2. Upon completion of this workshop, you will be able to:
ONE
Understand the difference between strength and significance for correlation
coefficients.
TWO
Choose the correct correlation coefficient to use based on the data.
THREE
Obtain correlations in SPSS and interpret the output.
Dr. Christine Pereira
ASK at Brunel (2013)
2
4. Correlation Coefficients
Measure the strength of a relationship between
variables.
First make a scatter plot
x-axis: Independent variable
y-axis: Dependent variable
What shape does the scatter plot make?
Linear (i.e., “straight line”)
Always increasing, but not linear
Always decreasing, but not linear
Curvilinear
Dr. Christine Pereira
ASK at Brunel (2013)
4
5. Correlation Coefficients
Measure the strength of a relationship between
variables.
First make a scatter plot
x-axis: Independent variable
y-axis: Dependent variable
What shape does the scatter plot make?
Linear (i.e., “straight line”)
Always increasing, but not linear
Always decreasing, but not linear
Curvilinear
Dr. Christine Pereira
ASK at Brunel (2013)
Pearson’s r
5
6. Correlation Coefficients
Measure the strength of a relationship between
variables.
First make a scatter plot
x-axis: Independent variable
y-axis: Dependent variable
What shape does the scatter plot make?
Linear (i.e., “straight line”)
Always increasing, but not linear
Always decreasing, but not linear
Curvilinear
Dr. Christine Pereira
ASK at Brunel (2013)
Spearman’s rho
6
11. Evaluating Strength. Graphically.
Both lines have
the same
correlation
coefficient
The correlation is NOT the steepness of the line.
The correlation is how close the data points are to a
line or curve.
Dr. Christine Pereira
ASK at Brunel (2013)
11
12. Evaluating Strength. Numerically.
Correlation coefficients are between -1 and 1.
Between -1 and 0: A negative relationship
• Higher values for the IV result in lower values for the DV
Y
Y
X
X
* IV stands for Independent Variable and DV for Dependent Variable
Dr. Christine Pereira
ASK at Brunel (2013)
12
13. Evaluating Strength. Numerically.
Correlation coefficients are between -1 and 1.
Between 0 and 1: A positive relationship
• Higher values for the IV result in higher values for the DV
Y
Y
X
X
* IV stands for Independent Variable and DV for Dependent Variable
Dr. Christine Pereira
ASK at Brunel (2013)
13
14. Evaluating Strength. Numerically.
Correlation coefficients are between -1 and 1.
Sign of
correlation
coefficient
Strong
+ values
0.5 to 1.0
Positive relationship
- values
Negative relationship
Dr. Christine Pereira
Moderate
Weak
Very weak
or None
-1.0 to -0.5
ASK at Brunel (2013)
14
15. Evaluating Strength. Numerically.
Correlation coefficients are between -1 and 1.
Sign of
correlation
coefficient
Strong
Moderate
+ values
0.5 to 1.0
0.3 to 0.49
-1.0 to -0.5
-0.49 to -0.3
Positive relationship
- values
Negative relationship
Dr. Christine Pereira
ASK at Brunel (2013)
Weak
Very weak
or None
15
16. Evaluating Strength. Numerically.
Correlation coefficients are between -1 and 1.
Sign of
correlation
coefficient
Strong
Moderate
Weak
+ values
0.5 to 1.0
0.3 to 0.49
0.1 to 0.29
-1.0 to -0.5
-0.49 to -0.3
-0.29 to -0.1
Positive relationship
- values
Negative relationship
Dr. Christine Pereira
ASK at Brunel (2013)
Very weak
or None
16
17. Evaluating Strength. Numerically.
Correlation coefficients are between -1 and 1.
Sign of
correlation
coefficient
Strong
Moderate
Weak
Very weak
or None
+ values
0.5 to 1.0
0.3 to 0.49
0.1 to 0.29
0 to 0.09
-1.0 to -0.5
-0.49 to -0.3
-0.29 to -0.1
-0.09 to 0
Positive relationship
- values
Negative relationship
A coefficient of zero means NO relationship.
Dr. Christine Pereira
ASK at Brunel (2013)
17
18. Exercise 2
Match r to the most appropriate scatter plot.
