Deck 17: Nonparametric Statistics

Question 1

Correlation coefficient cannot be used to analyze the association between two variables when only ordinal-level data are available.

Answer 1

False

Question 2

The appropriate test for comparing the means of two populations using ordinal-level data from two related samples is the Wilcoxon test and not Mann-Whitney U test.

Answer 2

True

Question 3

A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.

Answer 3

False

Question 4

The nonparametric counterpart of the t test to compare the means of two related samples is the Mann-Whitney U test.

Question 5

The nonparametric alternative to analysis of variance for a randomized block design is the Friedman test.

Question 6

The nonparametric alternative to the one-way analysis of variance is the Kruskal-Wallis test.

Question 7

The nonparametric counterpart of the t test to compare the means of two independent populations is the Mann-Whitney U test.

Question 8

The appropriate test for comparing the means of two populations using ordinal-level data from two independent samples is the Mann-Whitney U test.

Question 9

When only ordinal-level data are available, Spearman's rank correlation rather than the Pearson product-moment correlation coefficient must be used to analyze the association between two variables.

Question 10

Nonparametric statistics are sometimes called distribution-dependent statistics.

Question 11

Statistical techniques based on assumptions about the population from which the sample data are selected are called parametric statistics.

Question 12

To compare the means of two populations which cannot be assumed to be normally distributed and only ordinal-level data is available from two independent samples, we should use the t test for independent samples rather than the Mann-Whitney U test.

Question 13

An advantage of nonparametric statistics is that some nonparametric tests can be used to analyze situations in which data is available at only the nominal or the ordinal level.

Question 14

In the one-sample runs test for randomness of the observations in a large sample the sampling distribution of R, the number of runs, is approximately binomial.

Question 15

To compare the means of two populations which cannot be assumed to be normally distributed and only ordinal-level data is available from two independent samples, instead of the t test for independent samples we should use the Mann-Whitney U test.

Question 16

The sampling distribution of R, the number of runs, in the one-sample runs test for randomness of the observations in a large sample is approximately normal.

Question 17

The methods of parametric statistics can be applied to nominal or ordinal data.

Question 18

The one-sample runs test is a nonparametric test of randomness in the sample data.

Question 19

The one-sample runs test is a nonparametric test for sequential independence.

Question 20

Nonparametric statistical techniques are based on fewer assumptions about the population and the parameters compared to parametric statistical techniques.

Question 21

Which of the following tests should be used to compare the means of two populations if the samples are related?

A)Mann-Whitney test
B)Wilcoxon test
C)Runs test
D)Spearman's test
E)Kruskal-Wallis test

Question 22

The Wilcoxon test was used on 18 pairs of data.The total of the ranks (T)were computed to be 111 (for + ranks)and 60 (for - ranks).The z value for this test is ___.

A)-1.11
B)-0.05
C)-0.07
D)0.033
E)2.22

Question 23

Charles Kline monitors the daily performance of his investment portfolio by recording a "+" or a "-"sign to indicate whether the portfolio's value increased or decreased from the previous day.His record for the last eighteen business days is "- + + - - - + - - + + + + + + + + -".The number of runs in this sample is ___.

A)seven
B)six
C)four
D)three
E)one

Question 24

The Wilcoxon test was used on 16 pairs of data.The total of the ranks (T)were computed to be 76 (for + ranks)and 60 (for - ranks).The z value for this test is ___.

A)-0.41
B)-0.02
C)0.02
D)16
E)-0.041.

Question 25

Charles Kline monitors the daily performance of his investment portfolio by recording a "+" or a "-"sign to indicate whether the portfolio's value increased or decreased from the previous day.His record for the last eighteen business days is "- + + - - - + - - + + + - + + + + -".The number of runs in this sample is ___.

A)uncertain
B)four
C)five
D)nine
E)one

Question 26

The nonparametric counterpart of the t test to compare the means of two independent populations is the ___.

A)chi-square goodness-of-fit test
B)chi-square test of independence
C)Mann-Whitney U test
D)Wilcoxon test
E)Friedman test

Question 27

Which of the following tests should be used to compare the means of two populations if the samples are independent?

