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

PROBLEMS 527
rank-order a set of term papers. The ranks and the
instructor’s grades for these papers are as follows:
Rank
Grade
1 A
2 B
3 A
4 B
5 B
6 C
7 D
8 C
9 C
10 D
11 F
a. Compute the Spearman correlation for these data.
(Note: You must convert the letter grades to ranks,
using tied ranks to represent tied grades.)
b. Is the Spearman correlation statistically significant?
Use a two-tailed test with α = .05.
20. It appears that there is a significant relationship
between cognitive ability and social status, at least for
birds. Boogert, Reader, and Laland (2006) measured
social status and individual learning ability for a group
of starlings. The following data represent results
similar to those obtained in the study. Because social
status is an ordinal variable consisting of five ordered
categories, the Spearman correlation is appropriate for
these data. Convert the social status categories and the
learning scores to ranks, and compute the Spearman
correlation.
Subject
Social
Status
Learning
Score
A 1 3
B 3 10
C 2 7
D 3 11
E 5 19
F 4 17
G 5 17
H 2 4
I 4 12
J 2 3
21. Problem 13 presented data showing a positive relationship
between weight and income for a sample
of professional men. However, weight was coded
in five categories that could be viewed as an ordinal
scale rather than an interval or ratio scale. If so,
a Spearman correlation is more appropriate than
a Pearson correlation.
a. Convert the weights and the incomes into ranks
and compute the Spearman correlation for the
scores in problem 13.
b. Is the Spearman correlation large enough to be
significant?
22. Problem 13 in Chapter 10 presented data showing that
varsity athletes in contact sports (football and hockey)
who were regularly exposed to head impacts had
significantly lower cognitive scores than varsity
athletes from noncontact sports. The independentmeasures
t test produced t = 2.25 with df = 14 and
a value of r 2 = 0.265 (26.5%).
a. Convert the data from this problem into a form
suitable for the point-biserial correlation (use
1 for the noncontact athletes and 0 for the contact
athletes), and then compute the correlation.
b. Square the value of the point-biserial correlation
to verify that you obtain the same r 2 value that
was computed in Chapter 10.
23. Problem 14 in Chapter 10 presented data demonstrating
that handling money can reduce the perception
of pain. In the study, one group counted money and
another group counted blank pieces of paper. After the
counting task, each participant dipped a hand into very
hot water and rated how uncomfortable it was.
a. Convert the data from this problem into a form
suitable for the point-biserial correlation (use
1 for the money and 0 for the plain paper), and
then compute the correlation.
b. Square the value of the point-biserial correlation
to obtain r 2 .
c. The t test in chapter 10 produced t = 3.57 with
df = 16. Use the equation on p. 518 to compute
the value of r 2 directly from the t statistic and its
df. Within rounding error, the value of r 2 from the
equation should be equal to the value obtained
from the point-biserial correlation.
24. Studies have shown people with high intelligence are
generally more likely to volunteer as participants in
research, but not for research that involves unusual
experiences such as hypnosis. To examine this
phenomenon, a researcher administers a questionnaire
to a sample of college students. The survey asks for the
student’s grade point average (as a measure of intelligence)
and whether the student would like to take
part in a future study in which participants would be
hypnotized. The results showed that 7 of the 10 lower
intelligence people were willing to participant but only
2 of the 10 higher intelligence people were willing.
a. Convert the data to a form suitable for computing
the phi-coefficient. (Code the two intelligence
categories as 0 and 1 for the X variable, and code
the willingness to participate as 0 and 1 for the
Y variable.)
b. Compute the phi-coefficient for the data.