chap 016

Chapter 16Nonparametric Tests

True / False Questions1.Nonparametric tests can often be used in small samples.TrueFalse

2.Nonparametric tests may require special tables for small samples.TrueFalse

3.Nonparametric tests generally are more powerful than parametric tests when normality cannot be assumed.TrueFalse

4.Parametric tests generally are more powerful than nonparametric tests when normality can be assumed.TrueFalse

5.Rejection of a hypothesis using a nonparametric test is less convincing than using an equivalent parametric test since nonparametric tests generally make fewer assumptions.TrueFalse

6.Rejection of a hypothesis using a nonparametric test is more convincing than using an equivalent parametric test when the data are badly skewed.TrueFalse

7.If the population is normal, we would still prefer a nonparametric test.TrueFalse

8.Most nonparametric tests assume ordinal data.TrueFalse

9.Most nonparametric tests require data measured on a ratio scale.TrueFalse

10.The one-sample runs test compares medians of two or more groups.TrueFalse

11.The one-sample runs test uses binary data (only two possible values).TrueFalse

12.The Spearman rank correlation test compares medians of two paired data sets.TrueFalse

13.The one-sample runs test uses a test statistic that is normally distributed, as long as the number of runs of each type is large enough.TrueFalse

14.The one-sample runs test is useful to detect nonrandom patterns in time-series data.TrueFalse

15.The one-sample runs test is similar to a test for autocorrelation.TrueFalse

16.The one-sample runs test is also called the Wald-Wolfowitz test after its inventors.TrueFalse

17.The Wilcoxon signed-rank test is useful to compare one sample median with a benchmark.TrueFalse

18.The Wilcoxon signed-rank test is useful to compare more than two sample medians.TrueFalse

19.The Wilcoxon signed-rank test is analogous to a one-sample parametric test of a mean.TrueFalse

20.The Wilcoxon signed-rank test is analogous to a parametric two-sample t-test of means from independent samples.TrueFalse

21.The Wilcoxon signed-rank test is analogous to a parametric t-test comparing three or more medians.TrueFalse

22.The Wilcoxon signed-rank test is robust to outliers in the data if the population is at least somewhat symmetric.TrueFalse

23.The Wilcoxon signed-rank test does not assume a normal population, but it does require a roughly symmetric population.TrueFalse

24.The Wilcoxon signed-rank test is less powerful than a one-sample test of a mean when the population is actually normal.TrueFalse

25.The Wilcoxon signed-rank test has good power over a range of nonnormal populations.TrueFalse

26.The Wilcoxon signed-rank test is an alternative to the one-sample t-test for paired observations.TrueFalse

27.The Wilcoxon rank sum test (Mann-Whitney test) can be used as a test for equality of two population medians.TrueFalse

28.The Wilcoxon rank sum test (Mann-Whitney test) requires two independent samples.TrueFalse

29.The Wilcoxon rank sum test (Mann-Whitney test) can be used even if population variances are unequal.TrueFalse

30.The Wilcoxon rank sum test (Mann-Whitney test) utilizes the ranks of two independent samples.TrueFalse

31.The Mann-Whitney test is sometimes called the "Wilcoxon rank sum test" because it was formulated independently by different statisticians.TrueFalse

32.We sometimes call the Wilcoxon rank sum test the Mann/Whitney test, but the two are the same.TrueFalse

33.The Mann-Whitney test is analogous to a one-sample t-test comparing a mean with a benchmark.TrueFalse

34.The Kruskal-Wallis test requires c independent samples (where usually c > 2).TrueFalse

35.The Kruskal-Wallis test applies even if the c samples to be compared are not independent.TrueFalse

36.The Kruskal-Wallis test is analogous to the one-sample parametric t-test for a mean.TrueFalse

37.The Kruskal-Wallis test is analogous to the parametric one-factor ANOVA.TrueFalse

38.The Kruskal-Wallis test does not require normal populations, but it does require them to be of similar shape.TrueFalse

39.The Kruskal-Wallis test is equivalent to comparing medians in c groups.TrueFalse

40.The Kruskal-Wallis test is a test for randomness in sequential data.TrueFalse

41.The Kruskal-Wallis test is less useful in finance or marketing because normal populations can usually be assumed in financial or marketing data.TrueFalse

42.The Kruskal-Wallis test is almost as powerful as one-factor ANOVA even when normality can be assumed.TrueFalse

