Deck 16: Nonparametric Methods: Analysis of Ordinal Data

Question 1

What is the test statistic for the sign test if the sample size is large?

A)Chi-square
B)Standard normal z
C)Binomial
D)Wilcoxon signed-rank

Answer 1

Standard normal z

Question 2

To apply the large-sample procedure for the sign test,the sample size should be at least ________.

A)2
B)8
C)100
D)10

Answer 2

10

Question 3

The sign test is an appropriate nonparametric test for dependent samples.

Answer 3

True

Question 4

If a sign test is applied,what is the null hypothesis for a two-tailed test?

A)H₀: π = 0.50
B)H₀: π is not equal to 0.50
C)H₀: π > 0.50
D)H₀: π < 0.50

Question 5

The Wilcoxon rank-sum test compares two dependent populations.

Question 6

Spearman's rank-order correlation coefficient may assume a value from −1 to +1.

Question 7

The Wilcoxon rank-sum test computes a z-test statistic.

Question 8

The Wilcoxon signed-rank test of differences requires that the data be at least ordinal scaled and that the two samples be related.

Question 9

A Spearman's rank-order correlation coefficient of 0.91 indicates a very weak relationship.

Question 10

To use the sign test with paired data,trials must ________.

A)be independent
B)be dependent
C)have three or more outcomes
D)have a probability of 0.50

Question 11

The Wilcoxon rank-sum test includes a variable,W. It is the sum of the observed values from the larger sample.

Question 12

We can apply nonparametric tests to problems involving interval or ratio data.

Question 13

We can apply parametric tests,such as the t-test,to ordinal or ranked level of measurement.

Question 14

A one-tailed sign test is used to test for differences between two populations at the 0.10 level of significance. There were nine plus signs and five minus signs. What is the decision regarding the null hypothesis?

A)Fail to reject the null hypothesis.
B)Reject the null hypothesis.
C)Neither reject nor fail to reject the null hypothesis.
D)Should have used a paired t-test.

Question 15

To apply the Kruskal-Wallis test,the samples selected from the populations must be dependent.

Question 16

The test statistic for the null hypothesis that the correlation among the ranks is equal to zero is a chi-square statistic.

Question 17

The alternate hypothesis states that the correlation between two populations is greater than zero. The test of significance is one-tailed.

Question 18

The Kruskal-Wallis one-way analysis of variance by ranks is especially appropriate to test whether three or more population means are equal if the data are measured with an ordinal scale and/or the populations are not normal.

Question 19

For small samples,the test statistic for the sign test is the z-statistic.

Question 20

The Wilcoxon signed-rank test can replace the paired t-test when the assumptions for t cannot be met.

Question 21

For a given set of 12 ranked data values,the sum of the squared differences is 63.18. What is Spearman's coefficient of rank correlation for the data?

A)+0.7791
B)−0.7791
C)+0.2209
D)−0.2209

Question 22

A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman's (rho)is 0.86 for a sample of 15 observations,what is the computed value of the t-statistic?

A)0.456
B)6.08
C)0.425
D)2.16

Question 23

When testing H₀: Median equals $12.40 and the alternate hypothesis: Median does not equal $12.40,what is the critical value of z at the 10% level of significance?

A)±1.96
B)±1.65
C)±2.33
D)±0.10

Question 24

The decision rule for a small sample sign test is based on a(n)________.

A)binomial distribution
B)chi-square distribution
C)normal distribution
D)F-distribution

Question 25

The distribution of the sample statistic (H)for the Kruskal-Wallis test is approximately equal to the ________.

A)F-distribution
B)t-distribution
C)chi-square distribution
D)standard normal distribution

Question 26

What is the test statistic for Spearman's rank correlation?

A)t
B)z
C)F
D)Chi-square

Question 27

For the coefficient of rank correlation,what scale is used to measure the data?

A)Nominal
B)Ordinal
C)Interval
D)Ratio

Question 28

What test is an appropriate substitute for the ANOVA procedure if the assumptions for ANOVA cannot be met?

A)z
B)t
C)Rank correlation
D)Kruskal−Wallis

Question 29

What is a null hypothesis for a one-tailed sign test?

A)H₀: π = 0
B)H₀: π ≥ 1.00
C)H₀: π = 0.50
D)H₀: π ≤ 0.50

Question 30

A two-tailed test of hypothesis was conducted and 60 values were above the median. The computed z = 1.90. At the 0.05 level,what is the decision regarding the null hypothesis?

A)Reject the null hypothesis with a 0.05 Type I error rate.
B)Fail to reject the null hypothesis.
C)Reject the null hypothesis with a 0.025 Type I error rate.
D)None of these answers is correct.

Question 31

Which of the following tests is not a distribution-free test?

