Deck 15: A:nonparametric Statistics

Question 1

A two-sample t test with independent samples corresponds to which of the following tests?

A) a sign test
B) a Wilcoxon rank sum test
C) a Wilcoxon signed-rank test e
D) a Friedman test for randomized block design

Answer 1

B

Question 2

You are performing the Wilcoxon rank sum test. The 14th through 16th values in an ordered array of pooled sample data all equal $160 (while the 13th value is less and the 17th value is more). What are the appropriate ranks for the three $160 values?

A) 13.5, 14, 15.5
B) 14, 15, 16
C) 14.5, 15, 16.5
D) 15, 15, 15

Answer 2

D

Question 3

Which of the following correctly states the difference between parametric and nonparametric statistical methods?

A) Nonparametric tests do not make any distributional assumptions throughout the entire process.
B) Nonparametric tests do not have the hypotheses based on population parameters or assumptions based on the distributions of populations from which the samples are drawn.
C) Nonparametric tests involve only interval data, whereas parametric tests involve only ordinal data.
D) Nonparametric tests are involved with populations that have no parameters.

Answer 3

B

Question 4

What is the appropriate nonparametric method to compare two populations when the samples are independent and where the normality requirement necessary to perform the parametric test is NOT satisfied?

A) Wilcoxon rank sum test
B) sign test
C) Wilcoxon signed-rank sum test
D) equal-variance t test of

Question 5

Which of the following correctly describes the Wilcoxon rank sum test?

A) It is a nonparametric test based on two independent simple random samples.
B) It is designed to determine whether the relative frequency distributions of two statistical populations of continuous values are identical to or different from one another.
C) It is equivalent to a parametric t test of the difference between two independent means.
D) all of the above

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. The test is two-tailed and the level of significance is . What may be deduced from the given information?

A) The null hypothesis will be rejected.
B) The null hypothesis will not be rejected.
C) The alternative hypothesis will not be rejected.
D) The alternative hypothesis will be rejected.

Question 7

When assigning ranks during a Wilcoxon rank sum test, tied values are each given the mean of the next ranks to be assigned. Which of the following statements is NOT correct regarding this averaging procedure?

A) The procedure is crucial when the tied values belong to the same sample.
B) Although still employed, the procedure is not crucial (and an arbitrary assignment of ranks to tied values would be acceptable) when the tied values belong to the same sample.
C) The procedure is designed to avoid arbitrariness.

Question 8

Suppose we want to compare 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. Which of the following tests might we use?

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

Question 9

You are performing the Wilcoxon rank sum test. The 10th through 12th values in an ordered array of pooled sample data all equal $100, while the 9th value is less than $100 and the 13th value is more than $100. What are the appropriate ranks for the three $100 values?

A) 9, 9, 9
B) 10, 10, 10
C) 11, 11, 11
D) 12, 12, 12

Question 10

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The nonstandardized test statistic (that is, the rank sum) is T = 210. Under these circumstances, what is the value of the standardized test statistic z?

A) 14.0
B) 10.5
C) 6.0
D) -2.0

Question 11

The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample sizes are larger than or equal to which of these values?

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

Question 12

Which of the following techniques are statistical methods that require, among other assumptions, that the populations be normally distributed?

A) distribution-free techniques
B) nonparametric techniques
C) parametric techniques
D) both distribution-free and nonparametric techniques

Question 13

Consider the following two independent samples: In this case, what is the value of the test statistic for a right-tailed Wilcoxon rank sum test?

A) 3
B) 7
C) 11
D) 22

Question 14

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

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

Question 15

Under which of the following conditions are nonparametric tests appropriate for quantitative data?

A) One or more of the assumptions underlying a particular parametric statistical test has been violated.
B) The sample size is very large.
C) The underlying population can be assumed to be normally distributed.
D) All assumptions for a particular parametric statistical test have been met.

Question 16

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 5 and 7. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. In this case, what is the appropriate critical value at the 5% significance level?

A) 20
B) 29
C) 33
D) 35

Question 17

Which of the techniques listed below are statistical methods that require few assumptions, if any, about the population distribution?

A) parametric techniques
B) nonparametric techniques
C) free agent techniques
D) general techniques

Question 18

Consider the following two independent samples: Given this information, what is the value of the test statistic for a left-tailed Wilcoxon rank sum test?

