Deck 14: Nonparametric Methods

Question 1

In a Wilcoxon signed rank test for matched pairs,the test statistic is calculated as W = 48.The alternative hypothesis is H₁: m_d > 0.If there are n = 10 nonzero differences,and the 5% significance level is used,then the:

A) the null hypothesis will be rejected.
B) the null hypothesis will not be rejected.
C) the test results are inconclusive.
D) the t-test for matched pairs must be used.

Answer 1

the null hypothesis will be rejected.

Question 2

True or False The Wilcoxon signed rank test for comparing paired samples assumes the data are continuous and are of the interval or ratio scale of measurement.

Answer 2

True

Question 3

The significance level for a Wilcoxon signed rank test for matched pairs is 0.05.The alternative hypothesis is H₁: m_d > 0.The appropriate critical value for n = 20 nonzero differences is:

A) 158
B) 149
C) 61
D) 52
E) 112

Answer 3

149

Question 4

An NHL executive says that players who incur penalty time during a game have a median time of 1.2 minutes in the penalty box. A random sample of 28 hockey players with penalty time produced 24 non-zero differences when a Wilcoxon signed rank test was used. The W (R+) equaled 156.5. The alternate hypothesis is m 1.2 minutes. Assume the population is symmetrically distributed. The computed test statistic in this instance equals:

A) 156.5.
B) 0.186.
C) 6.5.
D) 35.
E) 143.5.

Question 5

The nonparametric counterpart to the paired sample,two-sample t-test is the:

A) Wilcoxon signed rank test for paired samples.
B) Wilcoxon rank sum test.
C) Wilcoxon signed rank test for one sample.
D) Friedman test for randomized block design.
E) Kruskal-Wallis test.

Question 6

True or False A one-sample t-test is the parametric counterpart to the Wilcoxon signed rank test for one sample.

Question 7

True or False Nonparametric tests are useful when data are of the nominal or ordinal scale of measurement.

Question 8

True or False The Kruskal-Wallis test requires that the scale of measurement of the data must be at least interval or ratio,and the samples are assumed to be randomly selected from their respective populations.

Question 9

In a Wilcoxon signed rank test for matched pairs with n = 35,the rank sums of the positive and negative differences are 380 and 225,respectively.The value of the standardized test statistic (that is,the value of z approximation test statistic)is:

A) 1.689.
B) 1.065.
C) 1.206.
D) 1.400.
E) 1.960.

Question 10

A nonparametric method to compare two populations,when the samples are matched pairs and the data are quantitative where the normality requirement necessary to perform the parametric test is unsatisfied,is the:

A) the Wilcoxon rank sum test.
B) the Friedman test.
C) the Kruskal-Wallis test.
D) the Matched pairs t-test.
E) the Wilcoxon signed rank test.

Question 11

True or False Compared to a parametric test,Nonparametric tests use the information in the data more efficiently.

Question 12

True or False The Kruskal-Wallis test compares the medians of more than two independent samples.

Question 13

True or False The Wilcoxon signed rank test is applied to a single sample in testing whether the population proportion could be a hypothesized value.

Question 14

True or False The sign test evaluates the randomness of a series of observations by analyzing the number of consecutive data values that are similar.

Question 15

True or False A Nonparametric test is one that assumes that the population from which a sample is drawn is normally distributed or approximately so.

Question 16

An NBA executive says that players who substitute as the sixth, seventh and eighth positions for the games starting five players have a median playing time of 24 minutes. A random sample of 25 substitutes (6, 7 or 8) produces 20 non-zero differences in a Wilcoxon signed rank test and a W (R+) equal to 146. The alternate hypothesis is m 24 minutes. Assume the population is symmetrically distributed. The computed test statistic in this situation equals:

A) 146.
B) 24.
C) 25.
D) 1.53.
E) 41.

Question 17

The Wilcoxon signed rank test assumes sample data to be

A) continuous with either nominal or ordinal measurement scale.
B) continuous with either interval or ratio measurement scale.
C) discrete with either nominal or ordinal measurement scale.
D) discrete with either interval or ratio measurement scale.
E) continuous with any measurement scale.

Question 18

True or False The Spearman coefficient of rank correlation measures both the strength and direction of paired observations that are at least a nominal measurement scale.

Question 19

The nonparametric counterpart to the one-sample t-test is the

A) Wilcoxon signed rank test.
B) Wilcoxon rank sum test.
C) Kruskal-Wallis test.
D) Friedman test for randomized block design.
E) run test.

