Chapter 20—Nonparametric and
Distribution-Free Statistical Tests
MULTIPLE CHOICE QUESTIONS
20.1 A distribution-free test
d) *all of the above
20.2+ If the usual assumptions behind parametric tests are met (at least approximately),
20.3 Which of the following is a nonparametric procedure?
20.4 When we speak about rank-randomization tests we are talking about procedures
that
20.5+ The major advantage of distribution-free tests is that
20.6 When the assumptions behind parametric tests are not met,
Chapter 20
20.7+ Distribution-free tests are
20.8+ Which of the distribution-free tests is roughly equivalent to the t test for two
independent means?
20.9 If the null hypothesis is true and we run the Mann-Whitney test on our data, the
expectation is that
20.10+ Each of the distribution-free tests that are covered in the book deal with
20.11+ One of the unusual things about distribution-free tests is that they are often set up
so that
20.12+ With at least some distribution-free tests, a two-tailed test
20.13 When we have relatively large sample sizes, the distribution-free tests for
comparing two groups or sets of data discussed in the text have
Test Bank
20.14+ Assume that we asked 20 subjects to participate in a smoking cessation study.
We recorded their craving for a cigarette before and after applying a nicotine
patch. One reason we might want to use a distribution-free test is because
20.15+ In the previous question, the most appropriate test would be
20.16+ In the previous example of the smoking cessation study we might be tempted to
apply Friedman’s test, because it can handle similar data. This would be a bad
idea because
20.17+ Tied scores often present a problem in distribution-free tests. The most common
way to deal with them in a Mann-Whitney test is to
20.18 Distribution-free tests and parametric tests differ in their null hypotheses in that
20.19 Wilcoxon’s test for paired samples focuses on
Chapter 20
20.20 When using Wilcoxon’s test for paired samples, subjects whose two scores are
equal, yielding a difference score of zero, are usually
20.21 The Kruskal-Wallis test is appropriate when
20.22 The Kruskal-Wallis test is based on
20.23 The Friedman test
20.24+ One major argument promoting the use of parametric tests over distribution-free
tests is that parametric tests are
20.25 The Mann-Whitney test is to independent samples t test as Wilcoxon’s matched–
pairs signed-ranks test is to
TRUE/FALSE QUESTIONS
or strong assumptions about distributions.
Test Bank
obtained value is smaller than the critical value.
groups.
degree of association between ranks, much like a correlation coefficient.
difference between related scores is calculated.
pairs signed ranks test as a repeated-measures ANOVA is to a paired samples t-
test.
OPEN-ENDED QUESTIONS
20.36 Would you reject or retain the null hypothesis in a Mann-Whitney test given the
following information and assuming a one-tailed test and = .05:
a) n1 = 1, n2 = 25, W = 3
b) n1 = 5, n2 = 6, W = 14
c) n1 = 8, n2 = 9, W = 60
20.37 Would you reject or retain the null hypothesis in a Wilcoxon’s matched-pairs
signed rank test given the following information and assuming a one-tailed test
and = .05:
a) n = 5, T = 0
b) n = 12, T = 19
c) n = 28, T = 129
20.38 In a Kruskal-Wallis one-way analysis of variance, would you retain or reject the
null hypothesis given the following information:
a) H = 15.6, df = 8
b) H = 35.75, df = 25
c) H = 45.7, df = 30
20.39 Under what conditions would you calculate
‘W
in the Mann-Whitney test?
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393
20.40 The following depression data using the two-tailed Mann-Whitney test. Describe
your conclusions.
Experimental
Group
Control
Group
150
90
140
40
80
100
70
60
220
200
360
150
190
20.41 Re-analyze the previous data using the normal approximation.
a) Calculate z and describe your conclusions.
b) Which analysis is more appropriate for these data? Explain.
20.42 A teacher wanted to see if her students could complete a multiplication review
sheet more quickly after practicing for a week. The total number of seconds it
took each time are reported below. Calculate Wilcoxon’s matched pairs signed
ranks test on the following data and describe the results.
Student
1
2
3
5
6
7
8
10
11
Before
60
75
48
30
55
75
80
85
60
After
50
60
49
35
45
68
59
70
50
20.43 Re-analyze the previous data using the normal approximation
a) Calculate and interpret z.
b) Which analysis is more appropriate? Explain.
20.44 A Pediatrician wants to know if number of children in the family is related to how
early parents arrive for regularly scheduled pediatric visits. The data follow in
terms of the number of minutes early. Analyze and interpret the data using the
Kruskal-Wallis procedure.
1 Child
2 Children
3 or More Children
10
1
0
8
0
0
15
2
2.5
5
3
1.75
9
1.5
2.75
12
20
6.5
14
7
13
11
6
0.5
21
4
Test Bank
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20.45 A critic for the Food Network asked five world-renown chefs to taste three types
of olive oil and rate them on a scale from 0 to 100 where 100 represents the
highest quality. Analyze and interpret the following data using the Friedman test.
Chef
Oil 1
Oil 2
Oil 3
1
50
100
0
2
75
95
25
3
45
70
30
4
55
85
40
5
65
90
15
Answers to Open-ended Questions