MBB.IntroProb13.
ch15sec8
TRUE/FALSE
1. The Spearman rank-correlation test is a nonparametric test that uses the directions of
differences observed in a matched-pairs sample to determine whether the relative frequency
distributions of two statistical populations are identical to or different from one another .
ANS: F PTS: 1
2. The Spearman rank-correlation is a nonparametric test that 1) uses the directions of
differences observed in a matched-pairs sample to determine whether the relative frequency
distributions of two statistical populations are identical to or different from one another and 2)
determines whether a sample comes from a population with a specified median.
ANS: F PTS: 1
3. The Spearman rank correlation coefficient is calculated by first ranking the data values, and
then calculating the Pearson correlation coefficient of the ranks.
ANS: T PTS: 1
4. The population Spearman correlation coefficient is labeled , and the sample statistic used to
estimate its value is labeled .
ANS: T PTS: 1
5. To determine if a relationship exists between two variables, the hypotheses to be tested are
.
ANS: F PTS: 1
MULTIPLE CHOICE
1. The rank correlation coefficient is used when one is:
a. correlating quantitative data
b. correlating rankings of individual values for two variables
c. analyzing data which are assumed to be linearly related
d. not interested in drawing inferences from the study
e. analyzing data which are assumed to be non-linearly related
ANS: B PTS: 1
2. Which of the following statements about Spearman's rank-correlation coefficient is false?
a. It is the test statistic used in Spearmen's rank-correlation test, symbolized by .
b. It can only take on values between 0 and + 1.
c. Positive values near + 1 point to a monotonically increasing relationship between
the two variables, such that steady increases in one are associated with steady
increases in the other.
d. None of these.
e. All of these.
ANS: B PTS: 1
3. Spearman's rank-correlation coefficient can only take on values between:
a. 0 and
b. and 0
c. 1 and +1
d. and +1
e. and
ANS: C PTS: 1
4. When the relationship between two variables is monotonically decreasing, the size of
Spearman's rank-correlation coefficient may well equal:
a. 0
b. 1
c.
d.
e.
ANS: B PTS: 1
5. The Spearman rank correlation coefficient allows us to measure and test to determine whether
there is evidence of a linear relationship between two variables if:
a. one or both variables ordinal
b. both variables are interval but the normality requirement for parametric tests is not
satisfied
c. both one or both variables ordinal and both variables are interval but the normality
requirement for parametric tests is not satisfied
d. neither one or both variables ordinal nor both variables are interval but the
normality requirement for parametric tests is not satisfied
e. none of these
ANS: C PTS: 1
6. In testing at the 5% significance level, a sample of size 20 is used.
The rejection region is:
a. -.377 . 377
b. .777 or -.377
c. .450 or -.450
d. -.450 . 450
e. none of these
ANS: C PTS: 1
PROBLEM
1. Two psychometricians (educators who are experts in the field of psychological test design)
were asked to rank six designs for a new standardized college entrance exam.
This problem uses Spearman's rank correlation coefficient to see if there is a (positive)
relationship between the educators' rankings.
The null and alternate hypotheses are as follows:
(There is no association between the rank pairs)
(The correlation between the rank pairs is positive)
Describe why the test statistic is called the rank correlation coefficient.
________________________________________________________
Test Statistic:
= ______________
Rejection region (for = 0.05):
Reject if > ______________
Conclude: ______________
There ______________ sufficient evidence to indicate there is any significant positive
correlation between the educators' rankings.
What does this result mean in the context of the problem?
________________________________________________________
What is the observed significance level for this test?
______________
ANS:
The test statistic rs is called the rank correlation coefficient simply because it is the usual
correlation coefficient applied to ranks.; .657; 0.829; Do not reject the null hypothesis; is not;
The two educators do not agree on the design rankings. One would hope for a positive
correlation indicating the designs one educator thought were better, the other educator also
thought were better.; p-value > 0.05
PTS: 1
2. A professor was interested in the relationship between a student's rank on an oral exam and
the student's rank on a written exam. The professor selected 8 students at random and ranked
their scores for both the oral exam and the written exam. The following data was recorded:
Find and interpret the rank correlation between a student's rank on the oral exam and the
student's rank on the written exam.
Compute : ______________
There is ______________ relationship between the student's rank on the oral exam and the
student's rank on the written exam.
ANS:
.881; a strong
PTS: 1
3. The following paired observations were obtained on two variables x and y:
Calculate Spearman's rank correlation coefficient :
______________
Do the data present sufficient evidence to indicate a correlation between x and y? Test using
= 0.05.
Reject Region:
Reject if | | > ______________
Conclude:
______________
There ______________ correlation between x and y.
ANS:
-1; .886; Reject the null hypothesis; is a
PTS: 1
4. A school principal suspected that a teacher's attitude toward a first-grader depended on his
original judgment of the child's ability. The principal also suspected that much of that
judgment was based on the first-grader's IQ score, which was usually known to the teacher.
After three weeks of teaching, a teacher was asked to rank the nine children in his class from 1
(highest) to 9 (lowest) as to his opinion of their ability.
Do the data provide sufficient evidence to indicate a positive correlation between the teacher's
ranks and the ranks of the IQs? Use = .05.
Test Statistic:
= ______________
Reject Region:
Reject if | | > ______________
Conclude:
______________
A positive correlation ______________ between the teacher's ranks of the IQs.
ANS:
.8333; .60; Reject the null hypothesis; exists
PTS: 1
