Deck 20: Nonparametric and Resampling Statistical Tests

Question 1

In the previous question, the most appropriate test would be

A) the Mann-Whitney test.
B) the Wilcoxon signed-ranks test.
C) Friedman's test.
D) the Kruskal-Wallis test.

Answer 1

the Wilcoxon signed-ranks test.

Question 2

With at least some distribution-free tests, a two-tailed test

A) is not appropriate.
B) requires an additional calculation.
C) is more likely to be significant than a one-tailed test.
D) is automatic.

Answer 2

requires an additional calculation.

Question 3

A distribution-free test

A) is almost synonymous with a nonparametric test.
B) is a test that makes few assumptions about the distribution from which the data were drawn.
C) usually has less power than a parametric test.
D) all of the above

Answer 3

all of the above

Question 4

When the assumptions behind parametric tests are not met,

A) they are not useful tests.
B) they cannot even be computed.
C) distribution-free tests may have more power.
D) none of the above

Question 5

When using Wilcoxon's test for paired samples, subjects whose two scores are equal, yielding a difference score of zero, are usually

A) given a random sign.
B) omitted from the data.
C) punished.
D) given a plus sign for one score and a minus sign for another.

Question 6

Distribution-free tests are

A) more sensitive to the effects of outliers than parametric tests.
B) more sensitive to the effects of scores near the mean than parametric tests.
C) largely unaffected by the presence of outliers.
D) both a and c

Question 7

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

A) flip a coin.
B) use a random number table.
C) assign tied ranks.
D) throw out the tied data.

Question 8

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

A) we have too few subjects for a parametric test.
B) there are some outliers that we don't want to have undue influence on the results.
C) the data are normally distributed.
D) the subjects are all male.

Question 9

Wilcoxon's test for paired samples focuses on

A) the mean of the two samples.
B) the sign of the difference scores.
C) the relative magnitude of the difference scores.
D) both b and c

Question 10

One of the unusual things about distribution-free tests is that they are often set up so that

A) they only work with equal sample sizes.
B) the null hypothesis is never assumed to be true.
C) we reject the null hypothesis when our test statistic is too small, rather than too large.
D) they are all named after people.

Question 11

If the usual assumptions behind parametric tests are met (at least approximately),

A) distribution-free tests are more powerful than parametric tests.
B) distribution-free tests are somewhat less powerful than parametric tests.
C) the tests are indistinguishable.
D) you shouldn't use a parametric test.

Question 12

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

A) Friedman's test really won't handle these data.
B) Friedman's test will not use some of the information inherent in the data.
C) Milton Friedman is a conservative economist, and we only like liberal psychologists.
D) We really should use Friedman's test.

Question 13

The major advantage of distribution-free tests is that

A) they do not rely on assumptions as severe as those for parametric tests.
B) they have more power.
C) they are substantially easier to run.
D) they are more common.

Question 14

Each of the distribution-free tests that are covered in the book deal with

A) ranks.
B) means.
C) standard deviations.
D) raw data.

Question 15

Distribution-free tests and parametric tests differ in their null hypotheses in that

A) distribution-free tests have a less specific null hypothesis.
B) distribution-free tests make very strong assumptions about the mean.
C) distribution-free tests don't really have a null hypothesis.
D) parametric tests have rather loose null hypotheses.

Question 16

If the null hypothesis is true and we run the Mann-Whitney test on our data, the expectation is that

A) the difference scores will all be zero.
B) the test will be significant.
C) the sum of the ranks in the two groups will be approximately equal (assuming equal sample sizes).
D) the number of subjects in each group will be about the same.

Question 17

Which of the following is a nonparametric procedure?

A) a , t test.
B) the analysis of variance.
C) the Mann-Whitney test.
D) Pearson's correlation coefficient ( r ).

Question 18

When we speak about rank-randomization tests we are talking about procedures that

A) deal with ranks.
B) ask how ranks would be distributed if the data were random.
C) form the basis of many distribution-free tests.
D) all of the above

Question 19

When we have relatively large sample sizes, the distribution-free tests for comparing two groups or sets of data discussed in the text have

A) a chi-square approximation.
B) a normal approximation.
C) no solution.
D) problems.

Question 20

Which of the distribution-free tests is roughly equivalent to the t test for two independent means?

A) the Mann-Whitney test
B) Wilcoxon's signed-ranks matched-pairs test
C) Friedman's test
D) the Kruskal-Wallis test

Question 21

Distribution free tests are more sensitive to means than to medians.

Question 22

The ranks of these numbers: 1, 5, 2, 4, 5 are 1, 4.5, 2, 3, 4.5.

Question 23

The Mann-Whitney test is to independent samples t test as Wilcoxon's matched-pairs signed-ranks test is to

A) Kruskal-Wallis ANOVA.
B) one-way repeated-measures ANOVA.
C) related sample means t-test.
D) Friedman's rank test for k correlated samples.

Question 24

As the sample size increases, non-parametric statistics approach normal.

Question 25

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

Question 26

Would you reject or retain the null hypothesis in a Mann-Whitney test given the following information and assuming a one-tailed test and α = .05:
a. n₁ = 1, n₂ = 25, W = 3
b. n₁ = 5, n₂ = 6, W = 14
c. n₁ = 8, n₂ = 9, W = 60

Question 27

When using Wilcoxon's matched pairs-signed ranks test, the rank of the difference between related scores is calculated.

Question 28

The Kruskal-Wallis test is based on

A) the t distribution.
B) the z distribution.
C) the χ ² distribution.
D) the F distribution.

Question 29

Friedman's rank test for k-related samples is to Wilcoxon's matched-pairs signed ranks test as a repeated-measures ANOVA is to a paired samples t-test.

Question 30

Friedman's rank test for k-correlated samples is used to assess the degree of association between ranks, much like a correlation coefficient.

Question 31

The Mann-Whitney test is used to compare the rank scores of two groups.

Question 32

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 α = .05:
a. n = 5, T = 0
b. n = 12, T = 19
c. n = 28, T = 129

Question 33

In distribution-free tests, you usually reject the null hypothesis when the obtained value is smaller than the critical value.

Question 34

Non-parametric tests are those that do not rely on parameter estimation or strong assumptions about distributions.

Question 35

Distribution-free tests tend to be greatly affected by outliers.

Question 36

The Kruskal-Wallis test is appropriate when

A) we have several independent groups.
B) we want to compare group medians rather than means.
C) we are worried about outliers.
D) all of the above

Question 37

The Friedman test

A) ranks the scores within each subject.
B) is appropriate when we have several repeated measures on each subject.
C) is largely insensitive to outliers.
D) all of the above

Question 38

One major argument promoting the use of parametric tests over distribution-free tests is that parametric tests are

A) easier to calculate.
B) usually robust enough to be unaffected by violation of assumptions.
C) less affected by outliers than distribution-free tests.
D) used less frequently and therefore must be more elite.

Question 39

The following depression data using the two-tailed Mann-Whitney test. Describe your conclusions.

Question 40

Under what conditions would you calculate
in the Mann-Whitney test?

Question 41

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.

Question 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.

Question 43

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.

Question 44

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.

Question 45

Re-analyze the previous data using the normal approximation
a. Calculate and interpret z .
b. Which analysis is more appropriate? Explain.