Question 20

True or False Like the randomized block ANOVA,the Friedman test has the goal of comparing treatments,though it is concerned their medians rather than their means.

Question 21

Which of the following tests would be an example of a nonparametric method?

A) Wilcoxon signed rank test
B) Kruskal-Wallis test
C) Friedman test
D) Wilcoxon rank sum test
E) All of these are nonparametric methods

Question 22

In a Kruskal-Wallis test at the 5% significance level,there are four samples and the value of the test statistic is calculated as H = 8.79.The most accurate statement that can be made about the p-value is that it is:

A) greater than 0.10.
B) greater than 0.05 but smaller than 0.10.
C) greater than 0.05.
D) greater than 0.025 but smaller than 0.05.
E) greater than 0.10 but smaller than 0.15.

Question 23

The significance level for a Wilcoxon signed rank test for one sample is 0.025.The alternative hypothesis is m > m₀,and the sample size is 14.What is the appropriate critical value?

Question 24

Consider the following two independent samples:
$\begin{array} { l l l l l l } \text { Sample A: } & 14 & 15 & 17 & 20 & 45 \\\text { Sample B: } & 25 & 29 & 32 & 35 & 38\end{array}$

-The value of the test statistic for a left-tail Wilcoxon rank sum test is:

A)6.
B)20.
C)35.
D)55.
E)9.

Question 25

In a Wilcoxon rank sum test n1 = 12, n2 = 15 and the sum of R1 = 108. The value of the test statistic for the normal approximation is:

A) -1.23.
B) -2.93.
C) -108.
D) 108.
E) 15.

Question 26

A randomized block design analysis of variance test corresponds to a:

A) Wilcoxon signed rank test for paired samples.
B) Wilcoxon rank sum test.
C) Wilcoxon signed rank test for one sample.
D) Friedman test for randomized block design.
E) Kruskal-Wallis test.

Question 27

The nonparametric counterpart to the randomized block design of the analysis of variance is:

A) Kruskal-Wallis test.
B) Friedman test.
C) Wilcoxon rank sum test.
D) Wilcoxon signed rank test.
E) Sign test for comparing paired samples.

Question 28

The Wilcoxon rank sum test assumes that the measurement scale of the data be at least:

A) nominal.
B) ordinal.
C) interval.
D) ratio.
E) Any measurement scale can be used for the Wilcoxon rank sum test.

Question 29

Which of the following statements are not true?

A) The sign test assumes the data are interval instead of ordinal.
B) The sign test makes less efficient use of the data than does the Wilcoxon signed rank test.
C) In the sign test,each observation (one-sample test)or difference between paired observations (paired samples)is expressed only as a plus (+)or a minus (-)to indicate the direction of the difference.
D) All of these statements are true.
E) None of these statements is true.

Question 30

Which of the following statements are not true?

A) A non-parametric test is one that makes no assumptions about the specific shape of the population from which a sample is drawn.
B) A non-parametric test is used instead of its parametric counterpart when the data are of the nominal or ordinal scales of measurement.
C) A non-parametric test is used instead of its parametric counterpart when the data are of the interval or ratio scales of measurement,but one or more other assumptions (e.g.,the normality of the underlying distribution)are not met.
D) Unlike parametric methods,non-parametric techniques can be applied even when the sample sizes are very small.
E) All of these statements are true.

Question 31

The nonparametric counterpart of the parametric one-way analysis of variance F-test is:

A) Kruskal-Wallis test.
B) Friedman test.
C) Wilcoxon rank sum test.
D) Wilcoxon signed rank test.
E) Sign test for comparing paired samples.

Question 32

A nonparametric method to compare two or more populations,when the samples are matched pairs and the data are either ranked or quantitative but not normal is the:

A) Wilcoxon signed rank test.
B) Wilcoxon rank sum test.
C) Friedman test.
D) Kruskal-Wallis test.
E) Sign test for comparing paired samples.

Question 33

The nonparametric counterpart to the two-sample t-test with independent samples is the:

A) Wilcoxon signed rank test for paired samples.
B) Wilcoxon rank sum test.
C) Wilcoxon signed rank test for one sample.
D) Friedman test for randomized block design.
E) Kruskal-Wallis test.

Question 34

In a normal approximation to the Wilcoxon rank sum test,the standardized test statistic value is calculated as z = 1.80.For a two- tail test,the p-value is:

A) 0.0359.
B) 0.4641.
C) 0.2321.
D) 0.0718.
E) 0.1077.