43.The Friedman test is a nonparametric equivalent to two-factor ANOVA without replication.TrueFalse

44.The Friedman test is a nonparametric equivalent to a parametric one-sample t-test comparing a mean with a benchmark.TrueFalse

45.The Friedman test requires groups of equal size.TrueFalse

46.The Friedman test compares medians when there are two grouping factors (rows, columns).TrueFalse

47.The Friedman test resembles the Kruskal-Wallis test except that there are two grouping factors (rows, columns) instead of one grouping factor (columns).TrueFalse

48.The Friedman test is often almost as powerful as two-factor ANOVA without replication (randomized block design).TrueFalse

49.Spearman's rank correlation always lies within the range -1.00 to +1.00.TrueFalse

50.Spearman's rank correlation coefficient lies within the range 0 to 1.00 inclusive.TrueFalse

51.Spearman's rank correlation is named for a British brewer who was testing beer samples.TrueFalse

52.Spearman's rank correlation is named for a British behavioral psychologist who was studying human intelligence.TrueFalse

53.Spearman's rank correlation is used to measure agreement in rankings of paired (x, y) data.TrueFalse

Multiple Choice Questions54.All of these are nonparametric tests except:

A.Spearman rank correlation test.

B.Friedman test.

C.Student's t-test.

D.Kruskal-Wallis test.

55.Which nonparametric test is analogous to a parametric two-sample t-test for means?

A.Wald-Wolfowitz one-sample runs test

B.Wilcoxon signed-rank test

C.Wilcoxon rank sum (Mann-Whitney) test

D.Kruskal-Wallis test

56.Which nonparametric test is analogous to a parametric k-sample test for means?

A.Kruskal-Wallis test



D.Wald-Wolfowitz one-sample runs test

57.Which nonparametric test is used to compare a one-sample median with a benchmark?





58.Which nonparametric test has no parametric counterpart?


B.Spearman rank correlation test



59.Which nonparametric test is analogous to a parametric one-sample t-test for differences in paired data?





60.Which nonparametric test would we use to compare ratings assigned to n pairs of bonds by two different rating agencies, if the bonds are rated on an ordinal scale (Aaa, Aa, A, Baa, Ba B, etc.)?





61.Which is not true of the one-sample runs test?

A.It is also called the Wald-Wolfowitz test after its inventors.

B.Its purpose is to detect nonrandomness.

C.It cannot be applied to sequential observations.

D.It is similar to a test for autocorrelation.

62.Which nonparametric test is used to detect nonrandomness in sequential observations?





63.Which is a nonparametric test for runs (autocorrelation) in a sequence of binary data?





64.Which parametric test resembles the nonparametric Spearman's rank test?

A.t-test of a correlation coefficient

B.t-test of two sample means

C.t-test of one sample mean

D.F-test of variances

65.Which nonparametric test is used to test for agreement in ranks of paired data?

A.Spearman test

B.Friedman test



66.Twenty customers are randomly chosen and each is given a sample of Nut Butter ice cream to taste. The customers rank the taste of the ice cream on a 10-point scale. Each is then given a sample of Chewy Gooey ice cream to taste and rank on a 10-point scale. Based on the 20 customers' ratings of each flavor, the research analyst conducting the survey wishes to determine if one flavor is preferred over the other. Which nonparametric test would you use to determine if there is a difference in the ratings?





67.Which is not a characteristic of the Wilcoxon rank sum (Mann-Whitney) test?

A.It can be used as a test for equality of two population medians.

B.It is analogous to a one-sample t-test comparing a mean with a benchmark.

C.It requires independent samples from populations with equal variances.

D.It is similar to one-factor ANOVA when we have c independent samples.

68.Delta Air Lines wants to determine if the number of no-shows for flights originating from Detroit are higher than from Minneapolis. A sample of 20 flights from each city is taken and the number of no-shows is determined for each flight. Which nonparametric test would you use to determine whether the number of no-shows is greater in Detroit?





69.The dean of Oxnard business school wants to know if there is a difference in computer skills in four majors (marketing, finance, operations, accounting). A 20-question skills test is given to 10 randomly chosen students in each major. Which nonparametric test could be used by the dean to see if there is a difference in computer skills of students in the various majors?

A.Wald-Wolfowitz test


C.Mann-Whitney test


70.Which is not a characteristic of the Kruskal-Wallis test?

