Deck 16: Nonparametric Tests

Question 1

Most nonparametric tests require data measured on a ratio scale.

Answer 1

False

Question 2

The one-sample runs test is similar to a test for autocorrelation.

Answer 2

True

Question 3

Parametric tests generally are more powerful than nonparametric tests when normality can be assumed.

Answer 3

True

Question 4

The Spearman rank correlation test compares medians of two paired data sets.

Question 5

The Wilcoxon signed-rank test is useful to compare more than two sample medians.

Question 6

The Wilcoxon signed-rank test is analogous to a one-sample parametric test of a mean.

Question 7

The one-sample runs test compares medians of two or more groups.

Question 8

Most nonparametric tests assume ordinal data.

Question 9

Nonparametric tests can be used in small samples.

Question 10

If the population is normal, we would usually prefer a nonparametric test.

Question 11

Rejection of a hypothesis using a nonparametric test is less convincing than using an equivalent parametric test, since nonparametric tests generally make fewer assumptions.

Question 12

The Wilcoxon signed-rank test is analogous to a parametric two-sample t test of means from independent samples.

Question 13

The one-sample runs test uses a test statistic that is normally distributed, as long as the number of runs of each type is large enough.

Question 14

The one-sample runs test uses binary data (only two possible values).

Question 15

The one-sample runs test is also called the Wald-Wolfowitz test named after its inventors.

Question 16

The one-sample runs test is useful to detect nonrandom patterns in time-series data.

Question 17

Rejection of a hypothesis using a nonparametric test is more convincing than using an equivalent parametric test when the data are badly skewed.

Question 18

Nonparametric tests generally are more powerful than parametric tests when normality cannot be assumed.

Question 19

Nonparametric tests may require special tables for small samples.

Question 20

The Wilcoxon signed-rank test is useful to compare one sample median with a benchmark.

Question 21

The Kruskal-Wallis test is analogous to the parametric one-factor ANOVA.

Question 22

The Wilcoxon signed-rank test is an alternative to the one-sample t test for paired observations.

Question 23

The Kruskal-Wallis test is equivalent to comparing medians in c groups.

Question 24

The Mann-Whitney test is sometimes called the "Wilcoxon rank sum test" because it was formulated independently by different statisticians.

Question 25

The Kruskal-Wallis test applies even if the c samples to be compared are not independent.

Question 26

The Kruskal-Wallis test is analogous to the one-sample parametric t test for a mean.

Question 27

The Wilcoxon rank sum test (Mann-Whitney test) can be used even if population variances are unequal.

Question 28

The Kruskal-Wallis test requires c independent samples (where usually c > 2).

Question 29

The Kruskal-Wallis test does not require normal populations, but it does require them to be of similar shape.

Question 30

The Wilcoxon signed-rank test does not assume a normal population, but it does require a roughly symmetric population.

Question 31

The Kruskal-Wallis test is a test for randomness in sequential data.

Question 32

The Wilcoxon rank sum test (Mann-Whitney test) requires two independent samples.

Question 33

The Wilcoxon signed-rank test is analogous to a parametric t test comparing three or more medians.

Question 34

We sometimes call the Wilcoxon rank sum test the Mann/Whitney test, but the two are the same.

Question 35

The Wilcoxon rank sum test (Mann-Whitney test) can be used as a test for equality of two population medians.

Question 36

The Mann-Whitney test is analogous to a one-sample t test comparing a mean with a benchmark.

Question 37

The Wilcoxon signed-rank test is less powerful than a one-sample test of a mean when the population is actually normal.

Question 38

The Wilcoxon signed-rank test is robust to outliers in the data if the population is at least somewhat symmetric.

Question 39

The Wilcoxon signed-rank test has good power over a range of nonnormal populations.

Question 40

The Wilcoxon rank sum test (Mann-Whitney test) utilizes the ranks of two independent samples.

Question 41

Which nonparametric test would we use to compare ratings assigned to n pairs of bonds by two different rating agencies, if the bonds are rated on an ordinal scale (Aaa, Aa, A, Baa, Ba B, etc.)?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 42

Spearman's rank correlation coefficient lies within the range 0 to 1.00 inclusive.

Question 43

The Friedman test compares medians when there are two grouping factors (rows, columns).

Question 44

Spearman's rank correlation always lies within the range -1.00 to +1.00.

Question 45

The Kruskal-Wallis test is less useful in finance or marketing, because normal populations can usually be assumed in financial or marketing data.

Question 46

The Friedman test is a nonparametric equivalent to two-factor ANOVA without replication.

Question 47

The Friedman test is often almost as powerful as two-factor ANOVA without replication (randomized block design).

Question 48

Spearman's rank correlation is named for a British behavioral psychologist who was studying human intelligence.

Question 49

The Friedman test is a nonparametric equivalent to a parametric one-sample t test comparing a mean with a benchmark.

Question 50

The Friedman test resembles the Kruskal-Wallis test except that there are two grouping factors (rows, columns) instead of one grouping factor (columns).

Question 51

Which nonparametric test is used to compare a one-sample median with a benchmark?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 52

Spearman's rank correlation is named for a British brewer who was testing beer samples.

