Deck 21: Nonparametric Techniques

Question 1

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

Answer 1

B

Question 2

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 to the left of the location of population 2. The appropriate critical value for a sample of size 20 (that is, the number of nonzero differences) is:

Answer 2

C

Question 3

Which of the following is the alternative hypothesis tested in applications of the Kruskal-Wallis test?

Answer 3

C

Question 4

In a Wilcoxon signed rank sum 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 standardised test statistic z is:

Question 5

A matched pairs experiment yielded the following paired differences: The value of the standardised sign test statistic z is:

Question 6

In a sign test, the following information is given: number of zero differences = 3, number of positive differences = 20, and number of negative differences = 5. The value of the standardised test statistic z is:

Question 7

Consider the following data set: The rank assigned to the four observations of value 22 is:

Question 8

Which of the following is the non-parametric equivalent to the parametric t-test of for matched pairs?

Question 9

In a Kruskal-Wallis test there are five samples and the value of the test statistic is calculated as H = 11.15. The most accurate statement that can be made about the p-value is that:

Question 10

Consider the following data set: The rank assigned to the three observations of value 1.3 is:

Question 11

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

Question 12

Consider the following two samples: The value of the test statistic for a right-tailed Wilcoxon rank sum test is:

Question 13

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 to the right of the location of population 2. The appropriate critical value for a sample of size 20 (that is, the number of nonzero differences is 20) is:

Question 14

The Kruskal-Wallis test statistic can be approximated by a Chi-squared 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:

Question 15

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 left to the location of population 2. The appropriate critical values for a sample of size 20 (that is the number of nonzero differences is 20) are:

Question 16

Which of the following is the correct sample size requirement for the Wilcoxon signed rank sum test statistic to be approximately normally distributed?

Question 17

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. The appropriate critical values at the 5% significance level are:

Question 18

In a normal approximation to the Wilcoxon signed rank sum test, the test statistic is calculated as z = 1.59. For a two-tail test, the p-value is:

Question 19

In a Wilcoxon signed rank sum test, the test statistic is calculated as T = 45. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. If there are n = 15 observations for which , and the 5% significance level is used, then:

Question 20

Consider the following two samples: The value of the test statistic for a left-tailed Wilcoxon rank sum test is:

Question 21

Which of the following tests would be an example of a non-parametric method?

Question 22

Compared to parametric tests, non-parametric tests use the information contained in the data:

Question 23

A non-parametric method to compare two populations, when the samples are independent but the assumptions behind the independent samples t-test are violated, is the:

Question 24

Which of the following best describes the hypotheses in the Kruskal-Wallis test and Friedman test?

Question 25

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The unstandardised test statistic (that is the rank sum) is T = 210. The value of the standardised test statistic z is:

Question 26

In a Kruskal-Wallis test for comparing five populations, the test statistic is calculated as H = 10.20. If the test is conducted at the 1% significance level, then:

Question 27

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

Question 28

A non-parametric method to compare two or more populations, when the samples are matched pairs and the data are either ordinal or interval but not normal, is the:

Question 29

The Wilcoxon rank sum test (like most of the non-parametric tests presented in your textbook) actually tests to determine whether the population distributions have identical: $\begin{array}{|l|l|}\hline A&\text {locations. }\\\hline B&\text {spreads (variances). }\\\hline C&\text {shapes. }\\\hline D&\text { All of the above are correct answers.}\\\hline \end{array}$

Question 30

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

Question 31

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:

Question 32

The non-parametric counterpart of the randomised block model of the analysis of variance is the:

Question 33

In a Friedman test for comparing four populations, provided that there are eight blocks, the test statistic is calculated as F = 10.98. If the test is conducted at the 5% significance level, the conclusion and p-value will be:

Question 34

A non-parametric method to compare two or more populations, when the samples are independent and the data are either ordinal or interval but not normal, is the:

Question 35

Which of the following best describes when a non-parametric test for comparing two or more populations should be used instead of its parametric counterpart?

Question 36

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

Question 37

A non-parametric method to compare two populations, when the samples consist of matched pairs of observations and the data are either ordinal or interval, and where the normality requirement necessary to perform the parametric test is not satisfied, is the:

Question 38

The appropriate measure of central location of ordinal data is the:

Question 39

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

Question 40

Which of the following statements is correct regarding the Kruskal-Wallis test?

Question 41

Which of the following best describes when to apply the Friedman test to determine whether the locations of two or more populations are the same?

Question 42

In a normal approximation to the sign test, the standardised 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, the p-value is:

Question 43

The Friedman test is the non-parametric counterpart of the randomised block experimental design of the analysis of variance.

Question 44

Which of the following will never be a required condition of a non-parametric test?

