Correlation coefficient: A measure of the magnitude and ...
LP 1E: Correlation, corr and cause 1
06/14/05
Correlation
Correlation: The relationship between two variables. A
correlation occurs between a series of data, not an
individual.
Correlation coefficient: A measure of the magnitude and
direction of the relationship (the correlation) between two
variables. The closer the correlation coefficient is to +1 or
-1, the stronger the relationship.
The relationship between height and weight
Height (inches)
67
70
63
72
65
66
Al
Bonnie
Cid
Darlene
Ed
Francis
Weight (lbs.)
135
146
125
155
140
130
Weight (lbs.)
160
150
140
130
120
62
64
66
68
70
Height (inches)
72
74
LP 1E: Correlation, corr and cause 2
06/14/05
Correlation
? A positive correlation indicates that as one variable
increases, the other tends to increase. For example,
the most crowded areas of a city are the most
impoverished.
? A zero correlation indicates that there is no relation
between the two variables. For example, there is no
relation between a person¡¯s telephone number and their
IQ score.
? A negative correlation indicates that as one variable
increases, the other tends to decrease. For example,
trust in other people and cheating other people are
negatively correlated.
Positive
correlation
Zero
correlation
Negative correlation
LP D1 Correlation 3
06/14/05
Correlation
Correlation: The relationship between two variables.
Correlations predict one variable from another (the quality
of the prediction depends on the correlation coefficient).
Being able to predict one variable from another does not
show causation.
Correlation coefficient: A measure of the magnitude and
direction of the relationship (the correlation) between two
variables. The closer the correlation coefficient is to +1 or
-1, the stronger the relationship.
? A positive correlation indicates that as one variable
increases, the other tends to increase. For example,
the most crowded areas of a city are the most
impoverished.
? A zero correlation indicates that there is no relation
between the two variables. For example, there is no
relation between a person¡¯s telephone number and
their IQ score.
? A negative correlation indicates that as one variable
increases, the other tends to decrease. For example,
trust in other people and cheating other people are
negatively correlated.
LP D1 Correlation 4
06/14/05
Association / Correlation does Not Imply Causation
From the movie High Fidelity, John Cusack makes a
personal observation that people who listen to pop music
are depressed. It is the pop music causing depression, or
the depression causing people to listen to pop music, or¡
People who listen
to pop music
Associated with
Depressed
One fallacy in thinking is the belief that if two things are
associated or correlated, then there is a causal relation
between them. For example,
People who live
near power lines
Associated with
Living shorter
lives
It is known that people who live near power lines live
shorter lives. It cannot be concluded that the power lines
cause people to live shorter lives. It is generally believed
to be another factor that causes people who live under
power lines to live shorter lives.
LP D1 Correlation 5
06/14/05
Problems with correlations:
(a) A third variable
(b) Direction of causality cannot be determined
Consumption of
red wine
associated with
Reduced incidents
of heart disease
# of alcoholics in
town
associated with
Number of
churches in town
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