A.It is analogous to the parametric one-factor ANOVA.

B.It does not make any assumptions about the populations.

C.It is useful in comparing the medians in c groups.

D.It does not require normal distributions of populations.

71.Individuals in four different age groups are asked to rate, on a scale of 1 to 10, three flavors of ice creams. Each group has the same number of individuals. Median ratings by the individuals are grouped by the flavor of ice cream and by age group. Which nonparametric test could be used to see if there is a difference in median ratings among the four age groups and three flavors?

A.Wilcoxon signed-rank test

B.Friedman test

C.Mann-Whitney test


72.Which nonparametric test is analogous to a two-factor ANOVA without replication?


B.Friedman test

C.Mann-Whitney test


73.If there are three or more populations with ordinal data, what is the appropriate test to determine whether the distributions are equal?

A.Friedman test

B.t-test

C.ANOVA


74.Hoping to reduce the waiting time, a doctor's office tried a new way of scheduling its appointments. Populations of waiting times are believed to be similar except in central tendency. However, waiting times may not be normally distributed so a nonparametric test was chosen to compare the waiting times. The Wilcoxon/Mann-Whitney test results are shown below:

Which is the best conclusion?

A.The medians differ at = .01.

B.The means differ at = .01.

C.The samples differ at = .01.

D.There are no differences at = .01.

75.At the Food Barn, children can order from the adult menu (A) or the child's menu (C). Below is the pattern of menu orders for 24 children last Wednesday evening.A, A, A, A, C, A, A, C, C, C, A, A, A, A, A, A, C, C, C, A, C, C, C, CWhich test would you choose to see if this pattern is random?


B.Wilcoxon rank sum (Mann-Whitney) test

C.Wald-Wolfowitz one-sample runs test

D.Wilcoxon test

76.At the Food Barn, children can order from the adult menu (A) or the child's menu (C). Below is the pattern of menu orders for 24 children last Wednesday evening.A, A, A, A, C, A, A, C, C, C, A, A, A, A, A, A, C, C, C, A, C, C, C, CWhich statement is most accurate?

A.Neither sample size (for outcomes A or C) is large enough for a runs test using z.

B.Both sample sizes (for outcomes A and C) are large enough for a runs test using z.

C.Only one outcome has a large enough sample for a runs test using z.

D.This type of data would not be suited for a runs test using z.

77.A clinic has four doctors. They wish to compare the amount of time that doctors spend with their patients. It is suspected that times may not be normally distributed but are otherwise assumed similar except in center, so a nonparametric test was chosen. The Kruskal-Wallis test results are shown below.


A.The doctors have the same median times at = .01.

B.The doctors have different median times at = .01.

C.The sample size is insufficient for this kind of test.

D.A one-factor ANOVA would be a better kind of test.

78.Returns on an investor's stock portfolio (n = 19 stocks) are compared for the same stock in each of two consecutive quarters. Since the returns are not normally distributed (normality test p-values were .005 and .126 respectively), a nonparametric test was chosen. The test results are shown below.


A.The means are the same at = .01.

B.The medians are the same at = .01.

C.The means differ at = .01.

D.The medians differ at = .01.



A.The returns are correlated neither at = .05 nor at = .01.

B.The returns are correlated at = .05 but not at = .01.

C.The returns are correlated at = .01 but not at = .05.

D.The returns are correlated both at = .05 and at = .01.

80.Attendees at an outdoor concert can buy pavilion tickets (A) or lawn tickets (B). Below is the output for the one-sample runs to test whether there is a pattern in 32 consecutive ticket purchases.

The best conclusion at = .05 would be:

A.the pattern is random.

B.there is a difference in medians.

C.the sample sizes are too small.

D.the sample sizes must be equal.

81.To compare the cost of three shipping methods, a firm shipped five orders to each of four different destinations over a six-month period. Their total shipping costs are shown below.

Which nonparametric test would you use to compare the median shipping costs among destinations and among shippers?

A.Friedman test

B.Kruskal-Wallis test


D.Lebesgue-Stieltjes test

82.At the Seymour Clinic, the total number of patients seen by three doctors over three days is as follows:

Which nonparametric test would you use to compare the median number of patients seen by the doctors on each day?