A)Rank correlation
B)Student's t
C)Kruskal-Wallis
D)Wilcoxon rank-sum

Question 32

What is a requirement that must be met before the Kruskal-Wallis one-way analysis of variance by ranks test can be applied?

A)Populations must be normal or near normal.
B)Populations must be independent.
C)Population standard deviations must be equal.
D)Data must be at least interval level.

Question 33

To determine whether four population means are equal,a sample from each population was selected at random. Using the Kruskal-Wallis test,H was computed to be 2.09. What is our decision at the 0.05 level of risk?

A)Fail to reject the null hypothesis because 0.05 < 2.09.
B)Fail to reject the null hypothesis because 2.09 < 7.815.
C)Reject the null hypothesis because 7.815 > 2.09.
D)Reject the null hypothesis because 2.09 > critical value of 1.96.

Question 34

Which statement is true when using the sign test and a large sample?

A)The chi-square value is applied to arrive at the degrees of freedom.
B)A normal distribution should be used to approximate a binomial distribution.
C)Wilcoxon z is the test statistic.
D)The F distribution is applied.

Question 35

A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is Spearman's coefficient of rank correlation?

A)−0.871
B)+0.224
C)+0.234
D)−0.234

Question 36

This nonparametric test requires at least ordinal level data. It is used if the assumptions required for the paired t-test cannot be met. Which test is it?

A)Wilcoxon signed-rank
B)ANOVA
C)Rank correlation
D)Kruskal-Wallis

Question 37

Which of the following statements is true regarding the sign test?

A)It is based on the sign of the differences.
B)It is used with independent populations.
C)The chi-square is used as the test statistic.
D)The "T" statistic is the test statistic.

Question 38

Which of the following values of Spearman's (rho)indicates the strongest relationship between two variables?

A)-0.91
B)-0.05
C)+0.64
D)+0.89

Question 39

What is the first step in applying the sign test?

A)Rank the paired data from high to low or vice versa.
B)Apply a correction factor to each observation.
C)Determine the sign of difference between each observed pair of data.
D)Determine the number of degrees of freedom.

Question 40

A data set has six values: 10,12,21,26,26,and 26. What ranks would be assigned to 26?

A)4,5,6
B)4,4,4
C)5,5,5
D)5.5,5.5,5.5

Question 41

A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is the computed value of t?

A)0.719
B)0.804
C)1.339
D)0.650

Question 42

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predicts an increase. The test statistic is ________.

A)0.224
B)1.179
C)1.707
D)0.179

Question 43

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. The Wilcoxon critical value is 3 for n = 7 with a 0.05 significance level. What decision should be made regarding the null hypothesis?

A)Reject the null hypothesis and conclude that the After is greater than Before.
B)Reject the null hypothesis and conclude that the Before is greater than After.
C)Fail to reject the null hypothesis.
D)Reject the null hypothesis and conclude that there is no difference between the Before and After.

Question 44

A nonparametric test requires that the data can be ________.

A)ranked
B)summed
C)graphed
D)transformed

Question 45

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The null hypothesis is ________.

A)H₀ : π = 0.5
B)H₀ : π ≠ 0.5
C)H₀ : π ≤ 0.5
D)H₀ : π ≥ 0.5

Question 46

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predicts an increase. Based on the analysis,we would conclude that ________.

A)the economists predict an increase in the economy
B)the economists predict a decrease in the economy
C)the economists predict no change in the economy
D)no conclusion can be reached

Question 47

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is the sum of the ranks for flavor #1?

A)144
B)139
C)156
D)153

Question 48

A nonparametric test ________.

A)assumes that the populations are normally distributed
B)assumes that the populations have equal standard deviations
C)makes no assumptions about the population distributions
D)assumes that the populations follow a standard normal distribution

Question 49

In the Wilcoxon signed-rank test,the ranks are ________.

A)assigned to paired observation with a difference of zero
B)assigned for each sample
C)assigned the sign (either positive or negative)of the difference between a pair of observations
D)all positive in sign

Question 50

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that there is no difference between the Before and After populations. What are the sum of the ranks?

A)4 and 6
B)5
C)17
D)6 and −11

Question 51

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is W,if flavor #1 is identified as population 1?

A)153
B)156
C)144
D)139

Question 52

A sign test cannot be applied when the data are ________.

A)nominal
B)ordinal
C)interval
D)ratio

Question 53

To test the hypothesis,the Wilcoxon signed-rank test uses a ________.

A)z-statistic
B)T-test statistic
C)chi-square statistic
D)student's t-statistic

Question 54

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. At the 0.05 level of significance,what is the decision?

A)Fail to reject null hypothesis; critical value is ±1.65.
B)Fail to reject null hypothesis; critical value is ±1.96.
C)Reject null hypothesis; critical value is 0.1732.
D)Reject null hypothesis; critical value is 0.3464.

