# Spurious Relationship - PowerPoint PPT Presentation

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Spurious Relationship. A correlation between two variables that have no causal relationship; both variables are caused by another variable. Example: Water causes drunkenness. . Once a group of students decided to study empirically the causes of drunkenness.

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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

### Example: Water causes drunkenness.

• Once a group of students decided to study empirically the causes of drunkenness.

• They drank vodka and water. Got drunk.

• They drank rum and water. Got drunk.

• They drank scotch and water. Got drunk.

• They drank bourbon and water. Got drunk.

• They drank gin and water. Got drunk.

• Conclusion: Water causes drunkenness

### 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 (by city)

• Number of churches and number of homicides (by city)

• Number of libraries and number of people on drugs (over time)

### What causes the price of rum?

• There is a positive relationship between the salaries of Presbyterian ministers in Massachusetts and the price of rum in Havana.

• What is the causal mechanism?

### Causal Mechanism?

International business conditions: prices and salaries increasing everywhere

Ministers’ salaries

Price of rum

• True or spurious?

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

### News reports

• Bottled water causes healthier babies

• Drinking tea makes you less likely to contract lung cancer

### 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

• 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.”

Relationship between Education and Political Tolerance

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

Relationship between Education and Political Tolerance

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

### Controlling for IQ

• X = high IQ

• Y = low IQ

Education and Political Tolerance

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

Education and Political Tolerance - High IQ

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

Education and Political Tolerance - High IQ

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

Education and Political Tolerance - Low IQ

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

Education and Political Tolerance - Low IQ

High

Political Tolerance

Medium

Low

Low

Medium

High

Education

### Conclusion?

• What was the hypothesis?

• What was the alternative explanation?

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

### Review

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

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

### 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

• 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.

Z = 1 or 2

A

Z = 1

B

Z = 2

A

A

B

B