Question 53

Which nonparametric test is analogous to a parametric one-sample t test for differences in paired data?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 54

Spearman's rank correlation is used to measure agreement in rankings of paired (x, y) data.

Question 55

Which nonparametric test is analogous to a parametric two-sample t test for means?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 56

The Friedman test requires groups of equal size.

Question 57

The Kruskal-Wallis test is almost as powerful as one-factor ANOVA even when normality can be assumed.

Question 58

Which nonparametric test is analogous to a parametric k-sample test for means?

A)Kruskal-Wallis test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Wald-Wolfowitz one-sample runs test

Question 59

All of these are nonparametric tests except:

A)Spearman rank correlation test.
B)Friedman test.
C)Student's t test.
D)Kruskal-Wallis test.

Question 60

Which nonparametric test has no parametric counterpart?

A)Wald-Wolfowitz one-sample runs test
B)Spearman rank correlation test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 61

Twenty customers are randomly chosen and each is given a sample of Nut Butter ice cream to taste. The customers rank the taste of the ice cream on a 10-point scale. Each is then given a sample of Chewy Gooey ice cream to taste and rank on a 10-point scale. Based on the 20 customers' ratings of each flavor, the research analyst conducting the survey wishes to determine if one flavor is preferred over the other. Which nonparametric test would you use to determine if there is a difference in the ratings?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 62

Delta Air Lines wants to determine if the number of no-shows for flights originating from Detroit is higher than from Minneapolis. A sample of 20 flights from each city is taken and the number of no-shows is determined for each flight. Which nonparametric test would you use to determine whether the number of no-shows is greater in Detroit?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 63

Which parametric test resembles the nonparametric Spearman's rank test?

A)t test of a correlation coefficient
B)t test of two sample means
C)t test of one sample mean
D)F test of variances

Question 64

Which nonparametric test is analogous to a two-factor ANOVA without replication?

A)Wilcoxon signed-rank test
B)Friedman test
C)Mann-Whitney test
D)Kruskal-Wallis test

Question 65

Attendees at an outdoor concert can buy pavilion tickets (A) or lawn tickets (B). Below is the output for the one-sample runs to test whether there is a pattern in 32 consecutive ticket purchases. Runs Test

$\begin{array}{|l|l|l|}\hline\text { n }&\text { runs }\\\hline 21 & 6& \text { A }\\\hline 11 & 6& \text { B }\\\hline 32 & 12& \text { total }\\\hline\end{array}$


15.44 expected value
$2.50$ standard deviation
$- 1.17 z$
$.2403$ p-value (two-tailed) The best conclusion at ? = .05 would be:

A)the pattern is random.
B)there is a difference in medians.
C)the sample sizes are too small.
D)the sample sizes must be equal.

Question 66

Which is a nonparametric test for runs (autocorrelation) in a sequence of binary data?

A)Kruskal-Wallis test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Wald-Wolfowitz one-sample runs test

Question 67

At the Food Barn, children can order from the adult menu (A) or the child's menu (C). Below is the pattern of menu orders for 24 children last Wednesday evening. A, A, A, A, C, A, A, C, C, C, A, A, A, A, A, A, C, C, C, A, C, C, C, C
Which test would you choose to see if this pattern is random?

A)Kruskal-Wallis test
B)Wilcoxon rank sum (Mann-Whitney) test
C)Wald-Wolfowitz one-sample runs test
D)Wilcoxon test

Question 68

At the Food Barn, children can order from the adult menu (A) or the child's menu (C). Below is the pattern of menu orders for 24 children last Wednesday evening. A, A, A, A, C, A, A, C, C, C, A, A, A, A, A, A, C, C, C, A, C, C, C, C
Which statement is most accurate?

A)Neither sample size (for outcomes A or C) is large enough for a runs test using z.
B)Both sample sizes (for outcomes A and C) are large enough for a runs test using z.
C)Only one outcome has a large enough sample for a runs test using z.
D)This type of data would not be suited for a runs test using z.

Question 69

If there are three or more populations with ordinal data, what is the appropriate test to determine whether the distributions are equal?

A)Friedman test
B)t test
C)ANOVA
D)Kruskal-Wallis test

Question 70

A clinic has four doctors. They wish to compare the amount of time that doctors spend with their patients. It is suspected that times may not be normally distributed but are otherwise assumed similar except in center, so a nonparametric test was chosen. The Kruskal-Wallis test results are shown below. $\text { Kruskal-Wallis Test }$
$\begin{array}{ccrl}\hline \text { Wedian } & n & \text { Avg. Rank } & \\\hline 27.00 & 11 & 19.18 & \text { Doc A } \\28.50 & 14 & 15.93 & \text { Doc B } \\46.00 & 9 & 36.39 & \text { Doc C } \\31.00 & 11 & 24.86 & \text { Doc D } \\\hline 31.00 & 45 & & \text { Total }\end{array}$
14.599 $\mathrm{H}$ (corrected for ties)
3 d.f.
, 0022 p-value Which is the best conclusion?

