Deck 17: Chi-Square and Other Nonparametric Tests

Question 1

In a 2 x 2 contingency table, if we keep the marginals at their observed values, how many f o scores are free to vary?

A) 3
B) 0
C) 1
D) all of them

Answer 1

1

Question 2

A contingency table _________.

A) is a two-way table
B) involves two variables
C) involves two mutually exclusive variables
D) all of these
E) is a two-way table and involves two variables

Answer 2

is a two-way table and involves two variables

Question 3

In most situations, parametric tests _________.

A) have the same power as nonparametric tests
B) are less powerful than nonparametric tests
C) are more powerful than nonparametric tests
D) are less sensitive than nonparametric tests
E) are less powerful than nonparametric tests and are less sensitive than nonparametric tests

Answer 3

are more powerful than nonparametric tests

Question 4

Which of the following are true?

A) f o is the symbol for the observed frequency
B) f e is the symbol for the expected frequency
C) c 2 is the symbol for chi-square
D) all of these

Question 5

The degrees of freedom for a contingency table equal _________.

A) rc - 1
B) ( r - 1)( c - 1)
C) ( r - 1)( c )
D) ( c - 1)( r )
E) N - 1

Question 6

For any given alpha level, c 2crit _________.

A) increases with increases in N
B) decreases with increases in N
C) increases with increases in degrees of freedom
D) increases with increases in N and increases with increases in degrees of freedom

Question 7

To compute c 2 , the entries in the contingency table should be _________.

A) frequencies
B) means
C) variances
D) degrees of freedom

Question 8

Chi-square should not be used if _________.

A) df = 1
B) f e is below 5
C) f o is below 5
D) f e = f o

Question 9

If N = 18 and a = 0.05_{2 tailed}, the value of T _crit is _________.

A) 40
B) ± 40
C) - 40
D) 47

Question 10

When evaluating c 2obt , the critical region for rejection of H 0 _________.

A) lies under both tails of the distribution
B) lies under the right hand tail of the distribution
C) lies under the left hand tail of the distribution
D) lies in the middle of the distribution

Question 11

The Wilcoxon signed ranks test _________.

A) is used with a correlated groups design
B) is used with data that is nominal in scaling
C) uses both the magnitude and direction of the data
D) all of these
E) is used with a correlated groups design and is used with data that is nominal in scaling

Question 12

Chi-square may be used with _________

A) nominal data
B) ordinal data
C) interval data
D) ratio data
E) all of these

Question 13

If a = 0.05, and df = 4, the value of c 2crit = _________.

A) 9.488
B) 0.711
C) 7.815
D) 11.070

Question 14

The sampling distribution of chi-square is _________.

A) skewed
B) varies with df
C) is a theoretical distribution
D) all of these
E) skewed and varies with df

Question 15

Chi-square is used to test differences between _________.

A) proportions
B) means
C) variances
D) none of these

Question 16

The computation of f e _________.

A) is based on population proportion estimates
B) is based on known population proportions
C) is based on population means
D) none of these

Question 17

Prior to a recent gubernatorial election, a survey was conducted to determine whether there was a relationship between sexual gender and preference for the Democratic or Republican candidate. The following data were recorded. Assume the data will be analyzed with Chi-square. Using a = 0.05, c 2crit = _________.

A) 3.841
B) 5.412
C) 2.706
D) - 3.841

Question 18

Prior to a recent gubernatorial election, a survey was conducted to determine whether there was a relationship between sexual gender and preference for the Democratic or Republican candidate. The following data were recorded. Assume the data will be analyzed with Chi-square. The value of c 2obt = _________.

A) 2.06
B) 2.09
C) 1.80
D) 1.75

Question 19

Prior to a recent gubernatorial election, a survey was conducted to determine whether there was a relationship between sexual gender and preference for the Democratic or Republican candidate. The following data were recorded. Assume the data will be analyzed with Chi-square. The value of df = _________.

A) 2
B) 1
C) 3
D) need more information

Question 20

The c 2 test is _________.

A) always directional
B) never directional
C) generally nondirectional
D) generally directional

Question 21

In the Mann-Whitney U test, the U value of 0 _________.