A.Wilcoxon test


C.Anderson-Darling test

D.Friedman test

83.Systolic blood pressure of randomly selected HMO patients was recorded on a particular Wednesday, with the results shown here:

The appropriate hypothesis test to compare the medians is:

A.Wilcoxon test.

B.Kruskal-Wallis test.

C.Levene's test.

D.Friedman test.

84.You do not wish to assume normality in the population, yet you wish to compare central tendency in c samples. You decide to utilize MegaStat, whose menu is shown here:

Which menu would you choose?

A.Hypothesis Tests

B.Nonparametric Tests

C.Correlation/Regression

D.Analysis of Variance

85.You do not wish to assume normality in the population, yet you wish to compare central tendency in c samples. You decide to utilize MINITAB, whose menu is shown here:


A.ANOVA

B.Regression

C.Nonparametrics

D.EDA

Chapter 16 Nonparametric Tests Answer Key

True / False Questions1.Nonparametric tests can often be used in small samples.TRUESpecial tables are required, however, when sample sizes are small.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-01 Define nonparametric tests and explain when they may be desirable.Topic: Why Use Nonparametric Tests?

2.Nonparametric tests may require special tables for small samples.TRUESpecial tables (or suitable computer software) will be required for small samples.


3.Nonparametric tests generally are more powerful than parametric tests when normality cannot be assumed.TRUEWhen justified, parametric tests generally have more power.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 16-01 Define nonparametric tests and explain when they may be desirable.Topic: Why Use Nonparametric Tests?

4.Parametric tests generally are more powerful than nonparametric tests when normality can be assumed.TRUEWhen justified, parametric tests generally have more power.


5.Rejection of a hypothesis using a nonparametric test is less convincing than using an equivalent parametric test since nonparametric tests generally make fewer assumptions.FALSERejection in a nonparametric test is persuasive because fewer assumptions are made.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 16-01 Define nonparametric tests and explain when they may be desirable.Topic: Why Use Nonparametric Tests?

6.Rejection of a hypothesis using a nonparametric test is more convincing than using an equivalent parametric test when the data are badly skewed.TRUERejection in a nonparametric test is persuasive when normality is in doubt.


7.If the population is normal, we would still prefer a nonparametric test.FALSEWhen justified, parametric tests generally have more power.

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 16-01 Define nonparametric tests and explain when they may be desirable.Topic: Why Use Nonparametric Tests?

8.Most nonparametric tests assume ordinal data.TRUEMany nonparametric tests convert ratio or interval data into ranks (ordinal data).

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-01 Define nonparametric tests and explain when they may be desirable.Topic: Why Use Nonparametric Tests?

9.Most nonparametric tests require data measured on a ratio scale.FALSEMany nonparametric tests convert ratio or interval data into ranks (ordinal data).


10.The one-sample runs test compares medians of two or more groups.FALSEThe runs test checks for randomness.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-02 Use the one-sample runs test.Topic: One-Sample Runs Test

11.The one-sample runs test uses binary data (only two possible values).TRUEData may be any sequence of two values (e.g., + or -).


12.The Spearman rank correlation test compares medians of two paired data sets.FALSETo compare medians we use a Mann-Whitney test (Wilcoxon rank sum test).

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-07 Use the Spearman rank correlation test.Topic: Spearman Rank Correlation Test

13.The one-sample runs test uses a test statistic that is normally distributed, as long as the number of runs of each type is large enough.TRUEAs long as we have enough runs of each type, we can use a normal z test.


14.The one-sample runs test is useful to detect nonrandom patterns in time-series data.TRUERandom pattern is essentially the null hypothesis.


15.The one-sample runs test is similar to a test for autocorrelation.TRUEWe can use the runs test to check for autocorrelation in regression residuals.


16.The one-sample runs test is also called the Wald-Wolfowitz test after its inventors.TRUEWald and Wolfowitz first demonstrated the runs test, so it goes by either name.


17.The Wilcoxon signed-rank test is useful to compare one sample median with a benchmark.TRUEThe null hypothesis is for one population median versus a target or benchmark.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 16-03 Use the Wilcoxon signed-rank test.Topic: Wilcoxon Signed-Rank Test

18.The Wilcoxon signed-rank test is useful to compare more than two sample medians.FALSEFor two medians, we would use the Wilcoxon rank sum test (Mann-Whitney test).


19.The Wilcoxon signed-rank test is analogous to a one-sample parametric test of a mean.TRUEThe idea is to test a measure of center (in this case, a median) against a benchmark.


