Deck 19: Nonparametric Statistics

Question 1

Nonparametric tests are methods of inference that make no assumptions whatsoever about the nature of underlying population distributions or their parameters.

Answer 1

True

Question 2

The first step in a Wilcoxon rank sum test is to combine the data values in the two samples and assign a rank of 1 to the:

A)smallest observation.
B)middle observation.
C)largest observation.
D)observation that occurs most frequently.

Answer 2

smallest observation.

Question 3

The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample sizes are larger than:

A)25
B)20
C)15
D)10

Answer 3

10

Question 4

In a normal approximation to the Wilcoxon rank sum test,the standardized test statistic 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

Question 5

You are performing the Wilcoxon rank-sum test.The 13^th through 15^th values in an ordered array of pooled sample data all equal $180 (while the 12^th value is less and the 16^th value is more).The appropriate ranks for the three $180 values are:

A)14,14,14
B)13,14,15
C)12.5,13,14.5
D)12.5,13,15

Question 6

In a Wilcoxon rank sum test,the two sample sizes are 4 and 6,and the value of the Wilcoxon test statistic is T = 20.If the test is a two-tail and the level of significance is α = 0.05,then:

A)the null hypothesis will be rejected.
B)the null hypothesis will not be rejected.
C)the alternative hypothesis will not be rejected.
D)not enough information has been given to answer this question.

Question 7

The nonparametric tests discussed in your book (Wilcoxon rank sum test,sign test,Wilcoxon signed rank sum test,Kruskal-Wallis test,and Friedman test)all require that the probability distributions be:

A)identical except with respect to shape (distribution).
B)identical except with respect to spread (variance).
C)identical except with respect to location.
D)different with respect to location,spread,and shape.

Question 8

A parametric test is a hypothesis test that depends on certain specific assumptions about the probability distribution of population values or the sizes of population parameters.

Question 9

Nonparametric methods are designed to test ordinal data.

Question 10

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the samples must be:

A)larger than 30.
B)independent.
C)drawn from normal populations.
D)drawn from matched pairs experiment.

Question 11

Statistical tests that are not very sensitive to errors in assumptions are called parametric tests.

Question 12

Statistical methods that require few assumptions,if any,about the population distribution are known as:

A)parametric techniques.
B)nonparametric techniques.
C)free agent techniques.
D)All of these choices are true.

Question 13

The Wilcoxon rank sum test is used to compare two populations when the samples are independent and the data are either ordinal or interval but not normally distributed.

Question 14

Which of the following will never be a required condition of a nonparametric test?

A)Data are ordinal.
B)Data are interval.
C)The samples are drawn from normally distributed populations.
D)The populations being compared are identical in spread and shape.

Question 15

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that both sample sizes are larger than 10.

Question 16

Statistical methods that require few assumptions,if any,about the population distribution are known as parametric techniques.

Question 17

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the samples must be independent.

Question 18

In a normal approximation to the Wilcoxon rank sum test,the standardized test statistic is calculated as z = 1.96.For a two-tail test,the p-value of the test is 0.025.

Question 19

The procedure for the Wilcoxon rank sum test requires that we rank each group separately rather than together.

Question 20

Statistical methods that require,among other assumptions,that the populations be normally distributed are known as:

A)distribution-free techniques.
B)nonparametric techniques.
C)parametric techniques.
D)both a and b are correct.

Question 21

Use the Wilcoxon rank sum test on the data below to determine at the 5% significance level whether the location of population A is to the left of the location of population B.

Question 22

When the sample sizes from both populations are larger than ____________________,the Wilcoxon rank sum statistic has an approximate normal distribution.

Question 23

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make a general assessment of relative fertilizer effectiveness,may well call for a:

A)Friedman test.
B)Kruskal-Wallis test.
C)Wilcoxon rank-sum test.
D)Spearman rank correlation test.

Question 24

A nonparametric method that is equivalent to the Wilcoxon rank sum test is the:

A)Wilcoxon signed rank sum test.
B)Friedman test.
C)Kruskal-Wallis test.
D)Mann-Whitney test.