A)Mann-Whitney test
B)Wilcoxon test
C)Runs test
D)Spearman's test
E)Kruskal-Wallis test

Question 28

The alternate hypothesis for a one-sample runs test is ___.

A)"the observations in the sample are not cross-linked"
B)"the observations in the sample are correlated"
C)"the observations in the sample are not statistically independent"
D)"the observations in the sample are not randomly generated"
E)"the observations are not systematically generated"

Question 29

In a Mann-Whitney U test, U statistic was calculated to be 38.78 based on sample sizes of 24 and 20.What is the z value for this test?

A)0.133
B)-4.74
C)240
D)42.43
E)8.75

Question 30

Most "before and after" types of experiments should be analyzed using ___.

A)chi-square goodness-of-fit test
B)Kruskal-Wallis test
C)Mann-Whitney U test
D)Wilcoxon test
E)Friedman test

Question 31

In the Wilcoxon test of the differences between two populations, the value z statistic was calculated to be 1.80.If the level of significance is 0.10, which of the following decisions is appropriate?

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
C)indeterminate without the sample size
D)indeterminate without all of the data
E)inconclusive

Question 32

In the Wilcoxon test of the differences between two populations, the value z statistic was calculated to be 1.80.If the level of significance is 0.05, which of the following decisions is appropriate?

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
C)indeterminate without the sample size
D)indeterminate without all of the data
E)inconclusive

Question 33

The one-sample runs test is a ___.

A)nonparametric test for statistical independence
B)parametric test for statistical independence
C)nonparametric test of randomness
D)nonparametric test for correlation
E)parametric test of sequences

Question 34

The null hypothesis for a one-sample runs test is ___.

A)"the observations in the sample are randomly generated"
B)"the observations in the sample are not correlated"
C)"the observations in the sample are statistically independent"
D)"the observations in the sample are cross-linked"
E)"the observations are systematically generated"

Question 35

The nonparametric counterpart of the t test to compare the means of two related samples is the ___.

A)chi-square goodness-of-fit test
B)chi-square test of independence
C)Mann-Whitney U test
D)Wilcoxon test
E)Friedman test

Question 36

The methods of parametric statistics require ___.

A)interval or ratio data
B)nominal or ordinal data
C)large samples
D)small samples
E)qualitative data

Question 37

Statistical techniques based on assumptions about the population from which the sample data are selected are called ___.

A)population statistics
B)parametric statistics
C)nonparametric statistics
D)chi-square statistics
E)correlation statistics

Question 38

Nonparametric statistics are sometimes called ___.

A)nominal statistics
B)interval statistics
C)distribution-dependent statistics
D)distribution-free statistics
E)qualitative statistics

Question 39

Statistical techniques based on fewer assumptions about the population and the parameters are called ___.

A)population statistics
B)parametric statistics
C)nonparametric statistics
D)chi-square statistics
E)correlation statistics

Question 40

In a Mann-Whitney U test, the U statistic was calculated to be 58.0 based on sample sizes of 22 and 28.What is the z value for this test?

A)51.17
B)308
C)0.117
D)-4.88
E)-2.44

Question 41

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The critical chi-square value is ___.

A)15.086
B)13.277
C)7.779
D)9.210
E)8.657

Question 42

Which of the following tests should be used to compare the means of three populations if the sample data is ordinal?

A)one-way analysis of variance
B)Kruskal-Wallis test
C)Wilcoxon test
D)Mann-Whitney test
E)Friedman test

Question 43

A Kruskal-Wallis test is to be performed.There will be four categories, and alpha is chosen to be 0.10.The critical chi-square value is ___.

A)6.251
B)2.706
C)7.779
D)4.605
E)3.234

Question 44

In the Friedman test of c treatment levels, the degrees of freedom will be ___.

A)n - 1
B)(r - 1)(c - 1)
C)c - 1
D)b - k - 1
E)c + 1

Question 45

In a Friedman test with 7 treatment levels and 5 blocks, df = ___.