A) represents a low degree of separation between the two groups
B) implies that the two groups are identical
C) represents the greatest degree of separation between the two groups
D) indicates that the power of the experiment is very low.

Question 22

If n 1 = 6, n 2 = 8 and a = 0.05 2 tail , U crit value is _________.

A) 8
B) 40
C) 6
D) 42

Question 23

A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression. Using the Wilcoxon signed ranks test to evaluate the data, the value of T obt is _________.

A) - 3
B) 3
C) 33
D) 4

Question 24

The statistics ( U or U' ) used in the Mann-Whitney U test, measure _________.

A) the differences between the means of the two groups
B) the direction of the differences between pairs of scores
C) the power of the experiment
D) the separation between the two groups

Question 25

If n 1 = 5, n 2 = 4, and a = 0.01 2 tail , the power of the Mann-Whitney U test equals _________.

A) 1
B) 0
C) 0.01
D) need more information

Question 26

A Mann-Whitney U value of zero indicates _________.

A) you can reject the null hypothesis
B) low degree of separation between the scores of each group
C) zero difference between the two groups
D) high degree of separation between the scores of each group

Question 27

Prior to a recent gubernatorial election, a survey was conducted to determine whether there was a relationship between sexual gender and preference for the Democratic or Republican candidate. The following data were recorded. Assume the data will be analyzed with Chi-square. Using a = 0.05, what is your conclusion?

A) accept H 0 ; there is no relationship between sex and candidate preference
B) reject H 0 ; there is a significant relationship between sex and candidate preference
C) retain H 0 ; the study does not show a significant relationship between sex and candidate preference
D) retain H 0 ; this study shows a significant relationship between sex and candidate preference

Question 28

The statistic used with the Kruskal-Wallis test is _________.

A) F obt
B) H obt
C) U obt
D) t obt

Question 29

Consider the following set of scores: 25, 28, 28, 28, 30. In assigning ranks to the scores, a score of 28 receives a rank of _________.

A) 2.5
B) 2
C) 4
D) 3

Question 30

A student at a Midwest college is interested in whether Psychology majors spend more or less time studying than English majors. She randomly selects 8 Psychology majors and 8 English majors and determines their weekly studying time. The following are the scores. Note one person dropped out of the study. An analysis is being conducted using the Mann-Whitney U test. Using a = 0.05 2 tail , what do you conclude?

A) reject H 0 ; there is a significant difference in the amount of time Psychology and English majors study
B) reject H 0 ; there is no difference in the amount of time Psychology and English majors study
C) accept H 0 ; there is no difference in the amount of time Psychology and English majors study
D) retain H 0 ; there is no difference in the amount of time Psychology and English majors study

Question 31

As the separation between the two groups of scores increases, U obt _________.

A) increases
B) decreases
C) stays the same
D) approaches U 'obt

Question 32

A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression. Using the Wilcoxon signed ranks test to evaluate the data, with a = 0.05 2 tail , T crit = _________.

A) 2
B) 5
C) ±3
D) 3

Question 33

A student at a Midwest college is interested in whether Psychology majors spend more or less time studying than English majors. She randomly selects 8 Psychology majors and 8 English majors and determines their weekly studying time. The following are the scores. Note one person dropped out of the study. An analysis is being conducted using the Mann-Whitney U test. The value of U obt is _________.

A) 6
B) 50
C) 14
D) 42

Question 34

Using the data in question 38, a score of 30 would receive a rank of _________.

A) 4
B) 5
C) 3
D) 0

Question 35

A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression. Using the Wilcoxon signed ranks test to evaluate the data with a = 0.05 2 tail , what do you conclude? Assume for the purpose of this question, that sunshine was the only systematic difference between the conditions.

A) reject H 0 ; sunshine appears to affect depression
B) reject H 0 ; sunshine has no effect on depression
C) retain H 0 ; we cannot conclude that sunshine affects depression
D) accept H 0 ; sunshine affects depression

Question 36

U + U' equals _________.

A) n
B) n 1 + n 2
C) n 1 x n 2
D) none of these

Question 37

Generally, if R 1 is greater than R 2 , _________.

A) the equation yields the U value
B) the equation yields the U value
C) the power of the test is necessarily low
D) we must reject

Question 38

The Mann-Whitney U test uses _________.

