Deck 16: Nonparametric Methods: Analysis of Ordinal Data

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

We can apply non-parametric tests to problems involving interval or ratio data.

Question 6

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 is measured with an ordinal scale and/or the populations are not normal.

Question 7

The Kruskal-Wallis method tests the hypothesis that ____________ or more population means are equal.

Question 8

The sign test requires the populations to be _____________.

Question 9

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

Question 10

The Kruskal-Wallis H statistic follows the __________ distribution.

Question 11

The Wilcoxon rank-sum test compares two dependent populations.

Question 12

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

Question 13

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

Question 14

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

Question 15

The Wilcoxon signed-rank test requires the populations to be _____________.

Question 16

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

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 Wilcoxon rank-sum test computes a z test statistic.

Question 19

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

Question 20

A _________ sign test should be applied, if H₀: π ≤ 0.50, H₁: π > 0.50 and the level of significance is 0.05.

Question 21

The ________ difference between "before and after" measurements is evaluated in a sign test.

Question 22

The Spearman coefficient of rank correlation computes the correlations for ____________ scaled data.

Question 23

Nonparametric tests require data that can be __________.

Question 24

In the Kruskal-Wallis method, testing for differences among populations is based on the sum of the ________.

Question 25

The sign test is one of a few tests that can test the value of the __________.

Question 26

A nonparametric test is also called a __________ test.

Question 27

The Wilcoxon rank-sum compares two populations based on the sum of the ________.

Question 28

The Wilcoxon rank-sum method tests for equality between two _____________ populations.

Question 29

In testing the significance of Spearman's rank-order coefficient, the alternate hypothesis is ______________________.

Question 30

The Kruskal-Wallis test is the nonparametric analogy to a one-way ________.

Question 31

The Spearman coefficient of rank correlation requires that observations be _______.

Question 32

The _____________ of the differences between "before and after" measurements is evaluated in a Wilcoxon signed-rank test.

Question 33

The Spearman coefficient of rank correlation method ____________ the observations in each sample.

Question 34

The Wilcoxon rank-sum uses the _____________ as the test statistic.

Question 35

In testing the significance of Spearman's rank-order coefficient, the null hypothesis is _______________.

Question 36

The test statistic for the Wilcoxon signed-rank test is the _________ statistic.

Question 37

In a sign test, the test statistic is based on the _______________ distribution.

Question 38

One difference between the Kruskal-Wallis method and one-way ANOVA is that the Kruskal-Wallace tests do not require the population ___________ to be the same.

Question 39

The ______ test statistic is used to test the significance of the Spearman coefficient of rank correlation.

Question 40

A Spearman rank-order correlation coefficient of _____ indicates that there is no association between the two variables.

Question 41

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 42

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

Question 43

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

A)
B)
C)
D)

Question 44

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

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

Question 45

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 46

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 47

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 48

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 49

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

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

Question 50

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

Question 51

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 52

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.

Question 53

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 54

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

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

Question 55

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 56

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 57

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 58

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 59

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 60

A one-tailed sign test is used to test for differences between two populations at the 0.10 level of significance. There were nine pluses and five minuses. 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 61

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 62

A study was conducted on the percent of total advertising dollars spent by ten 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 63

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 64

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 65

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) a sign test based on the standard normal distribution.
C) a chi-square test.
D) a Wilcoxon signed-rank test.

Question 66

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 67

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 test statistic is _______.

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

Question 68

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. Based on the analysis, we would conclude that:

A) the economists favor an increase in the economy.
B) the economists favor a decrease in the economy.
C) the economists favor no change in the economy.
D) No conclusion can be reacheD.

Question 69

A study was conducted on the percent of total advertising dollars spent by ten 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 70

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 71

A nonparametric test requires that the data can be:

A) ranked.
B) summed.
C) graphed.
D) transformeD.

Question 72

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 73

A nonparametric test cannot be applied when the data are:

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

Question 74

A study was conducted on the percent of total advertising dollars spent by ten 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 75

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 76

In the Wilcoxon signed-rank test, the ranks:

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

Question 77

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 78

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 79

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 80

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)
B)
C)
D)