Y
Y
r = -0.9
X
r = 0.6
r=0
Y
X
Y
r = -0.5
X
Dr. Christine Pereira
X
ASK at Brunel (2013)
18
19. Exercise 3
Which X is most strongly correlated with Y?
r
Y
Dr. Christine Pereira
X1
0.53
X2
-0.62
ASK at Brunel (2013)
X3
0.21
X4
0.07
19
20. Exercise 3
Which X is most strongly correlated with Y?
Which X is least correlated with Y?
r
Y
Dr. Christine Pereira
X1
0.53
X2
-0.62
ASK at Brunel (2013)
X3
0.21
X4
0.07
20
21. Exercise 4
Which X are most strongly correlated?
r
X1
1
X2
-0.44
1
X3
0.023
-0.71
1
X4
Dr. Christine Pereira
X1
X2
0.39
0.52
-.28
ASK at Brunel (2013)
X3
X4
1
21
22. Exercise 4
Which X are most strongly correlated?
Which X are least correlated?
r
X1
1
X2
-0.44
1
X3
0.023
-0.71
1
X4
Dr. Christine Pereira
X1
X2
0.39
0.52
-.28
ASK at Brunel (2013)
X3
X4
1
22
23. Exercise 4
Which X are most strongly correlated?
Which X are least correlated?
r
X1
X2
X3
X1
1
X2
-0.44
1
X3
0.023
-0.71
1
X4
0.39
0.52
-.28
X4
1
Why are these correlation coefficients 1?
Dr. Christine Pereira
ASK at Brunel (2013)
23
24. Correlation Coefficients
Measure the strength of a relationship
They only measure association
They do NOT imply causation!
Dr. Christine Pereira
ASK at Brunel (2013)
24
25. Example 2. Correlation ≠ Causation
Which variable is dependent? Independent?
Estimate the strength of the correlation:
Weak, moderate or strong?
Does age cause IQ to increase?
Dr. Christine Pereira
ASK at Brunel (2013)
25
26. Strength vs Significance
There are TWO parts to correlations:
Strength – Correlation coefficient
Significance – p-value vs. α (usually 1% or 5%)
Coefficient
Significance
Range of values
Btwn -1 and +1
Btwn 0 and 1
Purpose
How strongly
correlated are the two
variables
Is the observed correlation
significant OR has it just
occurred by chance?
Evaluation
Use table to
determine if weak,
medium or strong
Compare to α:
If p<α, significant correlation
If p>α, non-sig. correlation
Dr. Christine Pereira
ASK at Brunel (2013)
26
27. Strength vs Significance
There are TWO parts to correlations:
Strength – Correlation coefficient
Significance – p-value vs. α (usually 1% or 5%)
Coefficient
Significance
Range of values
Btwn -1 and +1
Btwn 0 and 1
Purpose
How strongly
correlated are the two
variables
Is the observed correlation
significant OR has it just
occurred by chance?
Evaluation
Use table to
determine if weak,
medium or strong
Compare to α:
If p<α, significant correlation
If p>α, non-sig. correlation
Dr. Christine Pereira
ASK at Brunel (2013)
27
28. Strength vs Significance
There are TWO parts to correlations:
Strength – Correlation coefficient
Significance – p-value vs. α (usually 1% or 5%)
Coefficient
Significance
Range of values
Btwn -1 and +1
Btwn 0 and 1
Purpose
How strongly
correlated are the two
variables
Is the observed correlation
significant OR has it just
occurred by chance?
Evaluation
Use table to
determine if weak,
medium or strong
Compare to α:
If p<α, significant correlation
If p>α, non-sig. correlation
Dr. Christine Pereira
ASK at Brunel (2013)
28
29. Strength vs Significance
There are TWO parts to correlations:
Strength – Correlation coefficient
Significance – p-value vs. α (usually 1% or 5%)
Coefficient
Significance
Range of values
Btwn -1 and +1
Btwn 0 and 1
Purpose
How strongly
correlated are the two
variables
Is the observed correlation
significant OR has it just
occurred by chance?
