Spurious relationship
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Spurious Relationship. A correlation between two variables that have no causal relationship; both variables are caused by another variable. Review: Concepts. Concepts must be unidimensional, with a name that suggests what is high or low on that unidimensional scale. Review: Causality.

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Spurious Relationship

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Spurious relationship

Spurious Relationship

A correlation between two variables that have no causal relationship; both variables are caused by another variable


Review concepts

Review: Concepts

Concepts must be unidimensional, with a name that suggests what is high or low on that unidimensional scale


Review causality

Review: Causality

When we see bad things happen, we want to know what causes them so that we can prevent it.

“Bad” is normative

“Bad things” must be concepts

The “what” doing the causing must also be a concept


Example of concepts

Example of concepts

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


Example of concepts1

Example of concepts

Religiosity

4

1

2

3


Example of concepts2

Example of concepts

Environmentalism

4

1

2

3


Example of correlation

Example of correlation

Environmentalism

Religiosity


Solution

Solution

Logic: deep concern about the logic of the causal mechanism

Statistical: at times, statistical analysis can help guide us

Problem for you: you have to get good at both


Problem

Problem

Sometimes, the concepts are not correlated because they are causally connected

Sometimes, they are correlated because some other variable is causing them both

We make grave errors in our estimation about what causes “bad things” because of spurious correlation


Examples of spurious relationships

Examples of spurious relationships

  • Amount of ice cream sold and death by drowning (units are months)

  • Number of doctors and number of people dying of disease (units are cities)

  • Number of libraries and number of people on drugs (units are years)


Popular study smoking causes bad grades

Popular study: smoking causes bad grades

  • True or spurious?

  • What could be the variable (or variables) that drive both?


News reports

News reports

  • Bottled water causes healthier babies

  • Drinking tea makes you less likely to contract lung cancer


Research question does education cause political tolerance

Research question: Does education cause political tolerance?

  • Many scholars have found a positive relationship between political tolerance (support for liberty for political enemies) and education.

  • Causal mechanism?

    • As people are educated, they are introduced to different kinds of people and perceived danger of political enemies decreases.

    • As people are educated, they are socialized to the correctness of constitutional rights.


Alternative explanation

Alternative Explanation

  • Political tolerance is actually caused by cognitive sophistication, as measured by IQ.

  • Causal mechanism?

    • It is difficult to reconcile the emotional reaction to named political enemies (i.e. Nazis) with constitutional rights and it takes a high IQ to understand that democracy benefits from giving liberties to “bad people.”


Spurious relationship

Relationship between Education and Political Tolerance

High

Political Tolerance

Medium

Low

Low

Medium

High

Education


Controlling for iq

Controlling for IQ

  • X = high IQ

  • Y = low IQ


Spurious relationship

Education and Political Tolerance

High

Political Tolerance

Medium

Low

Low

Medium

High

Education


Spurious relationship

Education and Political Tolerance - High IQ

High

Political Tolerance

Medium

Low

Low

Medium

High

Education


Spurious relationship

Education and Political Tolerance - Low IQ

High

Political Tolerance

Medium

Low

Low

Medium

High

Education


Conclusion

Conclusion?

  • What was the hypothesis?

  • What was the alternative explanation?

  • What do we conclude about the likely cause of political tolerance?


Review

Review

  • A spurious effect is a specific case when correlation is not causation.

  • There are many reasons two variables could be correlated but not causally connected; only one of them is spurious correlation

  • The specific case is related to whether the two things correlated are caused by a third variable.

  • Correlation does not always equal causation.


An illustration with a causal model

An illustration with a causal model

A and B are spuriously correlated if:

Z

B

A


A test of whether a and b are spurious

A test of whether A and B are spurious

  • Look at the relationship between A and B, controlling for Z

  • This means, that for all values of Z, you should look at the relationship between A and B.


Scatterplot illustration of a spurious relationship

Scatterplot illustration of a spurious relationship

Z = 1 or 2

A

Z = 1

B

Z = 2

A

A

B

B


Does truth lead to reconciliation

Does truth lead to reconciliation?

  • Research question?


Does truth lead to reconciliation1

Does truth lead to reconciliation?

  • Reconciliation:

  • I find it difficult to understand the customs and ways of [the opposite racial group].

  • It is hard to imagine ever being friends with a [the opposite racial group].

  • More than most groups, [the opposite racial group] are likely to engage in crime.

  • [The opposite racial group] are untrustworthy.

  • [The opposite racial group] are selfish, and only look after the interests of their group.

  • I feel uncomfortable when I am around a group of [the opposite racial group].

  • I often don't believe what [the opposite racial group] say to me.

  • South Africa would be a better place if there were no [the opposite racial group] in the country.

  • I could never imagine being part of a political party made up mainly of [the opposite racial group].


Does truth lead to reconciliation2

Does truth lead to reconciliation?

  • Truth:

  • Apartheid was a crime against humanity. (True).

  • There were certainly some abuses under the old apartheid system, but the ideas behind apartheid were basically good ones. (False)

  • The struggle to preserve apartheid was just.

  • (False) Both those struggling for and those struggling against the old apartheid system did unforgivable things to people. (True)

  • The abuses under apartheid were largely committed by a few evil individuals, not by the state institutions themselves. (False)


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