Question 35

The significance level for a Wilcoxon signed rank test for one sample is 0.025.The alternative hypothesis is m < m₀,and the sample size is 14.What is the appropriate critical value?

Question 36

A random sample of ten basketball players from the SLC revealed 3 (+ differences)who weighed more than 245 pounds.Test the null hypothesis that m_d = 0 versus the alternative hypothesis that m_d < 0.The p-value for the computed test statistic is:

A) 0.3438.
B) 0.9453.
C) 0.0547.
D) 0.1094.
E) 0.1719.

Question 37

The sign test for comparing paired samples assumes that the measurement scale of the sample data is:

A) nominal.
B) ordinal.
C) interval.
D) ratio.
E) Any measurement scale can be used for the sign test for comparing paired samples.

Question 38

A three independent samples one-way analysis of variance test corresponds to a:

A) Wilcoxon signed rank test for paired samples.
B) Wilcoxon rank sum test.
C) Wilcoxon signed rank test for one sample.
D) Friedman test for randomized block design.
E) Kruskal-Wallis test.

Question 39

The p-value for the computed test statistic is:

A) 0.623.
B) 0.9453.
C) 0.0547.
D) 0.1094.
E) 0.1719.

Question 40

A nonparametric method to compare more than two populations,when the samples are independent and the data are either ranked or quantitative but not normal,is:

A) Kruskal-Wallis test.
B) Friedman test.
C) Wilcoxon rank sum test.
D) Wilcoxon signed rank test.
E) Sign test for comparing paired samples.

Question 41

NARRBEGIN: Apartments
Residents of two different high rise apartment units may or may not have the same consumer indebtedness.A sample from each results in the following outstanding debt amounts:
The test question is: Do residents of the two apartment units have similar debt medians? What is the rank for 12832 debt amount?

Question 42

NARRBEGIN: Seven Dwarfs
Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were:
The test question is: Do the different age groups require the same median time to name the Dwarfs? In testing the hypotheses,what is the appropriate critical value for the 0.05 significance level?

Question 43

Writers
Eight professional food writers have been asked to rate the taste characteristics of a meat dish prepared first by flame grilling and then by charcoal grilling. After each of the dishes is prepared it is rated on a scale from 1 to 5 with 1 being best and 5 being worst. The results of the rating were:

The Wilcoxon signed rank test for paired samples is used to test the hypotheses What will be the rank for writer A?

Question 44

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the calculated value of the test statistic Fr?

Question 45

NARRBEGIN: FAA
The FAA recorded the number of complaints per month for three airlines.The data were:
The test question is: Do the three airlines have the same median number of complaints? What is the calculated test statistic H?

Question 46

NARRBEGIN: Seven Dwarfs
Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were:
The test question is: Do the different age groups require the same median time to name the Dwarfs? What is the rank of the value 38 in the Under 12 sample?

Question 47

NARRBEGIN: FAA
The FAA recorded the number of complaints per month for three airlines.The data were:
The test question is: Do the three airlines have the same median number of complaints? In testing the hypotheses,what is the appropriate critical value for the 0.025 significance level?

Question 48

NARRBEGIN: Diet programs
A consumer research organization will evaluate the results of two diet programs,Take-It-Off and Melt-Away.Persons are randomly sampled from each of the programs and their weight loss results follow.
The test question is: Do the data indicate that the two programs are equally effective? What is the calculated test statistic W?

Question 49

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the rank of the value in the third treatment and fourth block?

Question 50

In testing the hypotheses H₀: m_d = 0,H₁: m_d 0,data are drawn from a matched pairs experiment,and the following statistics are calculated: n = number of nonzero differences = 40; R+ = 238; R- = 582.Assume that the 5% level of significance is used.What is the p-value of this test?

Question 51

NARRBEGIN: Dataset
Consider the following data set:
What is the rank assigned to the four observations of value 22?

Question 52

NARRBEGIN: Dataset
Consider the following data set:
What is the rank assigned to the three observations of value 1.8?

Question 53

In testing the hypotheses H₀: m_d = 0,H₁: m_d 0,data are drawn from a matched pairs experiment,and the following statistics are calculated: n = number of nonzero differences = 40; R+ = 238; R- = 582.Assume that the 5% level of significance is used.Calculate the z-approximation test statistic.

Question 54

NARRBEGIN: Seven Dwarfs
Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were:
The test question is: Do the different age groups require the same median time to name the Dwarfs? What is the calculated test statistic H?