20.The Wilcoxon signed-rank test is analogous to a parametric two-sample t-test of means from independent samples.FALSEFor two medians, we would use the Wilcoxon rank sum test (Mann-Whitney test).


21.The Wilcoxon signed-rank test is analogous to a parametric t-test comparing three or more medians.FALSEThe null hypothesis is for one population median versus a target or benchmark.


22.The Wilcoxon signed-rank test is robust to outliers in the data if the population is at least somewhat symmetric.TRUEThe test does require reasonably symmetric populations.


23.The Wilcoxon signed-rank test does not assume a normal population, but it does require a roughly symmetric population.TRUEThe test does require reasonably symmetric populations.


24.The Wilcoxon signed-rank test is less powerful than a one-sample test of a mean when the population is actually normal.TRUEWhen justified, a t-test of a mean would generally be more powerful.


25.The Wilcoxon signed-rank test has good power over a range of nonnormal populations.TRUEStudies show good power when populations are not too skewed.


26.The Wilcoxon signed-rank test is an alternative to the one-sample t-test for paired observations.TRUEOne version of the Wilcoxon signed-rank test utilizes paired data.


27.The Wilcoxon rank sum test (Mann-Whitney test) can be used as a test for equality of two population medians.TRUEThis test for identical populations is a test of medians if variances are equal.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 16-04 Use the Wilcoxon rank sum test for two samples.Topic: Wilcoxon Rank Sum Test

28.The Wilcoxon rank sum test (Mann-Whitney test) requires two independent samples.TRUESamples must be independent.


29.The Wilcoxon rank sum test (Mann-Whitney test) can be used even if population variances are unequal.FALSEWMW is a test for identical populations, but it is a test for equal medians if variances are equal.


30.The Wilcoxon rank sum test (Mann-Whitney test) utilizes the ranks of two independent samples.TRUERaw data in each sample are converted into ranks.


31.The Mann-Whitney test is sometimes called the "Wilcoxon rank sum test" because it was formulated independently by different statisticians.TRUEThis test has two names.


32.We sometimes call the Wilcoxon rank sum test the Mann/Whitney test, but the two are the same.TRUEThis test has two names.


33.The Mann-Whitney test is analogous to a one-sample t-test comparing a mean with a benchmark.FALSEThe Wilcoxon rank sum test (Mann-Whitney test) compares two populations.


34.The Kruskal-Wallis test requires c independent samples (where usually c > 2).TRUEKruskal-Wallis compares several populations.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

35.The Kruskal-Wallis test applies even if the c samples to be compared are not independent.FALSESamples must be independent in the Kruskal-Wallis test.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

36.The Kruskal-Wallis test is analogous to the one-sample parametric t-test for a mean.FALSEKruskal-Wallis compares several populations.


37.The Kruskal-Wallis test is analogous to the parametric one-factor ANOVA.TRUEKruskal-Wallis compares c population medians (similar to comparing c means).


38.The Kruskal-Wallis test does not require normal populations, but it does require them to be of similar shape.TRUEKruskal-Wallis is a test for identical populations but becomes a test for equal medians if population shapes are the same.


39.The Kruskal-Wallis test is equivalent to comparing medians in c groups.TRUEKruskal-Wallis is a test for identical populations, but it becomes a test for equal medians if population shapes are the same.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

40.The Kruskal-Wallis test is a test for randomness in sequential data.FALSEKruskal-Wallis compares c population medians. To test for randomness, you would use a runs test rather than a Kruskal-Wallis test.


41.The Kruskal-Wallis test is less useful in finance or marketing because normal populations can usually be assumed in financial or marketing data.FALSENormal populations are rare in many business applications, so the K-W test is useful.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

42.The Kruskal-Wallis test is almost as powerful as one-factor ANOVA even when normality can be assumed.TRUEStudies suggest that the K-W test is about as powerful as the F-test (ANOVA).


43.The Friedman test is a nonparametric equivalent to two-factor ANOVA without replication.TRUEUnreplicated ANOVA data can be tested using the Friedman test.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 16-06 Use the Friedman test for related samples.Topic: Friedman Test for Related Samples

44.The Friedman test is a nonparametric equivalent to a parametric one-sample t-test comparing a mean with a benchmark.FALSEThe Friedman test is a nonparametric equivalent to two-factor ANOVA without replication.