A) 6
B) 20
C) 35
D) 55

Question 19

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

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

Question 20

The nonparametric tests discussed in your text (Wilcoxon rank sum test, sign test, Wilcoxon signed-rank test, Kruskal-Wallis test, and Friedman test) all require that the probability distributions have which of the following properties?

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

Question 21

Which of these tests employs matched pairs sampling?

A) the Wilcoxon signed-rank test
B) the Wilcoxon rank sum test
C) the Mann-Whitney test
D) the Friedman test

Question 22

To use the Wilcoxon rank sum test as a test for location, which of the following conditions must we assume?

A) that the obtained data are either ordinal or interval where the normality requirement necessary to perform the equal-variances t test ofis unsatisfied
B) that both samples are randomly and independently drawn from their respective populations
C) that both underlying populations from which the samples were drawn are equivalent in shape and dispersion
D) all of (a), (b), and (c)

Question 23

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

A) The samples are drawn from normally distributed populations.
B) The populations being compared are identical in spread and shape.
C) The samples are not drawn from normally distributed populations.
D) The populations being compared are not identical in spread and shape.

Question 24

The Wilcoxon rank sum test (like most of the nonparametric tests presented in your text) is used to determine whether the population distributions have certain identical characteristics. Which of these properties would be included in that list of characteristics?

A) locations
B) spreads (variances)
C) shapes
D) locations, spreads, and shapes

Question 25

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

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

Question 26

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. What is the rank assigned to the three observations of value 2.8?

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

Question 27

In the sign test applications, the normal approximation to the binomial distribution works very well even when the number of non-zero differences is as small as which of the following values?

A) 5
B) 10
C) 15
D) 25

Question 28

In the Wilcoxon signed-rank test, if two or more measurements have the same non-zero difference, signs ignored, then what would be the logical next step?

A) The scores are eliminated from the analysis.
B) The scores are assigned the lowest rank of the tied values.
C) The scores are assigned the highest rank of the tied values.
D) The average of the ranks of the tied values is assigned.

Question 29

Which one of the following is a disadvantage of the sign test?

A) Tied pairs are not considered in the analysis.
B) Only the signs of the differences and not the actual values are used in the analysis.
C) The sign test cannot cope with small samples.
D) Results from such tests have little practical use.

Question 30

In the case of the sign test, which of the following is the best formulation of the null hypothesis?

A) There is a difference in the probability distribution for the two populations.
B) There is no difference in the probability distribution for the two populations.
C) The two populations in questions are both normally distributed.
D) p $\neq$ 0.5.

Question 31

Which of the following statements correctly describes the sign test?

A) It often uses the directions of differences observed in matched pairs sample to determine whether the relative frequency distributions of two statistical populations are identical to or different from one another.
B) It is often used to determine whether a sample comes from a population with a specified median.
C) Both (a) and (b).
D) Neither (a) nor (b).

Question 32

In a normal approximation to the sign test, the standardized test statistic is calculated as z = -1.58. To test the alternative hypothesis that the location of population 1 is to left of the location of population 2, what would be the p-value of the test?

A) 0.0571
B) 0.1142
C) 0.2215
D) 0.2284

Question 33

The sign test is a nonparametric procedure for testing which of the following situations?

A) whether two populations have identical means
B) whether two populations have identical medians
C) whether two populations have identical probability distributions
D) the amount of skewness in a single population

Question 34

Which of the following is a nonparametric method to compare two populations when the samples are matched pairs and the data are ordinal?

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

Question 35

Which one of the following is NOT a reason for using a sign test to make a comparison between two populations?

A) Some studies yield responses that are difficult to quantify.
B) It is easy to use the sign-testing procedure.
C) The data in question consist of count data.
D) No assumptions need to be made about the form of the population probability distributions.

Question 36

In a normal approximation to the Wilcoxon rank sum test, the standardized test statistic is calculated as z = 1.80. In this case, what would the p-value be for a two-tailed test?

A) 0.0359
B) 0.0718
C) 0.2321
D) 0.4641

Question 37

What are inferential procedures that are free from restrictive assumptions about the sampled populations?

A) distribution-free tests (because no assumption about the nature of the population distribution is being made)
B) distribution-free tests (because no assumption about the nature of the sampling distributions of test statistics is being made)
C) parametric tests
D) general tests

Question 38

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 which of the following observations?

A) the smallest observation
B) the first observation
C) the largest observation
D) the observation that occurs most frequently

Question 39

Which of the following is a nonparametric method that is equivalent to the Wilcoxon rank sum test?