Question 55

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the rank of the value in the second treatment and third block?

Question 56

Writers
Eight professional food writers have been asked to rate the taste characteristics of a meat dish prepared first by flame grilling and then by charcoal grilling. After each of the dishes is prepared it is rated on a scale from 1 to 5 with 1 being best and 5 being worst. The results of the rating were:

The Wilcoxon signed rank test for paired samples is used to test the hypotheses What is the calculated test statistic,W?

Question 57

NARRBEGIN: IRS
As a guideline,a local Internal Revenue Service office recommends that auditors try to spend 16 minutes or less with taxpayers who are called for audit interviews.In a recent random sample of 22 interviews,the interview times were as shown below:
Using the appropriate statistical table,what is the most accurate statement we can make about the p-value test?
p-value = ____________________

Question 58

NARRBEGIN: Diet programs
A consumer research organization will evaluate the results of two diet programs,Take-It-Off and Melt-Away.Persons are randomly sampled from each of the programs and their weight loss results follow.
The test question is: Do the data indicate that the two programs are equally effective? What is the rank for observation 150?

Question 59

NARRBEGIN: FAA
The FAA recorded the number of complaints per month for three airlines.The data were:
The test question is: Do the three airlines have the same median number of complaints? What is the rank of 1544 from Airline C?

Question 60

NARRBEGIN: Apartments
Residents of two different high rise apartment units may or may not have the same consumer indebtedness.A sample from each results in the following outstanding debt amounts:
The test question is: Do residents of the two apartment units have similar debt medians? What is the calculated test statistic W?

Question 61

On a multiple-choice exam consisting of ten questions with A through E as choices,the correct answers were: A A D A C B A D C B.Use these data to test the hypothesis that the answer sequence is random.What is the test statistic?

Question 62

For one sample,the Wilcoxon signed rank method tests whether the sample could have been drawn from a population having a hypothesized value as its ____________________.

Question 63

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? For the hypotheses,what is the appropriate critical value for the 0.025 significance level?

Question 64

The ____________________ test for normality can be used for samples of any size,including those that are too small.

Question 65

The z-test approximation to the Wilcoxon rank sum test for comparing two independent samples is used whenever both sample sizes are at least ____________________.

Question 66

The nonparametric ____________________ test is used for the same purposes as the Wilcoxon signed rank test,but data need only be of the ordinal scale of measurement.

Question 67

The z-test approximation to the Wilcoxon signed rank test is used whenever the number of nonzero differences is at least ____________________.

Question 68

On a multiple-choice exam consisting of ten questions with A through D as choices,the correct answers were: C D C B C B D A C D.Use these data to test the hypothesis that the answer sequence is random.What is the test statistic?

Question 69

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? For the hypotheses,what is the appropriate critical value for the 0.05 significance level?

Question 70

In applying the Friedman test,either the number of blocks or the number of treatments should be at least ____________________.

Question 71

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
On a multiple-choice exam consisting of ten questions with A through D as choices,the correct answers were: C D C B C B D A C D.Use these data to test the hypothesis that the answer sequence is random.What is the expected number of runs?

Question 72

The ____________________ test evaluates the randomness of a series of observations by analyzing the number of ____________________ it contains.

Question 73

Compared to the chi-square method,the _________________________ does not require any minimum values for expected frequencies and can be used with relatively small samples.(Answer could be several words).

Question 74

The significance level for a Wilcoxon signed rank test for one sample is 0.02.The alternative hypothesis is m m₀,and the sample size is 14.What is/are the appropriate critical value(s)?
Separate your answers with commas,for example x,y,z,etc.

Question 75

Like the randomized block ANOVA,the ____________________ test compares the effectiveness of treatments,but it is concerned with their medians rather than their mean.

Question 76

The critical value of the Kruskal-Wallis test for comparing more than two independent samples is obtained from the ____________________ distribution whenever each sample size is at least ____________________.

Question 77

The ____________________ test is the nonparametric counterpart to the randomized block ANOVA design.

Question 78

Unlike the Wilcoxon signed rank test,the ____________________ test assumes data are ordinal.

Question 79

On a multiple-choice exam consisting of ten questions with A through E as choices,the correct answers were: A A D A C B A D C B.Use these data to test the hypothesis that the answer sequence is random.What is the expected number of runs?

Question 80

NARRBEGIN: Treatments No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal?
No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the calculated value of the test statistic Fr?