45.The Friedman test requires groups of equal size.TRUEBy definition, there must be one observation per cell.


46.The Friedman test compares medians when there are two grouping factors (rows, columns).TRUEWe can think of the Friedman test as comparing medians if population shape is similar.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-06 Use the Friedman test for related samples.Topic: Friedman Test for Related Samples

47.The Friedman test resembles the Kruskal-Wallis test except that there are two grouping factors (rows, columns) instead of one grouping factor (columns).TRUEThe Friedman test is analogous to unreplicated two-factor ANOVA.


48.The Friedman test is often almost as powerful as two-factor ANOVA without replication (randomized block design).TRUEThe Friedman test has good power versus two-factor unreplicated ANOVA.


49.Spearman's rank correlation always lies within the range -1.00 to +1.00.TRUESpearman's rho lies between -1 and +1.


50.Spearman's rank correlation coefficient lies within the range 0 to 1.00 inclusive.FALSESpearman's rho lies between -1 and +1.


51.Spearman's rank correlation is named for a British brewer who was testing beer samples.FALSECharles Spearman was a behavioral psychologist.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-02 Use the one-sample runs test.Topic: Spearman Rank Correlation Test

52.Spearman's rank correlation is named for a British behavioral psychologist who was studying human intelligence.TRUECharles Spearman was a behavioral psychologist studying human IQs.


53.Spearman's rank correlation is used to measure agreement in rankings of paired (x, y) data.TRUESpearman's rho is similar in this regard to the usual (Pearson) correlation.


Multiple Choice Questions54.All of these are nonparametric tests except:

A.Spearman rank correlation test.

B.Friedman test.

C.Student's t-test.

D.Kruskal-Wallis test.

Student's t-test (Chapter 10) is a parametric test.


55.Which nonparametric test is analogous to a parametric two-sample t-test for means?





The Wilcoxon rank sum (Mann-Whitney) test compares medians (assuming that populations have similar shape).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-04 Use the Wilcoxon rank sum test for two samples.Topic: Wilcoxon Rank Sum Test

56.Which nonparametric test is analogous to a parametric k-sample test for means?





The K-W test compares medians (assuming populations have similar shape).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

57.Which nonparametric test is used to compare a one-sample median with a benchmark?





The Wilcoxon signed-rank test compares a median with a benchmark or target.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-03 Use the Wilcoxon signed-rank test.Topic: Wilcoxon Signed-Rank Test

58.Which nonparametric test has no parametric counterpart?


B.Spearman rank correlation test



The runs test is not quite like any parametric test.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 16-02 Use the one-sample runs test.Topic: One-Sample Runs Test

59.Which nonparametric test is analogous to a parametric one-sample t-test for differences in paired data?





One version of the Wilcoxon signed-rank test is for paired data.


60.Which nonparametric test would we use to compare ratings assigned to n pairs of bonds by two different rating agencies, if the bonds are rated on an ordinal scale (Aaa, Aa, A, Baa, Ba B, etc.)?





One version of the Wilcoxon signed-rank test is for paired data.


61.Which is not true of the one-sample runs test?

A.It is also called the Wald-Wolfowitz test after its inventors.

B.Its purpose is to detect nonrandomness.

C.It cannot be applied to sequential observations.

D.It is similar to a test for autocorrelation.

The runs test is for randomness in a sequence of two-valued data (e.g., + and -).

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 16-02 Use the one-sample runs test.Topic: One-Sample Runs Test

62.Which nonparametric test is used to detect nonrandomness in sequential observations?






AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-02 Use the one-sample runs test.Topic: One-Sample Runs Test

63.Which is a nonparametric test for runs (autocorrelation) in a sequence of binary data?







64.Which parametric test resembles the nonparametric Spearman's rank test?

A.t-test of a correlation coefficient

B.t-test of two sample means

C.t-test of one sample mean

D.F-test of variances

The t-test of a correlation coefficient can be used to test for zero correlation.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-07 Use the Spearman rank correlation test.Topic: Spearman Rank Correlation Test

65.Which nonparametric test is used to test for agreement in ranks of paired data?

