Deck 15: Nonparametric Statistics

Question 1

The rank correlation coefficient is used when one is:

A) correlating quantitative data
B) correlating rankings of individual values for two variables
C) analyzing data which are assumed to be linearly related
D) not interested in drawing inferences from the study
E) analyzing data which are assumed to be non-linearly related

Answer 1

correlating rankings of individual values for two variables

Question 2

The Spearman rank correlation coefficient is calculated by first ranking the data values, and then calculating the Pearson correlation coefficient of the ranks.

Answer 2

True

Question 3

A school principal suspected that a teacher's attitude toward a first-grader depended on his original judgment of the child's ability. The principal also suspected that much of that judgment was based on the first-grader's IQ score, which was usually known to the teacher. After three weeks of teaching, a teacher was asked to rank the nine children in his class from 1 (highest) to 9 (lowest) as to his opinion of their ability. Do the data provide sufficient evidence to indicate a positive correlation between the teacher's ranks and the ranks of the IQs? Use = .05.
Test Statistic: = ______________
Reject Region:
Reject if | | > ______________
Conclude:
______________
A positive correlation ______________ between the teacher's ranks of the IQs.

Answer 3

.8333; .60; Reject the null hypothesis; exists

Question 4

The Spearman rank-correlation is a nonparametric test that 1) uses the directions of differences observed in a matched-pairs sample to determine whether the relative frequency distributions of two statistical populations are identical to or different from one another and 2) determines whether a sample comes from a population with a specified median.

Question 5

The following paired observations were obtained on two variables x and y: Calculate Spearman's rank correlation coefficient :
______________
Do the data present sufficient evidence to indicate a correlation between x and y? Test using = 0.05.
Reject Region:
Reject if | | > ______________
Conclude:
______________
There ______________ correlation between x and y.

Question 6

The Spearman rank correlation coefficient allows us to measure and test to determine whether there is evidence of a linear relationship between two variables if:

A) one or both variables ordinal
B) both variables are interval but the normality requirement for parametric tests is not satisfied
C) both one or both variables ordinal and both variables are interval but the normality requirement for parametric tests is not satisfied
D) neither one or both variables ordinal nor both variables are interval but the normality requirement for parametric tests is not satisfied
E) none of these

Question 7

The Spearman rank-correlation test is a nonparametric test that uses the directions of differences observed in a matched-pairs sample to determine whether the relative frequency distributions of two statistical populations are identical to or different from one another.

Question 8

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 9

Spearman's rank-correlation coefficient can only take on values between:

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

Question 10

If the Friedman test is applied to a data set that are generated from a randomized block experiment with 5 treatments and 7 blocks, then the rejection region at the 5% significance level is .

Question 11

A professor was interested in the relationship between a student's rank on an oral exam and the student's rank on a written exam. The professor selected 8 students at random and ranked their scores for both the oral exam and the written exam. The following data was recorded: Find and interpret the rank correlation between a student's rank on the oral exam and the student's rank on the written exam.
Compute : ______________
There is ______________ relationship between the student's rank on the oral exam and the student's rank on the written exam.

Question 12

Two psychometricians (educators who are experts in the field of psychological test design) were asked to rank six designs for a new standardized college entrance exam. This problem uses Spearman's rank correlation coefficient to see if there is a (positive) relationship between the educators' rankings.
The null and alternate hypotheses are as follows: (There is no association between the rank pairs) (The correlation between the rank pairs is positive)
Describe why the test statistic is called the rank correlation coefficient.
________________________________________________________
Test Statistic: = ______________
Rejection region (for = 0.05):
Reject if > ______________
Conclude: ______________
There ______________ sufficient evidence to indicate there is any significant positive correlation between the educators' rankings.
What does this result mean in the context of the problem?
________________________________________________________
What is the observed significance level for this test?
______________

Question 13

The population Spearman correlation coefficient is labeled , and the sample statistic used to estimate its value is labeled .

Question 14

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 15

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

Question 16

Which of the following statements about Spearman's rank-correlation coefficient is false?

A) It is the test statistic used in Spearmen's rank-correlation test, symbolized by.
B) It can only take on values between 0 and + 1.
C) Positive values near + 1 point to a monotonically increasing relationship between the two variables, such that steady increases in one are associated with steady increases in the other.
D) None of these.
E) All of these.

Question 17

To determine if a relationship exists between two variables, the hypotheses to be tested are .

Question 18

The Friedman test is the nonparametric counterpart to the randomized block design of the analysis of variance.

