variance = 32/7 = 4.57

Variance: Political Tolerance Causality

Number of People

Variance – Skewed Distribution Causality

Number of People

Low Variance Causality

Number of People

High Variance Causality

Number of People

Standard Deviation Causality

Square root of the average level of variance

We square the deviations from the mean, but then the units of squared numbers do not make sense, so we then take the square root of it.

Standard Deviation Causality

- The standard deviation is the sum of squared distance of each point to the mean, divided by the number of observations.

(4)2=16

(3)2=9

(0)2=0

(2)2=4

(1)2=1

(1)2=1

(1)2=1

Mean

No error

Total Variance = 4.57;

Standard Deviation = √32/7 = 2.13

We will spend a great deal of time on measurement in this class

Probability Causality

- The probability of an outcome …
- Is the frequency of that outcome
- if the process were repeated a large number of times…
- Under similar conditions

We will spend a great deal of time on causal theory in this class

Statistical Theory Causality

- Frequentist statistical theory assumes repeated observations.
- From large sample sizes, we assume that we have repeated observations.
- Large? 60.

Statistical Relationships Causality

40

3

3

3

2

35

2

3

3

1

3

2

30

1

3

Education

3

1

25

1

3

3

3

1

Lowest

Low

Medium

High

Highest

3

3

20

2

2

2

3

2

4

2

3

2

3

2

4

3

2

1

15

4

3

4

2

1

2

3

4

3

4

3

2

2

3

2

4

5

10

1

1

2

3

4

3

4

5

5

4

4

1

1

2

2

3

3

5

5

5

5

1

2

2

2

3

3

4

4

5

5

5

2

1

3

2

3

4

3

5

5

4

5

1

1

2

3

3

3

5

4

5

5

0

1 2 3 4 5

Political Tolerance

Probability Causality

- The probability of an outcome …
- Is the frequency of that outcome
- if the process were repeated a large number of times…
- Under similar conditions

Statistical Relationships Causality

6

Slope

5

4

Political Tolerance

Mean

3

2

1

0

0

1

2

3

4

5

6

Education

Probability: Best Guess Causality

- What is the probable value of tolerance, given condition of education?
- This is what the slope tells us.

6

Slope

5

4

Political Tolerance

Mean

3

2

1

0

0

1

2

3

4

5

6

Education

The Mean Causality

- The mean is the best guess if all you have is a single variable

Mean

No error

- The purpose of the mean is to minimize error in guessing
- The mean is the most probable expected value

Our job in statistical analysis Causality

- Is to do better than the mean at making the ‘best guess’

Variance: Explained and Unexplained Causality

6

Unexplained: Distance from the points to the slope

5

Slope

Explained: From slope to mean

4

Political Tolerance

Mean

3

2

1

0

0

1

2

3

4

5

6

Education

Remember when we said: Our job in statistical analysis is to do better than the mean?

We use the slope to…

- Minimize Error:
the distance between the points and the slope,

…while, by definition, simultaneously

- Maximizing Explained Variance:
the distance between the mean and the slope.

Variance: Explained and Unexplained do better than the mean?

6

5

Slope

4

Political Tolerance

Mean

3

2

1

0

0

1

2

3

4

5

6

Education

Unexplained do better than the mean?

Why does ‘y’ vary?- Our job as social scientists is to explain variance.
- Statistically, we do that by separating explained from unexplained.

Explained

Aspects of Political Science Data Analysis do better than the mean?

- Causal Theory
- Measurement Theory
- Explain Variation

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