Deck 18: Choosing and Reporting Statistics

Question 1

Does a person's letter grade in statistics depend on whether he or she is a member of a Greek organization? In three statistics classes, data is collected on the letter grades of students belonging to Greek organizations and of students who are not members.Which technique would be used to analyze the data?

A) independent-samples t test
B) paired-samples t test
C) Wilcoxon signed-rank test
D) Mann-Whitney U test

Answer 1

Mann-Whitney U test

Question 2

A researcher is transforming finishing times from a 5K race into ordinal data and has the following scores in minutes: 12.2, 16.5, 12.8, 13.4, 17.8, 13.4, 13.4, and 18.6.If the researcher ranks from fastest to slowest, what would be the rank of the three people with a finish time of 13.4?

A) 5
B) 4
C) 3.5
D) 3

Answer 2

5

Question 3

What is the formula for the Spearman's correlation coefficient?

A) $r _ { s } = 1 - \frac { N \left( \sum D \right) } { N \left( N ^ { 2 } - 1 \right) }$
B) $r _ { s } = 1 - \frac { 6 \left( \sum D \right) } { N \left( N ^ { 2 } - 1 \right) }$
C) $r _ { s } = 1 - \frac { N \left( \sum D ^ { 2 } \right) } { N \left( N ^ { 2 } - 1 \right) }$
D) $r _ { s } = 1 - \frac { 6 \left( \sum D ^ { 2 } \right) } { N \left( N ^ { 2 } - 1 \right) }$

Answer 3

$r _ { s } = 1 - \frac { 6 \left( \sum D ^ { 2 } \right) } { N \left( N ^ { 2 } - 1 \right) }$

Question 4

To calculate a Spearman rank-order correlation coefficient, first convert both variables to ranks.After that:

A) compute the difference between each pair of ranks.
B) sum the ranks for each pair.
C) square the ranks and add them together.
D) subtract the mean from each score and square the sum.

Question 5

The nonparametric equivalent of the independent-samples t test is the:

A) Kruskal-Wallis H test.
B) Mann-Whitney U test.
C) chi-square.
D) Wilcoxon signed-rank test.

Question 6

Nonparametric tests are usually used when the sample data are:

A) nominal or ordinal.
B) nominal or extremely skewed.
C) ordinal or extremely skewed.
D) ordinal or when participants have been randomly selected.

Question 7

Blake is interested in training for his first marathon and wants to determine whether the finishing time of non-elite marathon runners depends on the type of training program used.There are three training programs he is interested in comparing: Hal Higdon's, Jeff Galloway's, and Art Liberman's.Blake is able to track down 30 runners, 10 who have used Higdon's, 10 who have used Galloway's, and 10 who have used Liberman's.Blake asks the runners for their marathon finishing times.What statistic should he use to analyze his data?

A) Spearman rank-order correlation coefficient
B) Mann-Whitney U test
C) one-way ANOVA
D) Kruskal-Wallis H test

Question 8

To use a nonparametric test despite having scale data, transform the data from scale to:

A) nominal.
B) ordinal.
C) the square root of the scale values.
D) the square root of the ratio values.

Question 9

Does the number of points a person earns on the final exam in statistics depend on whether the person is a member of a Greek organization? In three statistics classes, data is collected on the final exam points of students belonging to Greek organizations and of students who do not belong.Which technique would be used to analyze the data?

A) independent-samples t test
B) paired-samples t test
C) Wilcoxon signed-rank test
D) Mann-Whitney U test

Question 10

You are interested in attempting to replicate the results of a 1973 study by Belmont and Marolla that found a negative correlation between birth order and IQ.You collect the necessary data using students in your school's participant pool.Which technique would you use to analyze your data?

A) Spearman rank-order correlation coefficient
B) Pearson correlation coefficient
C) Mann-Whitney U test
D) Kruskal-Wallis H test

Question 11

Now that you are an adult, you decide to test one of the truisms passed along by your mother: "Cheaters never win in the end." You randomly assign a group of 20 children to either cheat or to play fair on a scavenger hunt.You then rank the children by how many items they were able to get during the scavenger hunt.Which technique would you use to analyze the data to determine whether cheaters finish differently than non-cheaters?