A)16
B)34
C)4
D)35
E)6

Question 46

The nonparametric alternative to analysis of variance for a randomized block design is the ___.

A)chi-square test
B)Kruskal-Wallis test
C)Mann-Whitney U test
D)Wilcoxon test
E)Friedman test

Question 47

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The null hypothesis is ___.

A)Group 1 = Group 2 = Group 3
B)Group 1 $\neq$ Group 2 $\neq$ Group 3
C)Group 1 $\ge$ Group 2 $\ge$ Group 3
D)Group 1 $\le$ Group 2 $\le$ Group 3
E)Group 1 $\le$ Group 2 ≥ Group 3

Question 48

In a Wilcoxon matched-pairs signed rank test with 20 matched-pairs of observations, the observed value of the T statistic based on sample data is 76.33.The corresponding observed z value is ___.

A)−1.79
B)−2.07
C)−1.70
D)−1.59
E)−1.07

Question 49

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The calculated K value is ___.

A)15.086
B)1.715
C)7.779
D)9.210
E)8.657

Question 50

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. A Kruskal-Wallis test performed with $\alpha$ = 0.01 will result in a decision to ___.

A)reject the null hypothesis
B)reject the alternate hypothesis
C)not reject the null hypothesis
D)not reject the alternate hypothesis
E)do nothing

Question 51

In a Friedman test with 6 treatment levels and 7 blocks, the df = ___.

A)6
B)5
C)42
D)41
E)7

Question 52

The Kruskal-Wallis test is to be used to determine whether there is a significant difference (alpha = 0.05)between the three groups using the following data: For this situation, the critical (table)chi-square value is ___.

A)15.507
B)7.815
C)9.488
D)5.992
E)3.991

Question 53

The nonparametric alternative to the one-way analysis of variance is the ___.

A)chi-square goodness-of-fit test
B)Kruskal-Wallis test
C)Mann-Whitney U test
D)Wilcoxon test
E)Friedman test

Question 54

A randomized block design has 7 blocking levels and 5 treatment levels.Given the level of data, a nonparametric alternative to a randomized block design must be used to analyze the data.The number of degrees of freedom for the appropriate test statistic in this test of the null hypothesis that the treatment populations are equal is ___.

A)35
B)34
C)24
D)6
E)4

Question 55

Which of the following is not an assumption of the Friedman test?

A)The blocks are independent.
B)The population has a normal distribution.
C)There is no interaction between blocks and treatments.
D)Observations within each block can be ranked.

Question 56

The null hypothesis in the Kruskal-Wallis test is ___.

A)all populations are identical
B)all sample means are different
C)x and y are not correlated
D)the mean difference is zero
E)all populations are not identical

Question 57

The Kruskal-Wallis test is to be used to determine whether there is a significant difference (alpha = 0.05)between the three groups using the following data: For this test, how many degrees of freedom should be used?

A)3
B)2
C)4
D)8
E)1

Question 58

In a Friedman test with 8 treatment levels and 5 blocks, df = ___.

A)28
B)40
C)8
D)7
E)6

Question 59

A Kruskal-Wallis test is to be performed.There will be five categories, and alpha is chosen to be 0.01.The critical chi-square value is ___.

A)15.086
B)13.277
C)7.779
D)9.236
E)8.987

Question 60

In a Friedman test with 4 treatment levels and 5 blocks, the df = ___.

A)2
B)3
C)4
D)5
E)6

Question 61

Personnel specialist Steve Jones is assessing a new supervisor's ability to follow company standards for evaluating employees.Steve has the new supervisor rate five hypothetical employees on a scale of one to ten.He is interested in how the new supervisor's ratings correlate with company norms for these benchmark cases. The Spearman rank correlation coefficient is ___.

A)0.80
B)0.85
C)0.90
D)0.25
E)1.00

Question 62

What is the Spearman rank correlation coefficient for the following set of data?

A)-0.20
B)1.00
C)0.20
D)0.80
E)-1.20

Question 63

Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles.If there are differences, then that tire could promote its durability to potential customers.Using the data in the table below and an alpha of 0.05, what is the observed value of χ²?