Question 19

In testing at the 5% significance level, a sample of size 20 is used. The rejection region is:

A) -.377. 377
B) .777 or-.377
C) .450 or-.450
D) -.450. 450
E) none of these

Question 20

The Friedman test is a nonparametric test that can be used to compare more than two dependent samples when the assumptions for an analysis of variance are invalid.

Question 21

A three independent samples one-way analysis of variance test corresponds to:

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 Kruskal-Wallis test
E) a Friedman test

Question 22

A toy store manager was interested in determining whether the assembly time is the same for three models of baby strollers. The manager selected five employees at random and asked each of them to assemble each of the strollers. The assembly time, in minutes, was recorded as follows: The manager wasn't sure whether the assumptions for the usual analysis of variance were valid, so she decided to use a nonparametric procedure. Use the appropriate method to determine whether the assembly time is the same for the three models of baby strollers. Use = 0.05.
Test Statistic: = ______________
Reject Region:
Reject if > ______________
Conclude: ______________
The distributions of assembly time for the three models of baby strollers are ______________.

Question 23

The following data were generated from a blocked experiment. Conduct a Friedman test at the 5% significance level to determine if at least two population locations differ. Test Statistic: = ______________
Reject Region:
Reject if > ______________
Conclude: ______________
The locations of all four populations are ______________.

Question 24

If Friedman test is applied to a data set that are generated from a randomized block experiment with 4 treatments and 8 blocks, then the rejection region at the 5% significance level is:

A) 1.6450
B) 7.8147
C) 9.4877
D) 11.0705
E) 1.8450

Question 25

The reaction times to three stimuli were recorded for each of 8 subjects. The data, recorded in seconds, are shown below. This problem uses Friedman's test to determine if there is a difference among the population distributions of reaction times. What experimental design is being used in this problem?
____________________________
The null and alternate hypotheses are as follows: : The three population distributions are identical. : At least two of the three population distributions differ in location.
Describe what the Test statistic is.
________________________________________________________
Test statistic: = ______________
Rejection region for =0.05:
Reject if > ______________
Conclusion: ______________
There is ______________ evidence to conclude that the reaction times for the three stimuli are different.
Estimate the p-value for this problem?
______________

Question 26

Another school district also planned to evaluate two different workbooks and two distinct teaching machines to assess their effectiveness in teaching the concept of multiplication. However, the administrators in this school district consulted a statistician about the design of their study. Because they were looking for a method effective on children of all abilities, the statistician suggested they check the children's past scholastic records and divide the children into groups according to their ability level. These ability groups represent relatively homogeneous experimental units within which the comparison of teaching methods may be made. She assigned one child from each ability level to each teaching method. Twenty students participated in the study. After receiving instruction, the children took a multiplication test and the number of errors they made were recorded. What experimental design did the statistician use?
________________________________________________________
The null and alternate hypotheses are as follows: : The three population distributions are identical. : At least two of the three population distributions differ in location.
Describe what the test statistic is.
________________________________________________________
Test Statistic: = ______________
Reject Region:
Reject if F > ______________
Conclude: ______________
The teaching methods ______________ equally effective.
Estimate the observed significance level of this test.
______________

Question 27

A randomized block design analysis of variance test corresponds to:

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
E) all of these

Question 28

To apply the Friedman test to determine whether the locations of two or more populations are the same, the samples must be:

A) from matched pairs experiment
B) from normal populations
C) independent
D) larger than 20
E) from matched pairs experiment and from normal populations

Question 29

The restaurant critic on a newspaper claims that the hamburgers that one gets at the hamburger chain restaurants are all equally bad and that people who claim to like one hamburger over others are victims of advertising. In fact, he claims that if there were no differences in appearance, then all hamburgers would be rated equally. To test the critic's assertion, ten teenagers are asked to taste hamburgers from three different fast-food chains. Each hamburger is dressed in the same way (mustard, relish, tomato, and pickle) with the same type of bun. The teenagers taste each hamburger and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below. Which statistical technique is appropriate if you want to compare the quality of hamburger of the three chain restaurants?
______________
Can we infer at the 1% significance level that the critic is wrong?
Test Statistic: ______________
Reject Region:
Reject if the test statistic > ______________
Conclude: ______________
We ______________ infer at the 1% significance level that the critic is wrong.
Using the appropriate statistical table, what statement can be made about the p-value for this test?
______________

Question 30

The Friedman test is the nonparametric counterpart of the randomized block experimental design of the analysis of variance.

