Correlations using SPSS

Dr. Christine Pereira
Academic Skills Adviser
ask@brunel.ac.uk

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.


ASK at Brunel (2013)

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3

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



4

variables.









Curvilinear



Pearson’s r

5

variables.









Curvilinear



Spearman’s rho

6

Evaluating Strength. Graphically.
Strong relationships

Weak relationships

Y

Y

X
Y

X
Y

X

X

7

Increasing,
but not linear


Decreasing,
but not linear


8

NO relationship
Y

X



9

Curvilinear relationships
Y

X
Y

X


10

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.


11

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


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

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


13

Sign of
correlation
coefficient

Strong

+ values

0.5 to 1.0

Positive relationship

- values
Negative relationship


Moderate

Weak

Very weak
or None

-1.0 to -0.5


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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


- values



Weak

Very weak
or None

15

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


- values



Very weak
or None

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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


- values

 A coefficient of zero means NO relationship.


17

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

X

18

Exercise 3
 Which X is most strongly correlated with Y?

r
Y


X1
0.53

X2
-0.62


X3
0.21

X4
0.07

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Exercise 3
 Which X is most strongly correlated with Y?
 Which X is least correlated with Y?
r
Y


X1
0.53

X2
-0.62


X3
0.21

X4
0.07

20

Exercise 4
 Which X are most strongly correlated?

r

X1

1

X2

-0.44

1

X3

0.023

-0.71

1

X4


X1

X2

0.39

0.52

-.28


X3

X4

1

21

Exercise 4
 Which X are least correlated?
r

X1

1

X2

-0.44

1

X3

0.023

-0.71

1

X4


X1

X2

0.39

0.52

-.28


X3

X4

1

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Exercise 4
 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?


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 Measure the strength of a relationship
 They only measure association
 They do NOT imply causation!



24

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?



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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



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


Coefficient

Significance

Range of values

Btwn -1 and +1

Btwn 0 and 1

Purpose

How strongly
variables

occurred by chance?

Evaluation

Use table to
determine if weak,
medium or strong

Compare to α:



27




Coefficient

Significance

Range of values

Btwn -1 and +1

Btwn 0 and 1

Purpose

How strongly
variables

occurred by chance?

Evaluation

Use table to
determine if weak,
medium or strong

Compare to α:



28




Coefficient

Significance

Range of values

Btwn -1 and +1

Btwn 0 and 1

Purpose

How strongly
variables

occurred by chance?

Evaluation

Use table to
determine if weak,
medium or strong

Compare to α:



29




Coefficient

Significance

Range of values

Btwn -1 and +1

Btwn 0 and 1

Purpose

How strongly
variables

occurred by chance?

Evaluation

Use table to
determine if weak,
medium or strong

Compare to α:



30




Coefficient

Significance

Range of values

Btwn -1 and +1

Btwn 0 and 1

Purpose

How strongly
variables

occurred by chance?

Evaluation

Use table to
determine if weak,
medium or strong

Compare to α:



31

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?


32

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.



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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



34



35

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.


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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.



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Relationships/Association

r = Pearson’s r
ρ = Spearman’s rank
τ = Kendall’s tau
Χ2 = Chi-square test


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Example 5. Age vs Income


39




40



r = Pearson’s r


41


Example 6. Age Groups (3 grps) vs Income



42





43




ρ = Spearman’s rank


44


What happens if I
end up here?!


45


Recode your scale
variable into groups

– converting it to
an ordinal variable


46


**use τ instead of ρ if n is small or if the
observed count between 2 groups
(crosstabs) is small.


47


Effect Size
Phi – 2 x 2 table
Cramer’s V – bigger than 2 x 2 table


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But which one gives ‘better’ results?



49

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



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Click here



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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!!



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54


Variables to be
correlated go here

Tick the correct correlation
coefficient here
Puts * when p < 0.05
Puts ** when p < 0.01


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Correlations using SPSS

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