Evaluation
Use table to
determine if weak,
medium or strong
Compare to α:
If p<α, significant correlation
If p>α, non-sig. correlation
Dr. Christine Pereira
ASK at Brunel (2013)
29
30. Strength vs Significance
There are TWO parts to correlations:
Strength – Correlation coefficient
Significance – p-value vs. α (usually 1% or 5%)
Coefficient
Significance
Range of values
Btwn -1 and +1
Btwn 0 and 1
Purpose
How strongly
correlated are the two
variables
Is the observed correlation
significant OR has it just
occurred by chance?
Evaluation
Use table to
determine if weak,
medium or strong
Compare to α:
If p<α, significant correlation
If p>α, non-sig. correlation
Dr. Christine Pereira
ASK at Brunel (2013)
30
31. Strength vs Significance
There are TWO parts to correlations:
Strength – Correlation coefficient
Significance – p-value vs. α (usually 1% or 5%)
Coefficient
Significance
Range of values
Btwn -1 and +1
Btwn 0 and 1
Purpose
How strongly
correlated are the two
variables
Is the observed correlation
significant OR has it just
occurred by chance?
Evaluation
Use table to
determine if weak,
medium or strong
Compare to α:
If p<α, significant correlation
If p>α, non-sig. correlation
Dr. Christine Pereira
ASK at Brunel (2013)
31
32. Example 4.
r
Exam %
Exam
Anxiety
Exam %
-
Exam
Anxiety
Revision
Time
-0.441
-
.397
-.709
Revision
Time
-
How do we know if the correlation
between two variables is significant?
Dr. Christine Pereira
ASK at Brunel (2013)
32
33. Example 4. Let α = 0.05
r
Exam %
Exam %
-
Exam
Anxiety
Revision
Time
-0.441
.001
Exam
Anxiety
Revision
Time
Significance value
(p-value)
.397
-.709
.062
-
.000
p>α
H0: Correlation is not statistically significant.
p<α
H1: Correlation is statistically significant.
Dr. Christine Pereira
ASK at Brunel (2013)
33
34. Example 4. Conclusion for Anxiety vs Exam %
r = -.441, p = .001 and α = .05
p<α
Reject H0 in favour of H1.
There is strong evidence that a statistically significant
relationship exists between anxiety and exam score.
The relationship between student’s anxiety before an exam
is moderately negatively correlated with their exam score.
• Negative means higher scores for the IV resulted in lower
scores for the DV
Dr. Christine Pereira
ASK at Brunel (2013)
34
36. Levels of Measurement
Types of Data
Categorical
Scale
Qualitative
Quantitative
Nominal
Ordinal
(Unranked categories)
(Ranked categories)
Marital Status
Political Party
Eye Color
Satisfaction level
Level of agreement
Not Grouped
Age in years
Time
Weight
Height
No. of cars
No. of students
Determines types of correlation coefficients used to
analyse your variables.
Dr. Christine Pereira
ASK at Brunel (2013)
36
37. Parametric vs. Non-parametric
Parametric data
Usually, we are assuming normally distributed.
Typically, scale data are considered parametric
...but this assumption should still be checked.
Non-parametric data
Not assuming that the data is normally distributed
All nominal and ordinal data.
Sometimes scale data.
Dr. Christine Pereira
ASK at Brunel (2013)
37
49. But which one gives ‘better’ results?
Dr. Christine Pereira
ASK at Brunel (2013)
49
50. But which one gives ‘better’ results?
Do honest research:
Choose the coefficient that is most appropriate for
your data!
Do not choose the coefficient that gives you ‘better’
results!!
Your aim is accuracy
Dr. Christine Pereira
ASK at Brunel (2013)
50
53. Correlation Coefficients in SPSS
Download and Save EmployeeSurvey.sav from
Blackboard.
Under My Organisations select Academic Skills
Open SPSS 20
Open EmployeeSurvey.sav from within SPSS
If you try to open the file first SPSS will crash!!
Dr. Christine Pereira
ASK at Brunel (2013)
53
55. Correlation Coefficients in SPSS
Variables to be
correlated go here
Tick the correct correlation
coefficient here
Puts * when p < 0.05
Puts ** when p < 0.01
Dr. Christine Pereira
ASK at Brunel (2013)
55