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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