Deck 17: Nonparametric Statistics for Ordinal Data

Question 1

Nonparametric tests are appropriate to use for distributions that

A) are skewed.
B) do not meet the requirements for homogeneity of variance.
C) are made up of scores with ordinal level data.
D) All of the above are true.

Answer 1

D

Question 2

All of the following statements are true except:

A) Nonparametric tests should never be used if the scores can be measured on an interval or ratio scale.
B) Nonparametric tests can be used if a distribution is severely skewed.
C) Nonparametric tests can be used even if the distributions lack homogeneity of variance.
D) Nonparametric tests can be used for distributions that have scores that are not normally distributed.

Answer 2

A

Question 3

The Mann Whitney test is the nonparametric alternative to the

A) one-way ANOVA, independent samples design.
B) related samples t test.
C) independent samples t test.
D) Pearson r.

Answer 3

C

Question 4

The Wilcoxon matched-pairs signed-ranks test is the nonparametric alternative to the

A) one-way ANOVA, independent samples design.
B) related samples t test.
C) independent samples t test.
D) Pearson r.

Question 5

The nonparametric alternative to the related samples t test is the

A) Wilcoxon matched-pairs signed-ranks test.
B) Mann-Whitney test.
C) Kruskal-Wallis test.
D) Spearman test.

Question 6

The Kruskal-Wallis test is the nonparametric alternative to the

A) independent samples t test.
B) one-way ANOVA, independent samples design.
C) two-way ANOVA, independent samples design.
D) related samples t test.

Question 7

The nonparametric alternative to the one-way ANOVA, independent samples design is the

A) Wilcoxon matched-pairs signed-ranks test.
B) Mann-Whitney test.
C) Kruskal-Wallis test.
D) Spearman test.

Question 8

The nonparametric alternative to the Pearson correlation coefficient is the

A) Wilcoxon matched-pairs signed-ranks test.
B) Mann-Whitney test.
C) Kruskal-Wallis test.
D) Spearman test.

Question 9

The Spearman test is the non-parametric alternative to the

A) one-way ANOVA, independent samples design.
B) related samples t test.
C) independent samples t test.
D) Pearson r.

Question 10

Nonparametric tests are also called ____________________.

A) norm-free
B) parametric-free
C) distribution-free
D) home-free

Question 11

If the assumptions of normality, homogeneity of variance, and interval or ratio level data can be met, a _______________ statistic should be used.

A) parametric
B) nonparametric
C) descriptive
D) distribution-free

Question 12

If the size of one or both samples is greater than _________, the sampling distribution for the Mann-Whitney U test resembles the normal distribution.

A) 5
B) 10
C) 15
D) 20

Question 13

Which test statistic below can be converted into a z-score if the size of both samples is greater than 20?

A) Spearman
B) Mann-Whitney
C) Wilcoxon
D) Kruskal-Wallis

Question 14

In ranking the scores 8, 10, 7, 8, 6, and 12, the score of 10 is given a rank of __________.

A) 4
B) 5
C) 6
D) 4.5

Question 15

In ranking the scores 3, 5, 5, 7, 7, 7, and 9, the score of 7 is given a rank of __________.

A) 3
B) 4
C) 4.5
D) 5

Question 16

For the Mann-Whitney test,

A) scores from the groups are ranked separately.
B) it is the differences between the scores that are ranked.
C) difference values are determined after the scores are ranked.
D) scores from all groups are ranked together at the same time.

Question 17

In ranking the scores 6, 7, 8, 8, 9, 10, 10, 10, 11, and 12, the score of 10 is given a rank of

A) 7
B) 6
C) 5
D) 6.5

Question 18

Which of the following test(s) require(s) an obtained statistic that is equal to or smaller than the critical value in order to reject H₀?

A) Mann-Whitney test
B) Spearman test
C) Wilcoxon matched-pairs signed-rank test
D) Both "a" and "c" above

Question 19

Which of the following test(s) require(s) an obtained statistic that is equal to or greater than the critical value in order to reject H₀?

A) Mann-Whitney test
B) Spearman test
C) Wilcoxon matched-pairs signed-rank test
D) all of the above

Question 20

Which nonparametric test below calls for rejecting the null hypothesis if the obtained test value is less than the critical value?

A) Wilcoxon matched-pairs signed-ranks test
B) Spearman test
C) Chi-Square test
D) Kruskal-Wallis test

Question 21

The __________________ test calls for rejecting the null hypothesis if the obtained test value is _____________ the critical value.