A) independent-samples t test
B) paired-samples t test
C) Wilcoxon signed-rank test
D) Mann-Whitney U test

Question 12

The nonparametric equivalent of the Pearson correlation coefficient is the:

A) Kruskal-Wallis H test.
B) chi-square.
C) Wilcoxon signed-rank test.
D) Spearman rank-order correlation coefficient.

Question 13

A researcher wants to examine the relation between class rank and popularity among peers.Class rank is provided by the school and includes each student's rank in order.The researcher assesses popularity using a likability measure that provides scale data.What statistic should be used to assess this relation?

A) chi-square test for goodness-of-fit
B) independent-samples t test
C) Wilcoxon signed-rank test
D) Spearman rank-order correlation coefficient

Question 14

A researcher wants to examine the relation between class rank and popularity among peers.Class rank is provided by the school and includes each student's rank in order.The researcher assesses popularity using a likability measure that provides scale data.What does the researcher need to do to the data before calculating a statistic using a nonparametric test?

A) compute difference scores
B) convert the scale data to ordinal data
C) subtract the mean from each score
D) standardize the scores

Question 15

The nonparametric equivalent of the one-way between-groups ANOVA is the:

A) Kruskal-Wallis H test.
B) Mann-Whitney U test.
C) chi-square.
D) Wilcoxon signed-rank test.

Question 16

A researcher is transforming finishing times from a 5K race into ordinal data and has the following scores in minutes: 17.6, 25.3, 18.4, 28.2, 32.6, 31.5, and 25.3.If the researcher ranks from fastest to slowest, what would be the rank of the two people with a finish time of 25.3?

A) 4.5
B) 4
C) 3.5
D) 3

Question 17

When transforming scale data to ordinal data, if two people have exactly the same score, what is their rank?

A) They receive the average of the two ranks they would hold if the scores were different.
B) They receive the same lower rank.
C) They receive the highest and second-highest rank.
D) They receive the lowest and the second-lowest rank.

Question 18

Blake is interested in training for his first marathon and wants to determine whether the finishing place of non-elite marathon runners depends on the type of training program used.There are three training programs he is interested in comparing: Hal Higdon's, Jeff Galloway's, and Art Liberman's.Blake is able to track down 30 runners, 10 who have used Higdon's, 10 who have used Galloway's, and 10 who have used Liberman's.Blake asks the runners how they placed in the marathon.What statistic should he use to analyze his data?

A) Spearman rank-order correlation coefficient
B) Mann-Whitney U test
C) one-way ANOVA
D) Kruskal-Wallis H test

Question 19

Melanie is interested in whether science fiction movies typically get higher star ratings (on a five-star scale) than dramas.What kind of statistical test could be used to address this question?

A) parametric test
B) nonparametric test
C) correlation
D) independent-samples t test

Question 20

The nonparametric equivalent of the paired-samples t test is the:

A) Kruskal-Wallis H test.
B) Mann-Whitney U test.
C) chi square.
D) Wilcoxon signed-rank test.

Question 21

The paired scores for a Wilcoxon signed-rank test were 1, 1; 2, 4; 5, 2; 2, 1; 4, 4; 3, 5; 4, 3.What is the sample size for this test?

A) 5
B) 10
C) 4
D) 1

Question 22

The Mann-Whitney U test would be used in which of these examples?

A) Ranked job satisfaction was compared for members of five different work teams.
B) Ranked job satisfaction was compared for the same eight women before and after they had a child.
C) Ranked job satisfaction was compared for males and females at a local business.
D) Job satisfaction as a scale variable is compared for three different work teams.

Question 23

The paired scores for a Wilcoxon signed-rank test were: 1, 1; 2, 2; 5, 3; 3, 5; 2, 4; 4, 4.What is the sample size for this test?

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

Question 24

One of the assumptions of the Wilcoxon signed-rank test is that the distribution of the population of difference scores is:

A) skewed.
B) symmetric.
C) bimodal.
D) normal.

Question 25

A sample of 10 men and 12 women are compared on their ranked life satisfaction.Which of these is the null hypothesis for this study?

A) Men and women do not tend to differ in ranked life satisfaction.
B) Men and women tend to differ in ranked life satisfaction.
C) There is a relationship between gender and ranked life satisfaction.
D) The distributions of ranked life satisfaction for men and women are the same.