A) only the direction of the scores
B) only the magnitude of the scores
C) both the magnitude and direction of the scores
D) none of these

Question 39

The Mann-Whitney U test is used with _________.

A) an independent groups design
B) a replicated measures design
C) a correlated groups design
D) b and c

Question 40

A student at a Midwest college is interested in whether Psychology majors spend more or less time studying than English majors. She randomly selects 8 Psychology majors and 8 English majors and determines their weekly studying time. The following are the scores. Note one person dropped out of the study. An analysis is being conducted using the Mann-Whitney U test. If a = 0.05 2 tail, U crit = _________.

A) 7
B) 10
C) 46
D) 49

Question 41

The conclusion for the data in question 56 is _________.

A) reject H₀
B) reject H₁
C) retain H₀
D) fail to accept H₁

Question 42

If an experiment using frequency data tested the preference for 6 brands of soup, there would be _________ degrees of freedom.

A) 1
B) N - 1
C) 5
D) 6

Question 43

A researcher conducts a one-way ANOVA involving three groups. When she analyzes the data she realizes the data seriously violate the assumptions underlying parametric ANOVA. Therefore, she decides to use the Kruskal-Wallis test to conclude with regard to H 0. The data are given below. What is the appropriate conclusion concerning H 0 ?

A) reject H 0 ; the independent variable has a real effect
B) accept H 0 ; the independent variable has no effect
C) retain H 0 ; the independent variable has a real effect
D) retain H 0 ; we cannot conclude the independent variable has a real effect

Question 44

A researcher conducts a one-way ANOVA involving three groups. When she analyzes the data she realizes the data seriously violate the assumptions underlying parametric ANOVA. Therefore, she decides to use the Kruskal-Wallis test to conclude with regard to H 0. The data are given below. H obt = _________.

A) 4.25
B) 5.43
C) 2.68
D) 6.86

Question 45

A researcher conducts a one-way ANOVA involving three groups. When she analyzes the data she realizes the data seriously violate the assumptions underlying parametric ANOVA. Therefore, she decides to use the Kruskal-Wallis test to conclude with regard to H 0. The data are given below. Using a = 0.05, H crit = _________.

A) 9.210
B) 7.815
C) 5.991
D) 7.824

Question 46

The value of T obt for the following data is _________.

A) 21
B) - 6
C) 15
D) 6

Question 47

For the following table there is(are) _________ degrees of freedom. The value of c 2obt for the table is _________.

A) 47.43
B) 17.96
C) 4.07
D) 9.71

Question 48

The value of c 2crit for the data in Question 53 with a = 0.01 is _________.

A) 6.635
B) 15.086
C) 13.277
D) 11.668

Question 49

For a low value of df the c 2 distribution is _________.

A) normally distributed
B) positively skewed
C) negatively skewed
D) none of these

Question 50

The c 2 test can be used for variables with _________ scaling as long as the categories are mutually exclusive.

A) nominal
B) ordinal
C) interval
D) ratio
E) all thesee

Question 51

Which of the following tests are parametric statistical tests:

A) sign test
B) chi-square test
C) Wilcoxin signed ranks test
D) none of these

Question 52

The value of f e for the cell in row W , column A is _________.

A) 24.9
B) 3.2
C) 16.0
D) 63.0

Question 53

The value of c 2obt for the table in question 56 is _________.

A) 19.01
B) 21.38
C) 24.87
D) 16.82

Question 54

The _________ test is the most powerful test for a repeated measures design.

A) sign
B) t
C) Wilcoxin signed ranks
D) all the tests are equally powerful

Question 55

For the following table there is(are) _________ degrees of freedom.

A) k - 1
B) 1
C) 2
D) 4

Question 56

The value of c 2crit for the table in question 56 with a = 0.05 is _________.

A) 13.277
B) 7.779
C) 3.841
D) 9.488

Question 57

If there are 16 subjects in a repeated measures design then the sum of the unsigned ranks equals _________.

A) 136
B) 68
C) 272
D) 32

Question 58

The conclusion for the data in Question 53 is _________.

A) reject H₀
B) reject H₁
C) retain H₀
D) retain H₁

Question 59

The value of c 2obt for the table below is _________. (Assume equal probabilities for f e in each cell.)