Question 25

In testing the hypotheses
H₀: The two population locations are the same.
H₁: The location of population A is to the left of the location of population b.The statistics n_A = 6,T_A = 32,n_B = 8,and T_B = 58 are calculated with data drawn from two independent samples:
a.Which test is used for testing the hypotheses above?
b.What is the p-value of this test?

Question 26

The Wilcoxon rank sum test requires that the samples from the two populations be ____________________.

Question 27

Because of the rising costs of construction accidents many construction firms have instituted safety courses.Employees are encouraged to take these courses designed to heighten safety awareness.A company is trying to decide which one of two courses to institute.To help make a decision,eight employees take course 1 and another eight take course 2.Each employee writes a test,which is marked,out of a possible 25.The results are shown below.Does this data provide sufficient evidence at the 5% level of significance to conclude that the marks from course 2 are higher than those of course 1? Assume that the scores are not normally distributed.

Question 28

Each year the human resources department in a large corporation assesses the performance of all of its employees.Each employee is rated for various aspects of his or her job on a 7-point scale where 1 = very unsatisfactory and 7 = satisfactory.The CEO of the company believes that the assessment scores this year are lower than last year's.To examine the validity of this belief she draws a random sample of six employees' scores from last year and another six employees' scores this year.Do the data listed below allow the CEO to conclude at the 5% significance level that her belief is correct?

Question 29

In the Wilcoxon rank sum test statistic,let T represent the total rankings of sample 1 amongst all rankings.If T is small,this suggests that the location of population 1 is to the ____________________ of the location of population 2.

Question 30

Nonparametric procedures are often called ____________________-free statistics.

Question 31

When the sample sizes from both populations are larger than 10,the Wilcoxon rank sum statistic has an approximate ____________________ distribution.

Question 32

The sign test is employed to compare two populations when the experimental design is matched pairs,and the data are ordinal but not normally distributed.

Question 33

The sign test is always to be preferred to the t-test.

Question 34

Instead of testing whether population means differ,a nonparametric technique would test whether the population ____________________ differ.

Question 35

Consider the following data set: 2.2,2.3,2.3,2.5,2.6,2.7,2.8,2.8,2.8,2.9,3.1,3.2,and 3.5.The rank assigned to the three observations of value 2.8 is:

A)6
B)7
C)8
D)9

Question 36

Consider the following data set: 14,14,15,16,18,19,19,20,21,22,23,25,25,25,25,and 28.The rank assigned to the four observations of value 25 is:

A)12
B)12.5
C)13
D)13.5

Question 37

In testing the hypotheses
H₀: The two population locations are the same.
H₁: The two population locations are different.
The critical values and sample sizes are n₁ = 5,T_L = 22,n₂ = 9,and T_U = 53.
a.Which test is used for testing the hypotheses above?
b.What is the α-level of this test?

Question 38

One of the required conditions of the sign test is that the number of nonzero differences n must be greater than or equal to 30.

Question 39

H₀ in the Wilcoxon rank sum test is that the two population ____________________ are the same.

Question 40

Nonparametric methods are designed to test ____________________ data.

Question 41

The normal approximation to the Wilcoxon signed rank sum test statistic is used whenever the sample size is large (more than 30).

Question 42

A nonparametric test for comparing two or more populations should be used instead of its parametric counterpart if:

A)no information about the shape of the populations is available.
B)the sample sizes are large.
C)the populations have equal means.
D)the populations are normally distributed.

Question 43

A nonparametric method to compare two populations,when the samples are matched pairs and the data are ordinal,is the:

A)sign test.
B)matched pairs t-test
C)Wilcoxon rank sum test.
D)Wilcoxon signed rank sum test..

Question 44

Some statistical software perform the Mann-Whitney test.However,this test and the sign test are equivalent tests.

Question 45

A two-sample t-test is the parametric counterpart of the Wilcoxon signed rank sum test for matched pairs.

Question 46

The Wilcoxon signed rank sum test incorporates not only the sign of each difference,but the ____________________ of the difference as well.

Question 47

The sign test statistic has a(n)____________________ distribution.

Question 48

The sign test statistic is approximately normally distributed whenever the sample sizes are larger than:

A)30
B)10
C)5
D)None of these choices.

