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Probability, Statistics and the Logic of Scientific Causality PowerPoint PPT Presentation


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Probability, Statistics and the Logic of Scientific Causality. An Introduction to Social Science Data Analysis. Logic of Scientific Inquiry. Inter-subjective Standards Mathematics Logic Subjective Standards Religion Normative philosophy . What is the job of a social scientist?.

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Probability, Statistics and the Logic of Scientific Causality

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Probability, Statistics and the Logic of Scientific Causality

An Introduction to Social Science Data Analysis


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Logic of Scientific Inquiry

  • Inter-subjective Standards

    • Mathematics

    • Logic

  • Subjective Standards

    • Religion

    • Normative philosophy


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    What is the job of a social scientist?

    • 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

    • Always estimate the level of uncertainty in any claim


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    Approaches to Political Science

    • 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


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    The Research Question:Why 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?


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    Measurement


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    Measurement

    • Inter-subjective Measures

      • Inches

      • Degrees Fahrenheit

      • Dollars

    • Continuous v. Discrete


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    Concepts that are difficult to measure inter-subjectively

    • Democracy

    • Self-Esteem

    • Ideology


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    Face Validity: Political Tolerance

    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


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    Reliability

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

    Multiple questions at the same time.


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    High Variance

    Mean


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    Low Variance

    Mean


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    Variance

    • 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


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    Variance: Political Tolerance

    Number of People


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    Variance – Skewed Distribution

    Number of People


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    Low Variance

    Number of People


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    High Variance

    Number of People


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    Standard Deviation

    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.


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    Standard Deviation

    • 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


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    Measurement

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


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    Probability


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    Probability

    • The probability of an outcome …

    • Is the frequency of that outcome

    • if the process were repeated a large number of times…

    • Under similar conditions


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    Probability is not causality

    • Fire trucks  fire damage

    • Storks  babies


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    Causal Theory

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


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    Statistical Theory

    • Frequentist statistical theory assumes repeated observations.

    • From large sample sizes, we assume that we have repeated observations.

    • Large? 60.


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    Statistical Relationships

    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 34 5

    Political Tolerance


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    Probability

    • The probability of an outcome …

    • Is the frequency of that outcome

    • if the process were repeated a large number of times…

    • Under similar conditions


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    Statistical Relationships

    6

    Slope

    5

    4

    Political Tolerance

    Mean

    3

    2

    1

    0

    0

    1

    2

    3

    4

    5

    6

    Education


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    Probability: Best Guess

    • 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


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    The Mean

    • 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


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    Our job in statistical analysis

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


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    Variance: Explained and Unexplained

    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


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    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.


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    Decrease Error

    6

    Slope

    5

    4

    Political Tolerance

    Mean

    3

    2

    1

    0

    0

    1

    2

    3

    4

    5

    6


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    Variance: Explained and Unexplained

    6

    5

    Slope

    4

    Political Tolerance

    Mean

    3

    2

    1

    0

    0

    1

    2

    3

    4

    5

    6

    Education


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    Unexplained

    Why does ‘y’ vary?

    • Our job as social scientists is to explain variance.

    • Statistically, we do that by separating explained from unexplained.

    Explained


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    Aspects of Political Science Data Analysis

    • Causal Theory

    • Measurement Theory

    • Explain Variation


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