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

Question 40

Which of the following statements correctly describes the Wilcoxon signed-rank test?

A) It makes use of the sign and the magnitude of the rank of the differences between pairs of measurements.
B) It is concerned with the analysis of a single population.
C) It cannot cope with ordinal data.
D) It makes use of the sign but does not consider the magnitude of the differences between pairs of measurements.

Question 41

How is the alternative hypothesis to be tested always stated in all applications of the Kruskal-Wallis test?

A) The locations of all k populations are the same.
B) The locations of all k populations differ.
C) At least two population locations are the same.
D) At least two population locations differ.

Question 42

In which of the following situations might the Wilcoxon signed-rank test be more appropriate than the paired-difference t test?

A) when the population of differences is not normal
B) when the population of differences is normal
C) when the sample size is small
D) when the data values are quantitative

Question 43

In a Kruskal-Wallis test, there are four samples and the value of the test statistic is calculated as H = 8.79. Under these conditions, which of the following is the most accurate statement that can be made about the p-value?

A) It is greater than 0.10.
B) It is greater than 0.05 but smaller than 0.10.
C) It is greater than 0.05.
D) It is greater than 0.025 but smaller than 0.05.

Question 44

Which of these tests is a nonparametric method to compare two or more populations when the samples are independent and the data are either ordinal or interval but not normal?

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

Question 45

Which of these tests is the nonparametric counterpart of the parametric t test of for matched pairs?

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

Question 46

Which of the following is a nonparametric alternative to the Kruskal-Wallis test for differences in more than two medians?

A) the ANOVA F test for completely randomized experiments
B) the Student's t test for related samples
C) the Student's t test for independent samples
D) the Wilcoxon rank sum test for differences in two medians

Question 47

Which of the following is the nonparametric counterpart of the parametric one-way analysis of variance F-test?

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

Question 48

In a Kruskal-Wallis test for comparing three populations, the test statistic is calculated as H = 2.80. If the test is conducted at the 5% significance level, then what may one conclude?

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.

Question 49

The significance level for a Wilcoxon signed-rank test is 0.05. The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2. Under these circumstances, what is the appropriate critical value for a sample of size 20 (i.e., the number of non-zero differences)?

A) 37
B) 43
C) 52
D) 60

Question 50

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. What, then, is the value of the standardized test statistic z?

A) 1.065
B) 1.206
C) 1.400
D) 1.689

Question 51

Which of the following distributions approximates the Kruskal-Wallis test statistic H when the objective is to compare k distributions and the sample sizes are greater than or equal to 5?

A) the normal distribution
B) the chi-square distribution with k - 1 degrees of freedom
C) the Student t distribution with k - 2 degrees of freedom
D) either the chi-square distribution with k - 5 degrees of freedom or the Student's t distribution with k + 5 degrees of freedom

Question 52

Suppose there is interest in comparing the median response time for three independent groups learning a new specific task. In this case, what is the appropriate nonparametric procedure to use?

A) the Wilcoxon rank sum test
B) the Wilcoxon signed-rank test
C) the Kruskal-Wallis test for differences in medians
D) either a or b

Question 53

In a Wilcoxon signed-rank test for matched pairs with n = 32, the rank sums of the positive and negative differences are 367.5 and 160.5, respectively. Given this information, what is the value of the standardized test statistic z?

A) 3.764
B) 1.935
C) 1.882
D) 1.391

Question 54

The significance level for a Wilcoxon signed-rank sum test is 0.05. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. Given this information, what is the appropriate critical value for a sample of size 20 ?

A) 37
B) 43
C) 52
D) 60

Question 55

In a Wilcoxon signed-rank test, the test statistic is calculated as T = 75. If there are n = 15 observations for which the difference is not 0, and a two-tailed test is performed at the 5% significance level, what is an appropriate conclusion?

A) Reject the null hypothesis.
B) Don't reject the null hypothesis.
C) The test results are inconclusive.
D) Perform a parametric test.

Question 56

Which of these tests is 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?

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

Question 57

A paired sample, two-sample t test corresponds to which of the following tests?

A) a Wilcoxon signed-rank test
B) a Wilcoxon rank sum test
C) a Kruskal-Wallis H-test
D) a Friedman test for randomized block design

Question 58

In a normal approximation to the Wilcoxon signed-rank test, the test statistic is calculated as z = 1.36. For a two-tailed test, what is the p-value?