Question 26

One of the assumptions of the Mann-Whitney U test is that there are no ties.If there are ties in the data set:

A) do not use the Mann-Whitney U test.
B) use the Mann-Whitney U test if there are just a few ties as it is robust to violations of this assumption.
C) use the Mann-Whitney U test anyway, even if you have lots of ties in your data since it is robust to this assumption.
D) use the Kruskal-Wallis H test instead.

Question 27

Does a person's letter grade in statistics depend on whether he or she is a member of a Greek organization? In three statistics classes, data is collected on the letter grades of students belonging to Greek organizations and of students who are not members.Which of these is the null hypothesis for this study?

A) Members and nonmembers of Greek organizations do not tend to differ in letter grades.
B) Members and nonmembers of Greek organizations tend to differ in letter grades.
C) There is a relationship between Greek organization membership and letter grade.
D) The distributions of letter grades for members and nonmembers of Greek organizations is the same.

Question 28

A sample of 10 men and 12 women are compared on their ranked life satisfaction.Which of these is the research hypothesis for this study?

A) Men and women do not tend to differ in ranked life satisfaction.
B) Men and women tend to differ in ranked life satisfaction.
C) There is a relationship between gender and ranked life satisfaction.
D) The distributions of ranked life satisfaction for men and women are the same.

Question 29

A correlation of 0.56 is found between class rank and student likeability.What can be concluded based on this correlation?

A) Good grades cause increases in popularity.
B) Class rank is predictive of academic performance.
C) Low class ranks tend to be associated with low likeability ranks, and high class ranks tend to be associated with high ranks for likeability.
D) High likeability is associated with low class rank, and low likeability is associated with high class rank.

Question 30

Using a p level of 0.05, a researcher performed the Wilcoxon signed-rank test with a sample size of 10 and found that ∑R₊ = 3 and ∑R_- = 9.Which statement accurately describes the results of this hypothesis test?

A) Because T = 9, the researcher failed to reject the null hypothesis.
B) Because T = 9, the researcher rejected the null hypothesis.
C) Because T = 3, the researcher rejected the null hypothesis.
D) Because T = 3, the researcher failed to reject the null hypothesis.

Question 31

The sample size for the Wilcoxon signed-rank test is:

A) equal to the number of participants.
B) two times the number of participants.
C) the number of difference scores that are not 0.
D) N - 1.

Question 32

Does a person's letter grade in statistics depend on whether he or she is a member of a Greek organization? In three statistics classes, data is collected on the letter grades of students belonging to Greek organizations and of students who are not members.Which of these is the research hypothesis for this study?

A) Members and nonmembers of Greek organizations do not tend to differ in letter grades.
B) Members and nonmembers of Greek organizations tend to differ in letter grades.
C) There is a relationship between Greek organization membership and letter grade.
D) The distributions of letter grades for members and nonmembers of Greek organizations is the same.

Question 33

A Spearman's correlation coefficient can range from _____ to _____.

A) 0; 1.00
B) -1.00; 0
C) -1.00; 1.00
D) -10.00; 10.00

Question 34

When using the Wilcoxon signed-rank test, reject the null hypothesis only when the _____ of the two calculated statistics is equal to or _____ than the critical value.

A) smaller; less
B) larger; less
C) smaller; greater
D) larger; greater

Question 35

Using a p level of 0.05, a researcher performed the Wilcoxon signed-rank test with a sample size of 16 and found that the sum of the ranks for positive differences was 36 and the sum of the ranks for negative differences was 100.Which statement accurately describes the results of the hypothesis test for these data?

A) Reject the null because the test statistics sum to above 100.
B) The test statistic is larger than the critical cutoff, which is 29, so fail to reject the null hypothesis.
C) The test statistic is larger than the critical cutoff, which is 29, so reject the null hypothesis.
D) Fail to reject the null hypothesis because 36 is less than 100.

Question 36

The assumptions of the Wilcoxon signed-rank test are that:

A) the difference between pairs of scores can be ranked, participants are randomly selected, and the population distribution of differences is symmetric.
B) the mean difference between pairs of scores is 0, participants are randomly selected, and the population is symmetric.
C) participants are randomly selected and the population is symmetric.
D) the mean of the population of difference scores is 0 and its distribution is symmetric.

Question 37

The comparison distribution for the Wilcoxon signed-rank test is the _____ distribution.

