Pearson's
Product Moment Correlation Coefficient
Software
Output
Example
of one bivariate comparison with a scattergram. Comparing individual income in U.S.
dollars to years of education.
Pearson's
Correlation
INCOME: A
21779.0|
* *
|
* * *
|
* * * *
|
* *
*
14030.0|
*
*
| * * * * * *
| * *
| * *
| *
*
6281.0| *
*
---------------|--------------|
4.0 12.0 20.0
EDUC: B
Number
of cases: 32
Missing:
0 C
Pearson
Correlation: 0.751 D
p
< (2-tailed signif.): 0.0000 E
A
The Y axis of the scattergram. If theory suggests cause and effect, the Y axis is
commonly used for the dependent (response) variable.
B The X axis of the scattergram. If theory suggests cause and effect, the X axis is
commonly used for the independent variable.
C Since each observation (case) must have values
for both income and education, any observations where one or both of these variables have
no data will be removed from the analysis.
D Pearson correlation coefficient representing a
high positive correlation between education and income.
Interpretation: As years of education increases so does personal income.
E There is a statistically significant
association between income and education.
Correlation
Matrix
Example
of multiple bivariate comparisons displayed in a correlation matrix. Comparing individual income, education, and months
of work experience.
Correlation:
Pearson (R) Coefficients
--------------------------------------------
Coeff |
Correlation Matrix
|
Cases
|--------------------------------|
p < | INCOME |
EDUC | WORKEXP |
--------------------------------------------
INCOME | 1.000 A| 0.751 D|
-0.160 F|
| 32 B| 32
| 32
|
| . C| 0.000 E| 0.381 G|
--------------------------------------------
EDUC | 0.751 |
1.000 | -0.520 |
| 32 | 32 | 32 |
| 0.000 |
. |
0.002 |
--------------------------------------------
WORKEXP | -0.160 |
-0.520 | 1.000 |
| 32 | 32 | 32 |
| 0.381 |
0.002 |
. |
--------------------------------------------
2-tailed
significance tests
'.'
p-value not computed
A
The diagonal in the matrix represents Pearson
correlations between the same variable which will always be 1 since the variables are
identical. The correlations above the diagonal are a mirror reflection of these below the
diagonal, so you only interpret half of the matrix (in this case three correlation
coefficients).
B The number of paired observations for this
comparison.
C A statistical test is not performed when you
are comparing a variable to itself. Mathematically
this will always equal zero.
D Pearson correlation coefficient representing a
high positive correlation between education and income.
Interpretation: As years of education increases so does personal income.
E There is a statistically significant
association between income and education.
F Pearson correlation coefficient representing a
very weak negative correlation between work experience and income. Interpretation: As years of work experience
increases personal income decreases.
G There is not a statistically significant
association between work experience and income.
|
