Last time we looked at how to do a paired t-test analysis,
today we look at correlations. This examines whether 2 variables are related.
An example might be the time to complete an exam and the person's grade on the
exam. Our research question is – are the two variables related? Our null
hypothesis is that there will be no difference. Remember that a correlation
tells you 3 things about the relationship: (1) the direction of the relationship. In a positive correlation as one
variable increases the other increases. In a negative correlation, the 2
variables go in opposite directions – as one increases the other decreases. 2) The form of the relationship. The most
common type of correlation is the Pearson correlation, which measures a linear
(straight-line) relationship. However, there are other types of correlations.
3) The degree of the relationship. In
a Pearson correlation, it looks at how well the data fit a straight line. A
perfect correlation, which is absolutely on the line, would be a 1.0. At the
other extreme, data with no relationship would be a 0, and have no relationship
to a straight line.
Let's do an example of a Pearson correlation together. So
open SPSS and enter the following data for your sample:
Under Variable view (see tab at bottom of page), It should
look like:
|
Name
|
Type
|
Width
|
Decimals
|
Label
|
Values
|
Ignore the rest
|
|
Examtime
|
numeric
|
8
|
0
|
Time to complete exam
|
None
|
Ignore the rest
|
|
Grade
|
numeric
|
8
|
0
|
Exam grade
|
None
|
Ignore the rest
|
|
Examtime
|
Grade
|
|
20
|
63
|
|
45
|
89
|
|
36
|
75
|
|
59
|
92
|
|
56
|
96
|
|
27
|
66
|
|
39
|
70
|
|
52
|
89
|
|
43
|
82
|
|
55
|
99
|
Go to Analyze/ Correlate/ Bivariate. Move both of your variables into Variables. Click options and include means and standard deviations. Press Continue. Make sure Pearson, two-tailed, and Flag significant correlations are checked. Press ok.
Your results should look like the following:
|
Descriptive Statistics
|
|||
|
|
Mean
|
Std. Deviation
|
N
|
|
Time to complete exam
|
43.20
|
12.925
|
10
|
|
Exam grade
|
82.10
|
12.879
|
10
|
|
Correlations
|
|||
|
|
Time to complete exam
|
Exam grade
|
|
|
Time to complete exam
|
Pearson Correlation
|
1
|
.943**
|
|
Sig. (2-tailed)
|
|
.000
|
|
|
N
|
10
|
10
|
|
|
Exam grade
|
Pearson Correlation
|
.943**
|
1
|
|
Sig. (2-tailed)
|
.000
|
|
|
|
N
|
10
|
10
|
|
|
**. Correlation is significant at the 0.01 level
(2-tailed).
|
|||
To really understand what is going on, we need to do a
scatterplot. To do this, go to Graphs /Chart Builder /Scatter/Dot. Move the top
left example to the box on top right. Move Time to complete on Y axis and Exam
grade to X axis. Press ok.
It should look like this:
What does this
mean? Time to complete the exam is significantly related to the exam grade. So
let's write it up as you would in your paper:
A Pearson correlation was conducted comparing the time to
complete the exam (M = 43.2; SD = 12.93)
to the exam grade (M = 82.1; SD = 12.88).
The result (r(10) = .943, p= .0001) indicates that there is a
significant positive relationship between the two variables and the null
hypothesis is rejected.
What happens if the results were NOT significantly
different, as in this example?
Go back to Data View and enter the following:
|
Examtime
|
Grade
|
|
20
|
88
|
|
45
|
45
|
|
36
|
26
|
|
59
|
95
|
|
56
|
73
|
|
27
|
89
|
|
39
|
56
|
|
52
|
78
|
|
43
|
79
|
|
55
|
90
|
A great resource for SPSS is
Pallant, J. (2013). The
SPSS Survival Manual, 5th edition. Open University Press.
Next time, we will look at ANOVAs. Do you have an issue or a
question that you would like me to discuss in a future post? Send me an email
with your ideas. leann.stadtlander@waldenu.edu
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