A.Spearman test

B.Friedman test



To see if the ranks agree, we could use Spearman's rho.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-07 Use the Spearman rank correlation test.Topic: Spearman Rank Correlation Test

66.Twenty customers are randomly chosen and each is given a sample of Nut Butter ice cream to taste. The customers rank the taste of the ice cream on a 10-point scale. Each is then given a sample of Chewy Gooey ice cream to taste and rank on a 10-point scale. Based on the 20 customers' ratings of each flavor, the research analyst conducting the survey wishes to determine if one flavor is preferred over the other. Which nonparametric test would you use to determine if there is a difference in the ratings?





For two independent samples, use the Wilcoxon rank sum test (Mann-Whitney).

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 16-04 Use the Wilcoxon rank sum test for two samples.Topic: Wilcoxon Rank Sum Test

67.Which is not a characteristic of the Wilcoxon rank sum (Mann-Whitney) test?

A.It can be used as a test for equality of two population medians.

B.It is analogous to a one-sample t-test comparing a mean with a benchmark.

C.It requires independent samples from populations with equal variances.

D.It is similar to one-factor ANOVA when we have c independent samples.

The Wilcoxon/Mann-Whitney test uses two samples (not c samples).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-04 Use the Wilcoxon rank sum test for two samples.Topic: Wilcoxon Rank Sum Test

68.Delta Air Lines wants to determine if the number of no-shows for flights originating from Detroit are higher than from Minneapolis. A sample of 20 flights from each city is taken and the number of no-shows is determined for each flight. Which nonparametric test would you use to determine whether the number of no-shows is greater in Detroit?





For two independent samples, use the Wilcoxon rank sum test (Mann-Whitney).

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 16-04 Use the Wilcoxon rank sum test for two samples.Topic: Wilcoxon Rank Sum Test

69.The dean of Oxnard business school wants to know if there is a difference in computer skills in four majors (marketing, finance, operations, accounting). A 20-question skills test is given to 10 randomly chosen students in each major. Which nonparametric test could be used by the dean to see if there is a difference in computer skills of students in the various majors?

A.Wald-Wolfowitz test


C.Mann-Whitney test


Because we have four samples, we would use the K-W test to compare the medians.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

70.Which is not a characteristic of the Kruskal-Wallis test?

A.It is analogous to the parametric one-factor ANOVA.

B.It does not make any assumptions about the populations.

C.It is useful in comparing the medians in c groups.

D.It does not require normal distributions of populations.

The K-W test requires populations of similar shape if we want to compare medians.


71.Individuals in four different age groups are asked to rate, on a scale of 1 to 10, three flavors of ice creams. Each group has the same number of individuals. Median ratings by the individuals are grouped by the flavor of ice cream and by age group. Which nonparametric test could be used to see if there is a difference in median ratings among the four age groups and three flavors?


B.Friedman test

C.Mann-Whitney test


This is a two-factor comparison using medians, so we would use Friedman's test.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 16-06 Use the Friedman test for related samples.Topic: Friedman Test for Related Samples

72.Which nonparametric test is analogous to a two-factor ANOVA without replication?


B.Friedman test

C.Mann-Whitney test


Friedman's test uses a two-factor experiment with one observed median per cell.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 16-06 Use the Friedman test for related samples.Topic: Friedman Test for Related Samples

73.If there are three or more populations with ordinal data, what is the appropriate test to determine whether the distributions are equal?

A.Friedman test

B.t-test

C.ANOVA


K-W is a test for identical populations (or equal medians, if populations differ only in center).


74.Hoping to reduce the waiting time, a doctor's office tried a new way of scheduling its appointments. Populations of waiting times are believed to be similar except in central tendency. However, waiting times may not be normally distributed so a nonparametric test was chosen to compare the waiting times. The Wilcoxon/Mann-Whitney test results are shown below:


A.The medians differ at = .01.

B.The means differ at = .01.

C.The samples differ at = .01.

D.There are no differences at = .01.

The p-value is less than .01 so we reject equal medians.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-04 Use the Wilcoxon rank sum test for two samples.Topic: Wilcoxon Rank Sum Test

75.At the Food Barn, children can order from the adult menu (A) or the child's menu (C). Below is the pattern of menu orders for 24 children last Wednesday evening.A, A, A, A, C, A, A, C, C, C, A, A, A, A, A, A, C, C, C, A, C, C, C, CWhich test would you choose to see if this pattern is random?


B.Wilcoxon rank sum (Mann-Whitney) test

C.Wald-Wolfowitz one-sample runs test

D.Wilcoxon test

Use the runs test for sequences that indicate a nonrandom pattern.