Question 55

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The correct analysis would be a ________.

A)sign test based on the binomial distribution
B)sign test based on the standard normal distribution
C)chi-square test
D)Wilcoxon signed-rank test

Question 56

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is the z-test statistic?

A)−0.3464
B)0.3464
C)8.6602
D)0.2807

Question 57

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. What is the sum of the ranks?

A)41
B)28
C)19 and −7
D)6 and 15

Question 58

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is the sum of the ranks for flavor #2?

A)153
B)139
C)144
D)156

Question 59

A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is the sum of the differences in ranks?

A)128
B)100
C)0
D)1

Question 60

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. The Wilcoxon critical value is 3 for n = 7 with a 0.05 significance level. What decision should be made regarding the null hypothesis?

A)Reject the null hypothesis and conclude that After is greater than Before.
B)Reject the null hypothesis and conclude that Before is greater than After.
C)Fail to reject the null hypothesis.
D)Reject the null hypothesis and conclude that there is no difference between the Before and After.

Question 61

A nonparametric equivalent of a version of the ANOVA test,which tests the hypothesis that several population means are equal,is known as the ________.

A)Wilcoxon ranked-sum test
B)Spearman's coefficient of rank correlation
C)Kruskal-Wallis test
D)sign test

Question 62

If Spearman's rank correlation statistic is −0.91 with a sample size of 10,what is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?

A)−6.2080
B)6.2080
C)1.960
D)2.262

Question 63

The Spearman coefficient of rank correlation is a ________.

A)measure of correlation used to determine whether several population means are equal
B)measure of the association between sets of ranked data
C)measure of correlation based on the sign of a difference between two related observations
D)goodness-of-fit test used to test for normality

Question 64

A sign test is a ________.

A)parametric method used to determine the differences between two related observations
B)nonparametric method based on the sign of a difference between two related observations
C)nonparametric method that uses the chi-square distributions as the test statistic
D)parametric method for determining the differences between related observations where distribution dependent tests are used

Question 65

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 3?

A)9
B)80
C)3
D)23

Question 66

When the paired observations are equal in a Wilcoxon signed-rank test hypothesis ________.

A)observations are removed from the analysis.
B)the ranks are averaged.
C)a zero is assigned to the difference and retained in the analysis.
D)observations are removed from the analysis and n is not changed.

Question 67

For a given set of 12 ranked data values,the sum of the squared differences is 63.18. What is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?

A)0.221
B)0.673
C)0.779
D)0.327

Question 68

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 3?

A)57
B)80
C)4
D)210

Question 69

For the rank correlation coefficient,what test statistic is used to test the null hypothesis that the correlation is zero?

A)Chi-square
B)Student's t-statistic
C)z-statistic
D)H

Question 70

Which of the following tests would not be an example of a nonparametric method?

A)Sign test
B)t-test
C)Kruskal-Wallis test
D)Wilcoxon signed-rank test

Question 71

A hypothesis test that a rank correlation coefficient is zero is conducted at the 5% level of significance. If the correlation coefficient is 0.50 for a sample of 15 observations,what is the computed value of the t-statistic?

A)0.456
B)6.08
C)2.082
D)2.2361

Question 72

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 1?

A)9
B)163
C)3
D)23

Question 73

In the Kruskal-Wallis test for the following data,what are the degrees of freedom?

A)5
B)2
C)16
D)15

Question 74

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 1?

A)61.5
B)163
C)6
D)253

Question 75

A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman's (rho)is 0.75 for a sample of 15 observations,what is the computed value of the t-statistic?

A)0.456
B)4.088
C)4.391
D)2.236

Question 76

Twenty-five college seniors were given two brands of organic hamburgers to sample: Burger A and Burger B. Four students preferred Burger A and 21 preferred Burger B. A statistician wants to determine if one of the burgers is preferred over the other. The null hypothesis for this scenario is ________.

A)H₀: μ = 5.0
B)H₀: π = 5.0
C)H₀: μ = 0.5
D)H₀: π = 0.5

Question 77

In a Kruskal-Wallis test,the null hypothesis states equality among five different populations. The sample size for each population exceeds five. What is the critical value for the test using a 0.05 significance level?

A)1.960
B)5.05
C)9.488
D)2.776

Question 78

A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman's (rho)is 0.50 for a sample of 15 observations,what is the critical value?

A)±2.160
B)±2.131
C)±1.771
D)±1.753

Question 79

In the Kruskal-Wallis test for the following data,what are the degrees of freedom?

A)8
B)2
C)6
D)3

Question 80

In the Kruskal-Wallis test,the degrees of freedom are ________.

A)the total number of observations less one
B)the total number of observations
C)the number of populations less one
D)each sample size less one