Question 49

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

A)Wilcoxon rank sum test.
B)sign test.
C)matched pairs t-test.
D)Wilcoxon signed rank sum test.

Question 50

The nonparametric counterpart of the parametric t-test of μ_D for matched pairs is the:

A)Friedman test.
B)Kruskal-Wallis test.
C)Wilcoxon signed rank sum test.
D)Wilcoxon rank sum test.

Question 51

In a Wilcoxon signed rank sum test,the test statistic is calculated as T = 75.If there are n = 15 observations for which D≠ 0,and a two-tail test is performed at the 5% significance level,then:

A)reject the null hypothesis.
B)don't reject the null hypothesis.
C)the test results are inconclusive.
D)perform a parametric test.

Question 52

When data are interval,but not normal,and you want to analyze matched pairs differences,use the ____________________ test.

Question 53

The sign test statistic has what kind of distribution?

A)normal
B)binomial
C)nonparametric
D)None of these choices.

Question 54

When data are ordinal and you want to analyze matched pairs differences,you use the ____________________ test.

Question 55

When the data are interval,how does the Wilcoxon signed rank sum test compare to the sign test?

A)Wilcoxon uses the information in the data more effectively.
B)Wilcoxon uses the information in the data less effectively.
C)Cannot compare the two tests without knowing the sample size.
D)None of these choices.

Question 56

The Wilcoxon signed rank sum test is applied to compare two populations,when the samples are matched pairs and the data are interval but not normally distributed.

Question 57

A two independent sample t-test corresponds to a Wilcoxon signed rank sum test for paired samples.

Question 58

Which of the following tests employs matched-pairs sampling?

A)The Mann-Whitney test.
B)The Wilcoxon rank-sum test.
C)The Wilcoxon signed-rank sum test.
D)None of these choices.

Question 59

The Wilcoxon signed rank sum test for matched pairs is the nonparametric counterpart of the paired two-sample t-test of μ_D.

Question 60

The Wilcoxon signed rank sum test statistic is approximately normally distributed whenever the sample sizes are larger than:

A)5
B)10
C)30
D)None of these choices.

Question 61

The critical value is taken from the F-distribution whenever the test is a Kruskal-Wallis test.

Question 62

A one-sample t-test is the parametric counterpart of the Kruskal-Wallis test.

Question 63

Coffee
​ A supermarket chain has its own house brand of coffee.The general manager claims that their coffee is better than the coffee sold by a well-known Coffee Shop chain.To test the claim 40 individuals are randomly selected to participate in the following experiment.Each respondent is given the two brands of coffee to taste (without any identification)and asked to judge which one is better.Suppose that 25 people judge the Coffee Shop chain brand better,four say that the brands taste the same,and the rest claim that the supermarket brand is better. ​ ​
{Coffee Narrative} What is the p-value of the test in the previous question?

Question 64

The Kruskal-Wallis test is an extension of the Wilcoxon rank-sum test from two to more than two statistical populations.

Question 65

The Wilcoxon signed rank sum test requires you to rank the absolute ____________________.

Question 66

Movie Scripts
​ In general,before a producer agrees to make a movie,each script is thoroughly reviewed by movie editors.Suppose that the Big-Screen Film Company has recently received two scripts for new movies.To help them decide which one to produce,both are sent to 30 editors who rate the scripts to judge which one is better.Suppose that 10 editors rate script 1 better and 20 rate script 2 better. ​ ​
{Movie Scripts Narrative} What is the p-value of this test?

Question 67

The Kruskal-Wallis test can be conducted as one or two-tail test.

Question 68

Movie Scripts
​ In general,before a producer agrees to make a movie,each script is thoroughly reviewed by movie editors.Suppose that the Big-Screen Film Company has recently received two scripts for new movies.To help them decide which one to produce,both are sent to 30 editors who rate the scripts to judge which one is better.Suppose that 10 editors rate script 1 better and 20 rate script 2 better. ​ ​
{Movie Scripts Narrative} Can Big-Screen conclude at the 5% significance level that script 2 is more highly rated than script 1?