Question 45

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

Question 46

In a Wilcoxon rank sum test, the two sample sizes are 6 and 6, and the value of the Wilcoxon test statistic is T = 20. If the test is two-tailed and the level of significance is $\alpha = 0.05$ , then: $\begin{array}{|l|l|}\hline A&\text {the null hypothesis will be rejected. }\\\hline B&\text {the null hypothesis will not be rejected. }\\\hline C&\text {the alternative hypothesis will not be rejected. }\\\hline D&\text {not enough in formation has been given to answer this question. }\\\hline \end{array}$

Question 47

The F-test of the randomised block design of the analysis of variance requires that the random variable of interest must be normally distributed and the population variances must be equal. When the random variable is not normally distributed, we can use:

Question 48

Which of the following best describes when to apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2?

Question 49

The Kruskal-Wallis test requires independent sample.

Question 50

In the sign test applications, the normal approximation to the binomial distribution may be used whenever the number of nonzero differences is greater than or equal to:

Question 51

The Wilcoxon rank sum test for independent samples actually tests whether the population distributions are identical.

Question 52

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

Question 53

The Friedman test statistic is approximately chi-squared distributed with (k - 1) degrees of freedom, provided that either the number of blocks b or the number of treatments k is greater than or equal to 5.

Question 54

A non-parametric test is one that makes no assumptions about the specific shape of the population from which a sample is drawn.

Question 55

The Wilcoxon signed rank sum test is the nonparametric counterpart of the t-test of µ_D.

Question 56

A one-sample t-test is the parametric counterpart of the Friedman test for randomised block experimental design.

Question 57

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that at least one of the two sample sizes exceed 10.

Question 58

Which of the following best describes when the Wilcoxon rank sum test statistic T is approximately normally distributed?

Question 59

The sign test and the Wilcoxon signed rank sum test require matched pairs.

Question 60

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

Question 61

The Friedman test is employed to compare two or more populations when the data are generated from a matched pairs experiment, and are either ordinal or interval but not normally distributed.

Question 62

Use the 5% significance level to test the hypotheses. $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The location of population A is to the left of the location of population B,
given that the data below are drawn from a matched pairs experiment. $\begin{array} { | c | c | c | c | c | c | c | c | c | } \hline \text { Matched Pair } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \text { A } & 8 & 10 & 11 & 7 & 6 & 7 & 13 & 10 \\\hline \text { B } & 6 & 9 & 12 & 10 & 12 & 10 & 5 & 8 \\\hline\end{array}$

Question 63

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign test.

Question 64

We can use the Friedman test to determine whether two populations differ. The conclusion will be the same as that produced by the sign test.

Question 65

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 66

In a normal approximation to the sign test, the standardised test statistic is calculated as z = 2.07. If the alternative hypothesis states that the location of population 1 is to the right of the location of population 2, then the p-value of the test is 0.0192.

Question 67

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 68

The Kruskal-Wallis test can be used to test for a difference between two populations. It will produce the same outcome as the two-tailed Wilcoxon rank sum test.

Question 69

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 5 and 8. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using the 0.10 significance level, the appropriate critical values are 21 and 49.

Question 70

The Kruskal-Wallis test is applied to compare two or more populations when the samples are independent and the data are ordinal or numerical and non-normal.

Question 71

Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 10% significance level that the two population locations differ. , n = 50

Question 72

The Kruskal-Wallis test can be used to determine whether a difference exists between two populations. However, to determine whether one population location is larger than another, we must apply the Wilcoxon rank sum test.

Question 73

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 74

The Kruskal-Wallis test uses the Chi-squared distribution.

Question 75

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

Question 76

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 9. The alternative hypothesis is that the location of population 1 is to the left of the location of population 2. Using the 0.05 significance level, the appropriate critical values are 31 and 65.

Question 77

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The value of the unstandardised test statistic is T = 225. The value of the standardised test statistic is z = -1.50.

Question 78

One of the required conditions of the sign test is that the number of nonzero differences n must be smaller than or equal to 10.

Question 79

In a Wilcoxon rank sum test for independent samples, the two sample sizes are 4 and 6, and the value of the Wilcoxon test statistic is T = 25. If the test is two-tailed and the level of significance is 0.05, then the null hypothesis will be rejected.

Question 80

Radio advertising is big business, second only to television advertising. The objective for radio advertisements is to get listeners to remember as much as possible about the product/service being advertised. The advertising executive of a large company must decide between two pitched radio advertisements for their company. In order to ascertain the general public's perception, 12 randomly chosen people are selected to listen to both potential advertisements and are then asked a series of 5 questions regarding the radio advertisement's content. The number of correct responses are recorded and listed below. Assume that responses are non-normal. a. Which test is appropriate for this situation?
b. Do these data provide enough evidence at the 5% significance level to conclude that the two radio advertisements differ?