76.At the Food Barn, children can order from the adult menu (A) or the child's menu (C). Below is the pattern of menu orders for 24 children last Wednesday evening.A, A, A, A, C, A, A, C, C, C, A, A, A, A, A, A, C, C, C, A, C, C, C, CWhich statement is most accurate?

A.Neither sample size (for outcomes A or C) is large enough for a runs test using z.

B.Both sample sizes (for outcomes A and C) are large enough for a runs test using z.

C.Only one outcome has a large enough sample for a runs test using z.

D.This type of data would not be suited for a runs test using z.

We need 10 runs of each type to assume normality.


77.A clinic has four doctors. They wish to compare the amount of time that doctors spend with their patients. It is suspected that times may not be normally distributed but are otherwise assumed similar except in center, so a nonparametric test was chosen. The Kruskal-Wallis test results are shown below.


A.The doctors have the same median times at = .01.

B.The doctors have different median times at = .01.

C.The sample size is insufficient for this kind of test.

D.A one-factor ANOVA would be a better kind of test.

The p-value is less than .01.




A.The means are the same at = .01.

B.The medians are the same at = .01.

C.The means differ at = .01.

D.The medians differ at = .01.

The p-value is less than .01.




A.The returns are correlated neither at = .05 nor at = .01.

B.The returns are correlated at = .05 but not at = .01.

C.The returns are correlated at = .01 but not at = .05.

D.The returns are correlated both at = .05 and at = .01.

The correlation differs from zero at =.05 and .01 (close decision).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-07 Use the Spearman rank correlation test.Topic: Spearman Rank Correlation Test

80.Attendees at an outdoor concert can buy pavilion tickets (A) or lawn tickets (B). Below is the output for the one-sample runs to test whether there is a pattern in 32 consecutive ticket purchases.

The best conclusion at = .05 would be:

A.the pattern is random.

B.there is a difference in medians.

C.the sample sizes are too small.

D.the sample sizes must be equal.

The p-value is greater than .05 so we cannot reject randomness.


81.To compare the cost of three shipping methods, a firm shipped five orders to each of four different destinations over a six-month period. Their total shipping costs are shown below.

Which nonparametric test would you use to compare the median shipping costs among destinations and among shippers?

A.Friedman test



D.Lebesgue-Stieltjes test

Like unreplicated two-factor ANOVA except that data are converted to ranks.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-06 Use the Friedman test for related samples.Topic: Friedman Test for Related Samples

82.At the Seymour Clinic, the total number of patients seen by three doctors over three days is as follows:

Which nonparametric test would you use to compare the median number of patients seen by the doctors on each day?

A.Wilcoxon test


C.Anderson-Darling test

D.Friedman test

Like unreplicated two-factor ANOVA except that data are converted to ranks.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 16-06 Use the Friedman test for related samples.Topic: Friedman Test for Related Samples

83.Systolic blood pressure of randomly selected HMO patients was recorded on a particular Wednesday, with the results shown here:

The appropriate hypothesis test to compare the medians is:

A.Wilcoxon test.

B.Kruskal-Wallis test.

C.Levene's test.

D.Friedman test.

Like one-factor ANOVA except that data are converted to ranks.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-05 Use the Kruskal-Wallis test for c independent samples.Topic: Kruskal-Wallis Test for Independent Samples

84.You do not wish to assume normality in the population, yet you wish to compare central tendency in c samples. You decide to utilize MegaStat, whose menu is shown here:


A.Hypothesis Tests

B.Nonparametric Tests

C.Correlation/Regression

D.Analysis of Variance

We need the Kruskal-Wallis nonparametric test for c medians.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-08 Use computer software to perform the tests and obtain p-values.Topic: Why Use Nonparametric Tests?

85.You do not wish to assume normality in the population, yet you wish to compare central tendency in c samples. You decide to utilize MINITAB, whose menu is shown here:

Which menu would you choose?A.ANOVA

B.Regression

C.Nonparametrics

D.EDA

We need the Kruskal-Wallis nonparametric test for c medians.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 16-08 Use computer software to perform the tests and obtain p-values.Topic: Why Use Nonparametric Tests?

chap 016

Documents

rank test

sample test

test statistic

sample parametric test

sample ttest

parametric ttest

equivalent parametric

spearman rank correlation