Question 69

Keyboard Speed
Ten administration assistants were selected at random from a large university.The keyboard speed (number of words per minute)was recorded for each secretary on two different brands of computer keyboards.Assume that the typing speeds are not normally distributed.The following results were obtained. ​ ​
{Keyboard Speed Narrative} Perform the sign test to determine if these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to keyboard speed.

Question 70

Coffee
​ A supermarket chain has its own house brand of coffee.The general manager claims that their coffee is better than the coffee sold by a well-known Coffee Shop chain.To test the claim 40 individuals are randomly selected to participate in the following experiment.Each respondent is given the two brands of coffee to taste (without any identification)and asked to judge which one is better.Suppose that 25 people judge the Coffee Shop chain brand better,four say that the brands taste the same,and the rest claim that the supermarket brand is better. ​ ​
{Coffee Narrative} Which test is appropriate for this situation?

Question 71

Coffee
​ A supermarket chain has its own house brand of coffee.The general manager claims that their coffee is better than the coffee sold by a well-known Coffee Shop chain.To test the claim 40 individuals are randomly selected to participate in the following experiment.Each respondent is given the two brands of coffee to taste (without any identification)and asked to judge which one is better.Suppose that 25 people judge the Coffee Shop chain brand better,four say that the brands taste the same,and the rest claim that the supermarket brand is better. ​ ​
{Coffee Narrative} Can we conclude at the 1% significance level that the general managers' claim is false?

Question 72

Suppose using Kruskal-Wallis test,there are five samples,and the value of the test statistic is calculated as H = 12.32.Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.025 but smaller than 0.05

Question 73

When n is greater than or equal to 10,the sign test statistic has an approximate ____________________ distribution.

Question 74

For the sign test,n equals the number of differences in the sample that are ____________________.

Question 75

Campaign Commercials
It is important to sponsors of television shows that viewers remember as much as possible about the commercials.The campaign manager for a local politician is trying to decide which of two commercials to use on a weekly half-hour comedy.To help make a decision she decides to have 12 individuals watch both commercials.After each viewing,each respondent is given a quiz consisting of 10 questions.The number of correct responses is recorded and listed below.Assume that the quiz results are not normally distributed. ​ ​
{Campaign Commercials Narrative} Does this data provide enough evidence at the 5% significance level to conclude that the responses to the two commercials differ?

Question 76

Keyboard Speed
Ten administration assistants were selected at random from a large university.The keyboard speed (number of words per minute)was recorded for each secretary on two different brands of computer keyboards.Assume that the typing speeds are not normally distributed.The following results were obtained. ​ ​
{Keyboard Speed Narrative} Perform the Wilcoxon signed rank sum test at the 5% significance level.

Question 77

Movie Scripts
​ In general,before a producer agrees to make a movie,each script is thoroughly reviewed by movie editors.Suppose that the Big-Screen Film Company has recently received two scripts for new movies.To help them decide which one to produce,both are sent to 30 editors who rate the scripts to judge which one is better.Suppose that 10 editors rate script 1 better and 20 rate script 2 better. ​ ​
{Movie Scripts Narrative} Which test is appropriate for this situation?

Question 78

Movie Scripts
​ In general,before a producer agrees to make a movie,each script is thoroughly reviewed by movie editors.Suppose that the Big-Screen Film Company has recently received two scripts for new movies.To help them decide which one to produce,both are sent to 30 editors who rate the scripts to judge which one is better.Suppose that 10 editors rate script 1 better and 20 rate script 2 better. ​ ​
{Movie Scripts Narrative} Explain how to use the p-value for testing the hypotheses at the 5% significance level.

Question 79

The Kruskal-Wallis test is applied to compare two or more populations,when the samples are independent and the data are either ordinal or interval but not normal.

Question 80

Campaign Commercials
It is important to sponsors of television shows that viewers remember as much as possible about the commercials.The campaign manager for a local politician is trying to decide which of two commercials to use on a weekly half-hour comedy.To help make a decision she decides to have 12 individuals watch both commercials.After each viewing,each respondent is given a quiz consisting of 10 questions.The number of correct responses is recorded and listed below.Assume that the quiz results are not normally distributed. ​ ​
{Campaign Commercials Narrative} Which test is appropriate for this situation?