A) Mann-Whitney U; less
B) Kruskal-Wallis H; greater
C) Wilcoxon T; greater
D) Both "a" and "b" are correct.

Question 22

The ___________________ test calls for rejecting the null hypothesis if the obtained test value is ________________ than the critical value.

A) Mann-Whitney U; greater
B) Spearman r_s; greater
C) Wilcoxon T; greater
D) Kruskal-Wallis H; less

Question 23

Two values for U are calculated for the Mann-Whitney test. Which of the following is used for comparison with U_crit?

A) U₁ * U₂
B) the smallest U value
C) the largest U value
D) the difference between the largest and the smallest U value

Question 24

A sample of back pain sufferers rate their level of pain on a scale from 1 to 7. They then undergo acupuncture treatment. Afterwards, they again rate their level of pain. What is the appropriate test for this study?

A) Wilcoxon matched-pairs signed-ranks test
B) Mann-Whitney test
C) Kruskal-Wallis test
D) Spearman test

Question 25

The Wilcoxon T test would be appropriate for which of the following situations?

A) More than two groups are involved in the study.
B) Two sets of scores have been logically paired together.
C) Pre- and post-testing of the same participants.
D) Either "b" or "c" above.

Question 26

The Kruskal-Wallis test would be appropriate for which of the following situations?

A) More than two groups are involved in the study.
B) Two sets of scores that have been logically paired together.
C) Pre- and post-testing of the same participants.
D) Either "b" or "c" above.

Question 27

If a researcher was interested in comparing the distributions of scores for fathers and sons, which test would be appropriate?

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 28

If a researcher was interested in determining if a relationship exists between degree of education and attitudes towards tax reform, which test would be appropriate?

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 29

Which of the following tests would be appropriate to measure participants' attitude before a treatment intervention and then again after the intervention?

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 30

Annual income is known to form a skewed distribution but a researcher wants to know if there is a difference in the distributions of income for men and women in her company. She obtains a random sample of each, converts their annual income into ranks, and then uses the _____________________ test to determine if the overall salaries of one gender differ significantly from the other.

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 31

A new pain medication is being tested. One group receives a placebo and another group receives the medication. After two weeks, both groups rate their level of pain. Which of the following should be used to analyze the data?

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 32

In addition to end of course evaluations of their professors, a separate survey is also administered to measure their professors' sense of humor. The Director of Institutional Effectiveness compares the ranks of both sets of scores and uses the ______________________ to determine if there is a relationship between them.

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 33

The flavor of four different brands of chocolate ice cream were rated from 1 to 9. Which test should be used to analyze the data?

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Kruskal-Wallis test
D) Spearman test

Question 34

Which nonparametric test for ordinal data uses the same distribution as chi-square if the sample size for each group is a minimum of 5?

A) Kruskal-Wallis test
B) Spearman test
C) Mann-Whitney test
D) Wilcoxon matched-pairs signed-ranks test

Question 35

Which test involves ranking the difference scores rather than the scores themselves?

A) Mann-Whitney test
B) Wilcoxon matched-pairs signed-ranks test
C) Spearman correlation test
D) Kruskal-Wallis test

Question 36

________ is the symbol used for the Mann-Whitney test.

A) U
B) H
C) r_s
D) T

Question 37

________ is the symbol used for the Wilcoxon matched-pairs signed ranks test.

A) U
B) H
C) r_s
D) T

Question 38

________ is the symbol used for the Spearman correlation test.

A) U
B) H
C) r_s
D) T

Question 39

The symbol used for the ______________________ test is H.

A) Kruskal-Wallis
B) Spearman
C) Mann-Whitney
D) Wilcoxon matched-pairs, signed-ranks

Question 40

The symbol used for the ________________________ test is U.

A) Kruskal-Wallis
B) Spearman
C) Mann-Whitney
D) Wilcoxon matched-pairs signed-ranks

Question 41

The symbol used for the ________________________ test is T.

A) Kruskal-Wallis
B) Spearman
C) Mann-Whitney
D) Wilcoxon matched-pairs signed-ranks

Question 42

The symbol used for the ________________________ test is r_s.

A) Kruskal-Wallis
B) Spearman
C) Mann-Whitney
D) Wilcoxon matched-pairs signed-ranks

Question 43

What is the difference between a parametric test and a nonparametric test?

Question 44

Identify three situations for which a nonparametric test would be appropriate.

