Correlation

Question 1

What does correlation allow us to investigate?

Answer 1

The extent (strength and direction of relationship) to which 2 numerical variables are related to each other.

Question 2

What diagram is used to describe a linear relationship?

Answer 2

Scatter diagram

Question 3

What does a scatter diagram provide?

Answer 3

A visual representation of the relationship between two quantitative variables

Question 4

What is the direction in a scatter diagram indicated by?

Answer 4

A positive or negative slope

Question 5

What does the strength of the relationship between two variables on a scatter diagram depend on?

Answer 5

How closely the data points are scattered about a straight line

Question 6

What does a positive correlation mean?

Answer 6

As the x value increases so does the y value

Question 7

What does a negative correlation mean?

Answer 7

As the x value increases the y value decreases

Question 8

What is the correlation coefficient (r)?

Answer 8

A numerical measure of the strength and direction of the linear relationship between two quantitative variables.

Question 9

When calculating correlation coefficient what values do you need to find out?

Answer 9

You need to find Sxy, Sxx and Syy

• xy
• x² (xx)
• y² (yy)

Question 10

What indicates the direction of the linear relationship when the correlation coefficient has been calculated?

Answer 10

The sign of r

Positive or negative

Has to be between 1 and -1

Question 11

What indicates the strengh of the relationship when the correlation coefficient has been calculated?

Answer 11

The magnitude of r

If r is close to zero the linear relationship is very week

The strength of the association increases as r moves away from zero, approaching -1 or 1

Question 12

Why does the correlation coefficient not have any units of measurement?

Answer 12

Its value is independent of the scale of each variable

Question 13

What are the limitations of using correlation coefficient?

Answer 13

• The values of r can be adversley affected by extreme values
• Can only be used for quantitative variables
• Only describes the strength and direction of linear relationships

Question 14

What does the rank correlation coefficient show?

Answer 14

The linear relationship between two sets of ranked data

Question 15

What does r_s mean?

Answer 15

Spearmans rank correlation coefficient

Question 16

What is the equation of the rank correlation coefficient?

Answer 16

Question 17

What does n and d mean in the rank correlation coefficient formula?

Answer 17

n = the number of pairs of data values

d = the difference in ranks for each pair

Question 18

What does it mean if r_s is positive?

Answer 18

The ranks are positivley correlated

When one variable is ranked highly so is the other variable

Question 19

What does it mean if r_s is negative?

Answer 19

Higher rankings in one variable are measured against lower rankings in the other