Spurious Relationship

1
Spurious Relationship

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

2
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)

3
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?

4
Causal Mechanism?
International business conditions prices and
salaries increasing everywhere
Ministers salaries
Price of rum
5
Popular Study Smoking causes bad grades

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

6
News reports

• Bottled water causes healthier babies
• Drinking tea makes you less likely to contract
  lung cancer

7
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.

8
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.

9
Relationship between Education and Political
Tolerance



High
Political Tolerance
Medium
Low
Low
Medium
High
Education
10
Relationship between Education and Political
Tolerance
12.5 16.5 75
12.5 66.6 22.2
75 16.5 11.1
High
Political Tolerance
Medium
Low
Low
Medium
High
Education
11
Controlling for IQ

• X high IQ
• Y low IQ

12
Education and Political Tolerance
xx xxy xxxx xxxx xxyy
xyy xxxx xxyy yyyy xxy
yyyy yyyy xxxx xyy yy
High
Political Tolerance
Medium
Low
Low
Medium
High
Education
13
Education and Political Tolerance - High IQ
xx xx xxxx xxxx xx
x xxxx xx xx
xx x
High
Political Tolerance
Medium
Low
Low
Medium
High
Education
14
Education and Political Tolerance - High IQ
40.0 22.2 83.3
20.0 66.7 17.7
40.0 11.1
High
Political Tolerance
Medium
Low
Low
Medium
High
Education
15
Education and Political Tolerance - Low IQ
y yy
yy yy yyyy y
yyyy yyyy yy yy
High
Political Tolerance
Medium
Low
Low
Medium
High
Education
16
Education and Political Tolerance - Low IQ
11.1 40.0
17.7 66.7 20.0
83.3 22.2 40.0
High
Political Tolerance
Medium
Low
Low
Medium
High
Education
17
Conclusion?

• What was the hypothesis?
• What was the alternative explanation?
• What do we conclude about the likely cause of
  political tolerance?

18
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.
• Correlation does not always equal causation.

19
An illustration with a causal model
A and B are spuriously correlated if
Z
B
A
20
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.

21
Crosstab analysis testing for spurious
relationships, part I (z 1 or 2)
B 1 B 2
A 1 70 40
A 2 30 60
22
Crosstab analysis testing for spurious
relationships, part 2 (z 1)
B 1 B 2
A 1 55 50
A 2 45 50
23
Crosstab analysis testing for spurious
relationships, part 3 (z 2)
B 1 B 2
A 1 50 45
A 2 50 55
24
Scatterplot illustration of a spurious
relationship
Z 1 or 2
A
Z 1
B
Z 2
A
A
B
B