Question 31

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

A) p-value < 0.01
B) .05 < p-value < .10
C) .025 < p-value < .05
D) p-value > .10
E) 0.01< p-value < 0.025

Question 32

The Friedman test are always:

A) one-tail
B) two-tail
C) used with one sample
D) used when the populations are normally distributed
E) used all the time

Question 33

The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below. Which statistical technique the general manager can use to help him make a decision?
______________
Can the general manager infer at the 5% significance level that there are differences in the taste ratings of the four dinners?
Test Statistic: ______________
Reject Region:
Reject if test statistic > ______________
Conclude: ______________
The general manager ______________ infer at the 5% significance level that there are differences in the taste ratings of the four dinners.
Using the appropriate statistical table, what statement can be made about the p-value for this test?
______________

Question 34

The Friedman test is applied to problems with the following characteristics:

A) the problem objective is to compare two or more populations
B) the data are either ordinal or interval but not nominal
C) the data are generated from a randomized block experiment
D) all of these
E) the problem objective is to compare two or more populations and the data are either ordinal or interval but not nominal

Question 35

If the Friedman test is applied to a data set that are generated from a randomized block experiment with 3 treatments and 5 blocks, then the rejection region at the 2.5% significance level is > 12.8325.

Question 36

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

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
E) reject the null hypothesis, p-value = 0

Question 37

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

Question 38

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 39

The nonparametric counterpart of the randomized block model of the analysis of variance is the:

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

Question 40

A nonparametric 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:

A) the Wilcoxon signed rank sum test
B) the sign test
C) the Friedman test
D) the Kruskal-Wallis test
E) none of these

Question 41

Apply the Friedman test to the accompany table of ordinal data to determine whether we can infer at the 10% significance level that at least two population locations differ. Test Statistic: = ______________
Reject Region:
Reject if > ______________
Conclude: ______________
We ______________ infer at the 10% significance level that at least two population locations differ.

Question 42

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 43

A one-sample t-test corresponds to a Kruskal-Wallis test.

Question 44

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

Question 45

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

Question 46

In all applications of the Kruskal-Wallis test, the alternative hypothesis to be tested is always stated as:

A) the locations of all k populations are the same
B) at least two population locations differ
C) the locations of all w populations differ
D) the locations of all k populations differ
E) at least two population locations are the same

Question 47

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:

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 test results are inconclusive
E) the t-test for matched pairs must be used

Question 48

In a 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 49

The normal approximation to the Wilcoxon signed rank sum test is used whenever the number of none zero differences is 50 or more.

Question 50

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

Question 51

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 52

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

Question 53

Kruskal-Wallis test is a nonparametric test that can be used to compare more than two independent samples when the assumptions for an analysis of variance are invalid.

Question 54

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

A) Kruskal-Wallis test
B) Friedman test
C) Wilcoxon rank sum test
D) Wilcoxon signed rank sum test
E) two-tailed t-test

Question 55

In a Kruskal-Wallis test, there are four samples, and the value of the test statistic is calculated as H = 13.21. Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.005 but smaller than 0.01.

Question 56

In a Kruskal-Wallis test, there are three samples, and the value of the test statistic is calculated as H = 7.378. Then the p-value of the test is 0.025.

Question 57

The Kruskal-Wallis test is always:

A) one-tail
B) two-tail
C) used with one sample
D) used with only two samples
E) used when the populations are normally distributed

Question 58

The Kruskal-Wallis Test for Differences in more than 2 Medians is a nonparametric alternative to:

A) ANOVA F test for completely randomized experiments
B) Student's t-test for related samples
C) Student's t-test for independent samples
D) Wilcoxon's Rank Sum Test for differences in two medians
E) Student's t-test for related samples and Student's t-test for independent samples

Question 59

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

Question 60

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

Question 61

The Wilcoxon signed rank test is a nonparametric test that uses the directions of differences observed in a matched-pairs sample to determine whether the relative frequency distributions of two statistical populations are identical to or different from one another.

Question 62

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

Question 63

A computer laboratory manager was interested in whether there was a difference in functioning time before needing to be recharged for three battery packs for laptop computers. The manager took a random sample of six battery packs of each brand and tested them. The results, in hours of functioning before needing to be recharged, were recorded as The manager, unsure that the assumptions for the usual parametric analysis of variance were valid, decided to employ nonparametric methods. Use the appropriate nonparametric procedure to determine whether the distribution of functioning time before needing to be recharged is the same for the three brands of battery packs. Use = 0.05.
Test Statistic:
H = ______________
What is the critical value for the test statistic?
Reject if the test statistic > ______________.
Conclude: ______________
There ______________ sufficient evidence at = 0.05 to say that at least two of the distributions of functioning times before battery needing to be recharged differ in location.

