Chapter 4. Positive and Negative Correlations

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A correlation describes a relationship between two variables. Correlations are usually shown on a graph called a scatterplot. Each point on a scatterplot represents a single person or thing.

We can construct a scatterplot from the scores in the table below.

Students Variable 1 Variable 2
Harumi 30 32
Amy 10 5
Hans 25 20
Sally 70 57
Jamal 20 35
Heather 35 45
John 15 12
Keiko 42 52
Lech 50 50
Musaf 55 60
A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: thirty, thirty two; ten, five; twenty five, twenty; seventy, fifty seven; twenty, thirty five; thirty five, forty five; fifteen, twelve; forty two, fifty two; fifty, fifty; fifty five, sixty.

A correlation coefficient (r) is a precise measure of the strength of the relationship between the two variables. The relationship can take three forms: positive correlation (r up to +1.0), negative correlation (r as low as -1.0) or no correlation (r near zero).

Correlation: Positive

A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: five, five; ten, twelve; fifteen, thirty seven; twenty, twenty two; twenty five, thirty five; thirty two, forty six; thirty eight, fifty five; forty six, fifty two; fifty two, sicty two; sixty eight, sixty.

This scatterplot shows a strong positive correlation.

People who scored high on Variable 1 tended to also have high scores on Variable 2, and vice versa.

r = +0.91.

Correlation: Negative

A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: ten, sixty one; eighteen, forty six; twenty two, fifty eight; twenty five, fifty two; sixty, sixty five; sixty five, sixty; forty five, twenty six; fifty, ten; fifty six, fifteen; sixty eight, five.

This scatterplot shows a strong negative correlation.

People who scored high on Variable 1 tended to have low scores on Variable 2.

r = -0.96.

Correlation: None

A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: ten, thirty five; twelve, fifty five; fifteen, thirty seven; twenty four, forty two; thirty, fifty; thirty two, fifteen; forty two, fifty two; forty eight, sixty; fifty two, sixty five; seventy, forty.

This scatterplot shows no correlation between the two variables.

r = +0.03 (near zero)

No Correlation

Variable 1 Variable 2
Person 1 7 34
Person 2 12 55
Person 3 17 19
Person 4 25 42
Person 5 40 54
Person 6 32 13
Person 7 48 60
Person 8 52 25
Person 9 70 40
A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: seven, thirty four; twelve, fifty five; seventeen, nineteen; twenty five, forty two; forty, fifty four; thirty two, thirteen; forty eight, sixty; fifty two, twenty five; seventy, forty

Correlation is a measure of the strength of the relationship between two variables - that is, the extent to which scores on the two variables go up or down together. Two variables are positively correlated if they systematically vary in the same direction, increasing and decreasing together. A person with a high score on the first variable would also tend to have a high score on the second variable. Two variables are negatively correlated if they vary systematically in the opposite direction, with one increasing while the other decreases. A person with a high score on the one variable would tend to have a low score on the other variable. If two variables have no correlation, a person with a high score on one variable is equally likely to have either a high or a low score on the other variable. If two variables are correlated (either positively or negatively), then a person's score on one variable can be used to predict the score on the other variable.

A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: five, five; ten, twelve; twenty, twenty; fifteen, thirty seven; twenty five, thirty two; thirty two, forty eight; forty, fifty five; forty five, fifty; fifty two, sicty two; sixty eight, fifty.

QUESTION: What correlation is shown in the scatterplot above?
1
Correct.
Incorrect.
A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: eighteen, twenty; eight, thirty two; twelve, fifty five; twenty five, forty two; thirty, fifty; thirty two, fifteen; forty two, fifty two; forty eight, sixty; fifty two, twenty five; seventy, forty

QUESTION: What correlation is shown in the scatterplot above?
1
Correct.
Incorrect.
A scatterplot shows Variable 1 plotted on the x-axis versus Variable 2 plotted on the y-axis. There are 10 points with the following approximate coordinates: twelve, sixty two; eighteen, forty five; twenty two, fifty eight; twenty five, fifty two; thirty one, thirty eight; thirty five, thirty; forty five, twenty seven; fifty, ten; fifty eight, fifteen; sixty, five.

QUESTION: What correlation is shown in the scatterplot above?
1
Correct.
Incorrect.
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