A) 0.0869
B) 0.1738
C) 0.2066
D) 0.4131

Question 59

Which of the following is a characteristic of the Kruskal-Wallis test?

A) It is always one-tailed.
B) It is always two-tailed.
C) It is always used with one sample.
D) It is always used when the populations are normally distributed.

Question 60

The Wilcoxon signed-rank test statistic is approximately normally distributed whenever the sample sizes are larger than or equal to which of the following values?

A) 10
B) 20
C) 25
D) 35

Question 61

Which of the following is characteristic of the Friedman test?

A) It is always one-tailed.
B) It is always two-tailed.
C) It is always used with one sample.
D) It is always used when the populations are normally distributed.

Question 62

To which of the following tests does a randomized block design analysis of variance test correspond?

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

Question 63

The Kruskal-Wallis test statistic can be approximated by a chi-square distribution with k - 1 degrees of freedom (where k is the number of populations) whenever the sample sizes are all greater than or equal to which of the following values?

A) 5
B) 15
C) 25
D) 30

Question 64

When the relationship between two variables is monotonically decreasing, what might the size of Spearman's rank correlation coefficient be?

A) -2
B) -1
C) 0
D) +1

Question 65

We can safely employ nonparametric tests even when we know nothing at all about the populations from which sample data are being drawn.

Question 66

Nonparametric methods can be applied to a wider variety of s because they have less rigid requirements than parametric methods.

Question 67

Which of the following statements is NOT a property of the Spearman's rank correlation coefficient?

A) It is the test statistic used in Spearmen's rank correlation test.
B) It can take on values only between 0 and +1.
C) Positive values near +1 point to a monotonically increasing relationship between the two variables.
D) It specifies hypotheses in terms of population distributions rather than parameters.

Question 68

In testing at the 5% significance level, a sample of size 20 is used. In this case, what is the rejection region?

A) -0.4500.450
B) -0.3770.377
C) 0.450 or-0.450
D) 0.777 or-0.377

Question 69

In a Friedman test for comparing four populations, provided that there are eight blocks, the test statistic is calculated as = 10.98. If the test is conducted at the 5% significance level, what may we conclude about the null hypothesis and the p-value?

A) Reject the null hypothesis, and 0.01 < p-value < 0.025.
B) Reject the null hypothesis, and p-value > 0.025.
C) Do not reject the null hypothesis, and 0.025 < p-value < 0.05.
D) Do not reject the null hypothesis, and p-value > 0.05.

Question 70

In a Friedman test for comparing three populations, provided that there are five blocks, the test statistic is calculated as = 6.594. In this case, what is the most accurate statement that can be made about the p-value?

A) the p-value < 0.025
B) 0.025 < p-value < 0.05
C) 0.05 < p-value < 0.10
D) the p-value > 0.10

Question 71

The Wilcoxon rank sum test is a nonparametric test that measures the degree of association between two variables for which only rank-order data are available.

Question 72

Using a nonparametric test when we could employ a parametric test can be less efficient because a nonparametric test often tends to ignore available sample information; for example, by focusing only on the directions rather than the sizes of observed differences.

Question 73

To apply the Friedman test to determine whether the locations of two or more populations are the same, what is a necessary property of the samples drawn?

A) They must be from a matched pairs experiment.
B) They must be from normal populations.
C) They must be independent.
D) They must be larger than 20.

Question 74

We can conduct nonparametric tests even with nominal and ordinal data.

Question 75

Under which of the following conditions is the rank correlation coefficient used?

A) when one is correlating quantitative data
B) when one is correlating rankings of individual values for two variables
C) when one is analyzing data that are assumed to be linearly related
D) when one is not interested in drawing inferences from the study

Question 76

Given sample size and specified significance level , the probability of a Type II error is larger for a nonparametric test.

Question 77

Which test is the nonparametric counterpart of the randomized block model of the analysis of variance?

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

Question 78

The Spearman's rank correlation coefficient must lie between which of the following values?

A) 0 and
B) and 0
C) -1 and +1
D) and +1

Question 79

We can conduct nonparametric tests only with data of a higher order than nominal or ordinal.

Question 80

A Friedman test is applied to a data set that is generated from a randomized block experiment with four treatments and eith blocks. What is the rejection region at the 5% significance level?

A) 1.6450
B) > 7.8147
C) 9.4877
D) > 11.0705