A)77.82
B)5.00
C)84.67
D)9.35
E)4.00

Question 64

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels, the ranks for block 2 are ___.

A)2, 3, 4, 1
B)1, 2, 3, 4
C)4, 1, 2, 3
D)4, 2, 3, 1
E)3, 4, 1, 2

Question 65

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α = 0.05, the calculated value of chi-square is ___.

A)4.51
B)5.27
C)2.83
D)3.48
E)1.48

Question 66

Correlation coefficients may be computed for parametric and nonparametric data.If the data are interval data, which of the following should be used?

A)Pearson correlation coefficient
B)Spearman correlation coefficient
C)Gaussian correlation coefficient
D)De Moivre correlation coefficient
E)Gossett correlation coefficient

Question 67

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels, the ranks for block 1 are ___.

A)2, 3, 4, 1
B)3, 4, 1, 2
C)4, 1, 2, 3
D)4, 2, 3, 1
E)1, 2, 3, 4

Question 68

Correlation coefficients may be computed for parametric and nonparametric data.If the data are nonparametric, which of the following should be used?

A)Pearson correlation coefficient
B)Spearman correlation coefficient
C)Gaussian correlation coefficient
D)De Moivre correlation coefficient
E)Gossett correlation coefficient

Question 69

Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles.If there are differences, then that tire could promote its durability to potential customers.Using the data in the table below and an alpha of 0.05, what is the critical value of χ²?

A)7.82
B)5.99
C)4.61
D)9.35
E)3.84

Question 70

Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles.If there are differences, then that tire could promote its durability to potential customers.Using the data in the table below and an alpha of 0.05, what is the appropriate decision?

A)Reject the null and conclude that all four tires have the same durability.
B)Fail to reject the null and conclude that there is at least one tire whose durability is different from another tire.
C)Reject the null and conclude that there is at least one tire whose durability is different from another tire.
D)Fail to reject the null and conclude that all four tires have the same durability.
E)Fail to reject the null and conclude that the durability of tires does not change by city.

Question 71

Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles.If there are differences, then that tire could promote its durability to potential customers.Using the data in the table below and an alpha of 0.05, what is the null hypothesis?

A)The durability of the tires between the cities is equal.
B)The durability of the tires is dependent on the city and type of tire.
C)The durability of the tires is dependent on the type of tire.
D)The durability between the types of tire is equal.
E)The durability of the tires is dependent on the city.

Question 72

A randomized block design has 7 blocking levels and 5 treatment levels.Given the level of data, a nonparametric alternative to a randomized block design must be used to analyze the data.For the test of the null hypothesis that the treatment populations are equal at a 1% level of significance, the critical value of the test statistic is ___.

A)16.81
B)15.09
C)13.28
D)9.49
E)3.48

Question 73

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α = 0.05, the critical value of chi-square is ___.

A)7.81
B)5.99
C)11.07
D)9.49
E)6.81

Question 74

Two stock analysts rank five investment portfolios for overall performance and risk. The Spearman rank correlation coefficient is ___.

A)0.80
B)0.20
C)0.05
D)0.95
E)1.00

Question 75

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels, the df = ___.

A)6
B)5
C)4
D)3
E)1

Question 76

The Spearman correlation coefficient is calculated for a set of data on two variables, x and y.It appears that as the rank of x increases, the rank of y is decreasing.We would expect the Spearman correlation coefficient to be ___.

A)equal to zero
B)positive
C)negative
D)greater than 5
E)greater than 1

Question 77

What is the Spearman rank correlation coefficient for the following set of data?

A)-10.2
B)-2.35
C)0.65
D)0.50
E)0.05

Question 78

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α = 0.01, the critical value of chi-square is ___.

A)13.28
B)11.34
C)15.09
D)9.21
E)9.18

Question 79

When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α =0.05, the appropriate conclusion is ___.

A)reject H₀: the block populations are equal
B)do not reject H₀: the block populations are equal
C)reject H₀: the treatment populations are equal
D)do not reject H₀: the treatment populations are equal
E)that the test is inconclusive