A) t
B) F
C) z
D) T

Question 38

The interpretation of the Spearman correlation coefficient is identical to that for the:

A) independent-samples t test.
B) Pearson correlation coefficient.
C) chi-square test for independence.
D) Mann-Whitney U test.

Question 39

The assumptions of the Mann-Whitney U test are that:

A) the data are ordinal and randomly distributed.
B) participants are randomly selected and the population is symmetric.
C) the data are ordinal, the participants are randomly selected, and ideally no ranks are tied.
D) the data are ordinal, the participants are randomly selected, and the population is symmetric.

Question 40

A Spearman correlation of r_s = -0.30 between birth order and IQ means that:

A) having a lower birth order causes a person to have a lower IQ.
B) people with lower birth orders tend to have lower IQs.
C) having a lower birth order causes a person to have a higher IQ.
D) people with lower birth orders tend to have higher IQs.

Question 41

A Mann-Whitney U test is used to compare two groups of 18 on ranked athleticism.Which of these U test statistics would be considered significant?

A) 100
B) 115
C) 121
D) 91

Question 42

Three different ethnic groups are compared on their ranked language skills and an H statistic of 5.1 is computed.What conclusion could be made about a hypothesis test at a p level of 0.05?

A) Reject the null hypothesis and conclude there are differences among these groups for ranked language skills.
B) Reject the null hypothesis and conclude that all three groups are significantly different from each other.
C) Fail to reject the null hypothesis and conclude no differences exist.
D) Fail to reject the null hypothesis and conclude there was no statistical power.

Question 43

A sample of 10 men and 12 women are compared on their ranked life satisfaction.What is the critical cutoff for a two-tailed Mann-Whitney U test comparing these groups?

A) 30
B) 29
C) 23
D) 20

Question 44

One should reject the null hypothesis using the Kruskal-Wallis H test when the calculated H statistic is _____ the critical value.

A) less than or equal to
B) greater than
C) five times
D) less than five times

Question 45

One should fail to reject the null hypothesis using the Kruskal-Wallis H test when the calculated H statistic is _____ the critical value.

A) less than
B) greater than
C) five times
D) less than five times

Question 46

Four different sports teams are compared for the athleticism of their members.The data on athleticism is available as ranks only.What would be the critical cutoff for the Kruskal-Wallis test on these data, assuming a p level of 0.05?

A) 3.841
B) 5.992
C) 7.815
D) 9.488

Question 47

The process of representing an entire population of data by repeatedly sampling from the original sample is called:

A) repeated sampling.
B) bootstrapping.
C) transformation.
D) null hypothesis testing.

Question 48

The assumptions of the Kruskal-Wallis H test are that the:

A) data are ordinal and participants are randomly selected.
B) data are ordinal, participants are randomly selected, and the population distribution of ranks is symmetric.
C) data are scale and participants are randomly selected.
D) participants are randomly selected and the population distribution is symmetric.

Question 49

To determine the critical cutoff for Mann-Whitney U, which of these must be known?

A) sample size of both groups
B) degrees of freedom for both groups
C) degrees of freedom for the smallest group
D) size of the population

Question 50

The process of bootstrapping requires:

A) sampling without replacement.
B) access to the entire population of scores.
C) performing a log transformation of all scores.
D) sampling with replacement.

Question 51

Parametric tests are appropriate for scale data, but they are not appropriate for ordinal data.

Question 52

Bootstrapping is used on a sample of data with the following values: 520, 515, 480, 420, 610, 470, 420, and 630.The confidence interval created through bootstrapping will be centered around what value?

A) mean of the original sample
B) mean of the distribution of sample means
C) zero
D) mean of the test

Question 53

Jasmine wonders whether the ratings for movies that are dramas differ, on average, from the ratings of movies that are comedies.She retrieves the ratings of five comedies and five dramas from the Internet Movie Database (IMDB).The $\\ \Sigma$ R for drama is 32 and $\\ \Sigma$ R for comedies is 23.Using a p level of 0.05, what conclusion should be drawn on the basis of these results?

A) Given that the largest of the $\\ \Sigma$ R (32) is greater than the critical value of 2, reject the null hypothesis.The ratings of dramas and comedies differ.
B) Given that the smallest U (U = 8) is not equal to or less than the critical value of 2, fail to reject the null hypothesis.There is no evidence that the ratings of dramas and comedies differ.
C) Given that the smallest of the $\\ \Sigma$ R (23) is greater than the critical value of 2, reject the null hypothesis.The ratings of dramas and comedies differ.
D) Given that the smallest of the $\\ \Sigma$ R (23) is not equal to or less than the critical value of 2, fail to reject the null hypothesis.There is no evidence that the ratings of dramas and comedies differ.

