Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

524 CHAPTER 15 | Correlation
STEP 2
Compute the Pearson correlation For these data, the Pearson correlation is
r 5
SP 5 40
ÏSS X
SS Y
Ï40s54d 5 40
Ï2160 5 40
46.48 5 0.861
In Step 1, our preliminary estimate for the correlation was between +0.80 and +0.90. The
calculated correlation is consistent with this estimate.
STEP 3
Evaluate the significance of the correlation The null hypothesis states that, for the
population, there is no linear relationship between X and Y, and that the value obtained for
the sample correlation is simply the result of sampling error. Specifically, H 0
says that the
population correlation is zero (ρ = 0). With n = 5 pairs of X and Y values the test has df = 3.
Table B.6 lists a critical value of 0.878 for a two-tailed test with α = .05. Because our correlation
is smaller than this value, we fail to reject the null hypothesis and conclude that the
correlation is not significant.
PROBLEMS
1. What information is provided by the sign (+ or –) of
the Pearson correlation?
2. What information is provided by the numerical value
of the Pearson correlation?
3. Calculate SP (the sum of products of deviations) for
the following scores. Note: Both means are whole
numbers, so the definitional formula works well:
X
Y
4 5
0 2
1 1
3 4
4. Calculate SP (the sum of products of deviations) for
the following scores. Note: Both means are decimal
values, so the computational formula works well:
5. For the following scores,
X
Y
0 4
1 1
0 5
4 1
2 1
1 3
X
Y
2 7
5 4
4 7
7 5
2 6
4 7
a. Sketch a scatter plot showing the six data points.
b. Just looking at the scatter plot, estimate the value
of the Pearson correlation.
c. Compute the Pearson correlation.
6. For the following scores,
X
Y
0 4
2 9
1 6
1 9
a. Sketch a scatter plot and estimate the Pearson
correlation.
b. Compute the Pearson correlation.
7. For the following scores,
X
Y
4 0
1 5
1 0
4 5
a. Sketch a scatter plot and estimate the Pearson
correlation.
b. Compute the Pearson correlation.
8. For the following scores,
X
Y
3 6
5 5
6 0
6 2
5 2
a. Sketch a scatter plot and estimate the value of the
Pearson correlation.
b. Compute the Pearson correlation.