A)The doctors have the same median times at ? = .01.
B)The doctors have different median times at ? = .01.
C)The sample size is insufficient for this kind of test.
D)A one-factor ANOVA would be a better kind of test.

Question 71

Which is not a characteristic of the Wilcoxon rank sum (Mann-Whitney) test?

A)It can be used as a test for equality of two population medians.
B)It is analogous to a one-sample t test comparing a mean with a benchmark.
C)It requires independent samples from populations with equal variances.
D)It is similar to one-factor ANOVA when we have c independent samples.

Question 72

Which is not true of the one-sample runs test?

A)It is also called the Wald-Wolfowitz test named after its inventors.
B)Its purpose is to detect nonrandomness.
C)It cannot be applied to sequential observations.
D)It is similar to a test for autocorrelation.

Question 73

Returns on an investor's stock portfolio (n = 19 stocks) are compared for the same stock in each of two consecutive quarters. Since the returns are not normally distributed (normality test p-values were .005 and .126 respectively), a nonparametric test was chosen. The test results are shown below. Spearman Rank Correlation

$\begin{array}{|r|r|r|}\hline&\text { Qtr1 }&\text { Qtr2}\\\hline \text { Qtr1 }&1.000 & \\\hline \text { Qtr2 }&.577 & 1.000 \\\hline\end{array}$

19 sample size
$\pm .456$ critical value .05 (two-tail)
$\pm .575$ critical value .01 (two-tail) Which is the best conclusion?

A)The returns are correlated neither at ? = .05 nor at ? = .01.
B)The returns are correlated at ? = .05 but not at ? = .01.
C)The returns are correlated at ? = .01 but not at ? = .05.
D)The returns are correlated both at ? = .05 and at ? = .01.

Question 74

Which is not a characteristic of the Kruskal-Wallis test?

A)It is analogous to the parametric one-factor ANOVA.
B)It does not make any assumptions about the populations.
C)It is useful in comparing the medians in c groups.
D)It does not require normal distributions of populations.

Question 75

Hoping to reduce the waiting time, a doctor's office tried a new way of scheduling its appointments. Populations of waiting times are believed to be similar except in central tendency. However, waiting times may not be normally distributed, so a nonparametric test was chosen to compare the waiting times. The Wilcoxon/Mann-Whitney test results are shown below: $\text { Mann/Whitney Test }$

$\begin{array}{|c|c|c|}\hline\text { n }&\text { sum of ranks }\\\hline 21 & 600.5& \text { Old Way}\\\hline 25 & 480.5& \text { New Way}\\\hline 46 & 1081& \text { Total}\\\hline\end{array}$

$493.50$ expected value
$45.31$ standard deviation
$2.35 \mathrm { z }$ , corrected for ties
$.0094 \mathrm { p }$ -value (one-tailed, upper) Which is the best conclusion?

A)The medians differ at ? = .01.
B)The means differ at ? = .01.
C)The samples differ at ? = .01.
D)There are no differences at ? = .01.

Question 76

The dean of Oxnard business school wants to know if there is a difference in computer skills in four majors (marketing, finance, operations, accounting). A 20-question skills test is given to 10 randomly chosen students in each major. Which nonparametric test could be used by the dean to see if there is a difference in computer skills of students in the various majors?

A)Wald-Wolfowitz test
B)Wilcoxon signed-rank test
C)Mann-Whitney test
D)Kruskal-Wallis test

Question 77

Individuals in four different age groups are asked to rate, on a scale of 1 to 10, three flavors of ice creams. Each group has the same number of individuals. Median ratings by the individuals are grouped by the flavor of ice cream and by age group. Which nonparametric test could be used to see if there is a difference in median ratings among the four age groups and three flavors?

A)Wilcoxon signed-rank test
B)Friedman test
C)Mann-Whitney test
D)Kruskal-Wallis test

Question 78

Returns on an investor's stock portfolio (n = 19 stocks) are compared for the same stock in each of two consecutive quarters. Since the returns are not normally distributed (normality test p-values were .005 and .126 respectively), a nonparametric test was chosen. The test results are shown below. $\text { Wilcoxon Paired Data Test}$

$\begin{array}{|l|l|l|}\hline\text { n }&\text { sum of ranks }\\\hline 19 & 247& \text {Qtr 1 }\\\hline 19 & 494& \text {Qtr 2 }\\\hline 38 & 741& \text { total}\\\hline\end{array}$


$370.50$ expected value
$34.25$ standard deviation
$- 3.59 z$
$.0003 \mathrm { p }$ -value (two-tailed) Which is the best conclusion?

A)The means are the same at ? = .01.
B)The medians are the same at ? = .01.
C)The means differ at ? = .01.
D)The medians differ at ? = .01.

Question 79

Which nonparametric test is used to test for agreement in ranks of paired data?

A)Spearman test
B)Friedman test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test

Question 80

Which nonparametric test is used to detect nonrandomness in sequential observations?

A)Wald-Wolfowitz one-sample runs test
B)Wilcoxon signed-rank test
C)Wilcoxon rank sum (Mann-Whitney) test
D)Kruskal-Wallis test