Question 45

Identify the nonparametric alternative for each of the following parametric tests:
a. Independent samples t test
b. Related samples t test
c. One-way ANOVA, independent samples design
d. Pearson correlation

Question 46

Identify the parametric test for which the following nonparametric alternatives would be appropriate:
a. Mann-Whitney test
b. Wilcoxon matched-pairs signed-ranks test
c. Kruskal-Wallis test
d. Spearman correlation

Question 47

Based on the critical and obtained values of the various tests below, determine if the null hypothesis can be rejected:

Question 48

Compare the obtained and critical values for the test results below and determine if the null hypothesis can be rejected.

Question 49

For each of the following situations, decide which nonparametric test should be used. Assume that there is concern about meeting the assumptions of a parametric test or that the scores are measured on an ordinal scale.
a. A random sample of students taking statistics classes take a study skills assessment prior to the first class meeting. They take the assessment again at the end of the semester and their ratings are compared.
b. A dietician randomly assigns bunches of carrots into four groups, each of which will involve a different cooking method: roasting, steaming, boiling, and microwaving. Afterward, the nutrient content of each approach was evaluated and compared.
c. Study skill ratings for a sample of students who have taken a statistics course are compared with the ratings of students who have not taken a statistics course.
d. The business manager of a large company wants to know if there is a relationship between sociability and productivity. She randomly selects 20 employees and administers a sociability survey. She then determined the productivity ratings of the same employees and compared them with their sociability ratings to assess the degree of relationship.
e. A homesickness questionnaire is administered to incoming freshmen at their student orientation. The ratings are compared for male and female students.
f. Improvement ratings are compared for three different types of therapy for people who suffer from social anxiety.

Question 50

Rank the following scores as if to conduct a Mann-Whitney u test:
Group A: 42, 36, 37, 49, 52, 37, 41
Group B: 29, 32, 37, 40, 31, 42, 27

Question 51

Conduct the Mann-Whitney U values for the following ranked scores and identify which one would be used as U_obt.

Question 52

The ordinal level scores below were obtained before and after a treatment intervention. Calculate the Wilcoxon T value.
Before: 12, 15, 8, 10, 12, 7
After: 8, 12, 10, 10, 13, 5

Question 53

Calculate the Kruskal-Wallis H value for the following ranked scores:

Question 54

Calculate the Spearman Correlation coefficient for the following ranked scores:

Question 55

A large bicycle store is testing two newly designed bicycle seats. One sample of cyclists rates the comfort level of model A. Another sample rates the comfort level of model B. The seats are rated on a scale from 1 to 10 with 10 representing the highest level of comfort. The cyclists' ratings are shown below. Do the ratings suggest that one model is more comfortable than the other? Conduct a Mann-Whitney U test at α = .05, two-tailed.
Model A: 6, 3, 7, 5, 4, 3
Model B: 8, 6, 9, 7, 8, 7

Question 56

Nine individuals who experience social anxiety rate their level of discomfort in various social situations on a scale from 0 to 20 with 20 representing the highest level of discomfort. They then participate in an interpersonal group therapy program for three months after which they again rate their level of discomfort. Before and after therapy ratings are shown below. Use the Wilcoxon matched-pairs signed-ranks T test to determine if the ratings after therapy were significantly different from those before therapy. Use α = .05, two-tailed.
Before: 17, 18, 14, 16, 15, 17, 12, 13, 18
After: 8, 12, 12, 16, 8, 13, 13, 6, 10

Question 57

Three groups of wine connoisseurs rated the flavor profile of the same wine on a 10-point scale with 10 being the most favorable rating. Different comments were made to each group about the wine prior to the tasting in order to determine their possible influence on the ratings. The comments were as follows:
Group A: "Don't expect much."
Group B: "Not bad."
Group C: "Exceptional."
The ratings for each group are shown below. Use the Kruskal-Wallis H test to determine if there were significant differences in the ratings. Use α = .01, two-tailed.
Group A: 4, 3, 4, 5, 6, 2, 7
Group B: 6, 7, 6, 5, 8, 7, 5
Group C: 8, 10, 7, 9, 10, 8, 7

Question 58

Judges for a debate competition rated eight debaters on presentation, clarity, argumentation, and rebuttal. The composite ratings of two judges are shown below. Use the Spearman r_s to determine the degree of relationship between the judges' ratings. Test at α = .05, two-tailed.
Judge A: 16, 20, 22, 14, 18, 12, 17
Judge B: 14, 21, 19, 13, 20, 11, 18