Question 54

When using the Mann-Whitney U test, the null hypothesis is rejected when the _____ of the two calculated statistics is equal to or _____ than the critical value.

A) smaller; greater
B) larger; greater
C) smaller; less
D) larger; less

Question 55

What is the formula for the Kruskal-Wallis H test?

A) $\left[ \frac { 12 } { N ( N + 1 ) } \right] \left[ \sum n ( M - G M ) ^ { 2 } \right]$
B) $\left[ \frac { 12 } { N ( N + 1 ) } \right] \left[ \sum n ( M - G M ) \right]$
C) $\left[ \sum n ( M - G M ) ^ { 2 } \right]$
D) $\left[ \frac { N } { N ( N + 1 ) } \right] \left[ \sum n ( M - G M ) \right]$

Question 56

There is rarely an established nonparametric alternative to a parametric test.

Question 57

If one rejects the null hypothesis when using the Kruskal-Wallis H test, then:

A) all the groups differ significantly from one another.
B) at least one of the groups differs significantly from another, but you do not know which one.
C) the group ranks are similar.
D) the largest difference between a ranked pair is at least two times the smallest difference.

Question 58

Three different ethnic groups are compared on their ranked language skills and an H statistic of 7.1 is computed.What conclusion could be made about a hypothesis test at a p level of 0.05?

A) Reject the null hypothesis and conclude there are differences among these groups for ranked language skills.
B) Reject the null hypothesis and conclude that all three groups are significantly different from each other.
C) Fail to reject the null hypothesis and conclude no differences exist.
D) Fail to reject the null hypothesis and conclude there was no statistical power.

Question 59

The H distribution for the Kruskal-Wallis H test is very close to the _____ distribution, so the latter is often used for determining the critical values for the Kruskal-Wallis H test.

A) F
B) t
C) T
D) chi-square

Question 60

Bootstrapping is used on a sample of data with the following values: 520, 515, 480, 420, 610, 470, 420, and 630.Each sample collected during the bootstrapping process must have how many scores?

A) 2
B) 4
C) 5
D) 8

Question 61

The Spearman correlation can be performed to examine the relation between one ordinal variable and one scale variable.

Question 62

The Wilcoxon signed-rank test has three assumptions, including that the differences are normally distributed.

Question 63

The Kruskal-Wallis H test is the nonparametric equivalent to the one-way between-groups ANOVA.

Question 64

The Kruskal-Wallis H test has two assumptions that must be met.

Question 65

Bootstrapping involves using limited sample data to represent the entire population through repeated sampling.

Question 66

The Kruskal-Wallis H test has four assumptions that must be met.

Question 67

The Wilcoxon signed-rank test examines matched pairs.

Question 68

When converting data to ranks, scores of the same value receive the average of the two ranks they would hold if different.

Question 69

The Kruskal-Wallis test result, H, is compared to the chi-square distribution.

Question 70

The Spearman correlation can be performed to examine the relation between two ordinal variables.

Question 71

The Wilcoxin signed-rank test is the nonparametric equivalent of the paired-samples t test.

Question 72

The Wilcoxin signed-rank test is the nonparametric equivalent of the independent-samples t test.

Question 73

When converting data to ranks, scores of the same value receive the lowest of the two ranks they would hold if different.

Question 74

The Mann-Whitney U test is the nonparametric equivalent of the independent-samples t test.

Question 75

Even with scale data, one may choose to run a nonparametric test when there is a small sample size and the data are skewed.

Question 76

The Mann-Whitney U test has three assumptions: the data are ordinal, random selection is used, and ideally no ranks are tied.

Question 77

The Kruskal-Wallis H test is the nonparametric equivalent of the two-way within-groups ANOVA.

Question 78

The Mann-Whitney U test is the nonparametric equivalent of the one-way between-groups ANOVA.

Question 79

To quantify the strength of association between an ordinal and a scale variable, first transform the scale variable into an ordinal variable.

Question 80

The Mann-Whitney U test is the nonparametric equivalent of the paired-samples t test.