A) 96.00
B) 9.42
C) 8.13
D) 13.28

Question 60

If T obt = 12 and T crit = 10, one would _________.

A) reject H₀
B) retain H₀
C) accept H₀
D) reject H₁

Question 61

All inference tests depend on population characteristics.

Question 62

In Chapter 16, we presented the data from an independent groups design and asked if it was appropriate to use parametric ANOVA. The data are presented again below. The correct answer was that it was not appropriate to use parametric ANOVA because of unequal n s and homogeneity of variance assumption violation. Is it possible to analyze the data with an alternate test?

A) yes
B) no

Question 63

In Chapter 16, we presented the data from an independent groups design and asked if it was appropriate to use parametric ANOVA. The data are presented again here. The correct answer was that it was not appropriate to use parametric ANOVA because of unequal n s and homogeneity of variance assumption violation. Instead, analyze the data with the Kruskal-Wallis test. H obt = _________ .

A) 10.25
B) 10.63
C) 15.96
D) 5.96

Question 64

In Chapter 16, we presented the data from an independent groups design and asked if it was appropriate to use parametric ANOVA. The data are presented again below. The correct answer was that it was not appropriate to use parametric ANOVA because of unequal n s and homogeneity of variance assumption violation. Instead, analyze the data with the Kruskal-Wallis test. What are the df?

A) 1
B) 2
C) 3
D) need more information

Question 65

Parametric tests are more versatile than nonparametric tests.

Question 66

An assumption of c 2 is that the scores in each cell are independent. (

Question 67

To answer this question, refer to the following data. Assume the data are being analyzed with the Mann-Whitney U test. The value of U _obt (not U ?2 _obt) is _________.

A) 14.5
B) 20.5
C) 21.5
D) 27.5

Question 68

Consider the following set of scores: 81, 83, 84, 84, 87. What rank would you give to a score of 84?

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

Question 69

To find f e for any cell, multiply the marginals for that cell and divide by N .

Question 70

Parametric tests depend less on population characteristics than nonparametric tests.

Question 71

If your answer to question 71 is yes, what is the name of the test?

A) t test for independent groups
B) F test
C) Kruskal-Wallis
D) Mann-Whitney U test

Question 72

c 2obt cannot be negative.

Question 73

To answer this question, refer to the following data. Assume the data are being analyzed with the Mann-Whitney U test. The conclusion using a = 0.05_{2 tail} is _________.

A) reject H₀
B) reject H₁
C) retain H₀
D) retain H₁

Question 74

In Chapter 16, we presented the data from an independent groups design and asked if it was appropriate to use parametric ANOVA. The data are presented again below. The correct answer was that it was not appropriate to use parametric ANOVA because of unequal n s and homogeneity of variance assumption violation. Instead, analyze the data with the Kruskal-Wallis test. Using a = 0.05, H crit = _________.

A) 3.841
B) 7.815
C) 5.991
D) 7.824

Question 75

To answer this question, refer to the following data. Assume the data are being analyzed with the Mann-Whitney U test. The value of U _crit using a = 0.05_{2 tail} is _________.

A) 36
B) 5
C) 6
D) 30

Question 76

The Wilcoxin signed ranks test is more powerful than the t test for correlated groups.

Question 77

To use the Wilcoxin signed ranks test, the difference scores must be at least of ordinal scaling.

Question 78

The Wilcoxin signed ranks test is less powerful than the sign test.

Question 79

The statistics used for the Mann-Whitney U test measure _________.

A) the mean differences between the two groups
B) the direction of the differences between pairs of scores
C) the power of the experiment
D) the separation between the two sets of scores

Question 80

In Chapter 16, we presented the data from an independent groups design and asked if it was appropriate to use parametric ANOVA. The data are presented again here. The correct answer was that it was not appropriate to use parametric ANOVA because of unequal n s and homogeneity of variance assumption violation. Instead, analyze the data with the Kruskal-Wallis test. What do you conclude, using a = 0.05?

A) retain H₀ . There is no difference in the populations.
B) accept H₀ . There is no difference in the populations.
C) reject H₀ . At least one of the population means differs from at least one of the others.
D) reject H₀ . At least one of the distributions differs from at least one of the others.