Question 64

Apply the Kruskal-Wallis test to determine if there is enough evidence at the 5% significance level to infer that at least two populations differ. Test statistic: H = ______________
Reject if H > ______________
Conclude: ______________
There ______________ enough evidence at the 5% significance level to infer that at least two populations differ.

Question 65

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

Question 66

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

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
E) it is less than 0.025

Question 67

An experiment was conducted to examine the effect of age on heart rate when a person is subjected to a specific amount of exercise. Ten men randomly selected from each of four age groups: 10-19, 20-39, 40-59, and 60-69. Each man walked a treadmill at a fixed grade for a period of 12 minutes, and the increase in heart rate (the difference before and after exercise) was recorded (in beats per minute). The data are shown in the table. Do the data present sufficient evidence to indicate differences in location for at least two of the four age groups? Test using the Kruskal-Wallis H test with = 0.01.
What is H?
______________
What is the critical value for the test statistic?
Reject if H > ______________
Conclude: ______________
There is ______________ of a difference in location.
Find the approximate p-value for the test above.
______________

Question 68

A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of the most recently watched movies. The rating categories were: 1 = terrible, 2 = fair, 3 = good, and 4 = excellent. Each respondent was also asked to categorize his or her age as either: 1 = teenager, 2 = young adult (20-34), 3 = middle age (35-50), and 4 = senior (over 50). The results are shown below. Do these data provide sufficient evidence to infer at the 5% significance level that there were differences in ratings among the different age categories?
Test statistic:
H = ______________
What is the critical value for the test statistic?
Reject if the test statistic > ______________.
Conclude: ______________
There ______________ sufficient evidence to infer at the 5% significance level that there were differences in ratings among the different age categories.
What statement can be made about the p-value for this test?
______________

Question 69

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:

A) 5
B) 15
C) 25
D) 30
E) 45

Question 70

In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: Conduct the test at the 5% significance level.
Test statistic: H = ______________
Reject if H > ______________
Conclude: ______________
There ______________ enough evidence to conclude that differences exist among three different advertisements.
What is the most accurate statement that can be made about the p-value of this test?
______________

Question 71

The critical value is taken from the F-distribution whenever the Wilcoxon signed rank test is employed.

Question 72

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, is the:

A) Kruskal-Wallis test
B) Friedman test
C) Wilcoxon rank sum test
D) Wilcoxon signed rank sum test
E) chi-square test

Question 73

Suppose there is interest in comparing the median response time for three independent groups learning a new specific task. The appropriate nonparametric procedure is:

A) the Wilcoxon Rank Sums Test
B) the Wilcoxon Signed Rank Test
C) the Kruskal-Wallis Test for Differences in Medians
D) the Friedman test
E) none of these

Question 74

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

Question 75

The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlors, hamburger emporiums, and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed. Do these data provide enough evidence at the 10% significance level to infer that there are differences in ages among the customers of the three restaurants?
Test statistic: H = ______________
Reject if H > ______________
Conclude: ______________
There ______________ enough evidence at the 10% significance level to infer that there are differences in ages among the customers of the three restaurants.

Question 76

Three treatments were compared using a completely randomized design. The data are shown in the table. Do the data provide sufficient evidence to indicate a difference in location for at least two of the population distributions? Test using the Kruskal-Wallis H statistic with = 0.05.
Test statistic:
H = ______________
What is the critical value for the test statistic?
Reject if the test statistic > ______________.
Conclude: ______________
There ______________ a difference in location among the three treatments.

Question 77

Which of the following distributions approximate 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?

A) normal distribution
B) chi-squared distribution with k - 1 degrees of freedom
C) Student t-distribution with k - 2 degrees of freedom
D) Student t-distribution with k - 3 degrees of freedom
E) either chi-squared distribution with k - 5 degrees of freedom or Student t distribution with k + 5 degrees of freedom

Question 78

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

Question 79

Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A fourth grade class of 24 subjects was randomly assigned to 4 groups and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This problem uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another. What is the value of H in this problem?
______________
Find the rejection region for = 0.05.
Reject if H > ______________
Conclude: ______________
There is ______________ evidence at = 0.05 to say that the number of errors differs from one teaching method to another.
What is the p-value for this test?
______________

Question 80

The Wilcoxon signed-rank test is a nonparametric test that 1) uses the directions of differences observed in a matched pairs sample to determine whether the relative frequency distributions of two statistical populations are identical to or different from one another and 2) determines whether a sample comes from a population with a specified median.