PS 225! Exam 3 *\
Ignore Bold Questions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1. The chi square test is frequently used because it is relatively easy to satisfy the model assumptions (step 1 of
the five-step model). These assumptions require, in the case of chi square,
a. a normal population distribution
b. no assumption about the shape of the sampling distribution
c. expected frequencies of equal value
d. a difference in expected and observed frequencies
2. Unlike other tests of significance, Chi square easily handles situations in which
a. the variables have more than two categories or scores
b. the variables have less than two categories or scores
c. variables are all ordinal in level of measurement
d. degrees of freedom exceed 100
3. To conduct a chi square test, the variables must first be organized into
a. a univariate table
b. a bivariate table
c. a list, which is then ranked
d. frequency distributions
4. Which pattern of cell frequencies in a 2  2 table would indicate that the variables are independent?
a. all cell frequencies are exactly the same
b. there are a different number of cases in each of the four cells
c. only the cells in the top row of the table have cases in them
d. there are no cases in any cell
5. In the chi square test of hypothesis, the null hypothesis states that the variables are
a. dependent
b. independent
c. causally related
d. non-random
6. When the null hypothesis in the chi square test for independence is true, there should be
a. a large difference between the observed frequencies and the expected frequencies
b. little difference between the observed frequencies and the expected frequencies
c. no difference between the observed frequencies and the marginals
d. no difference between the row and the column marginals
7. Cell frequencies computed under the assumption that the null hypothesis is true are called
a. observed frequencies
b. experimental frequencies
c. expected frequencies
d. random frequencies
8. A researcher reports that her obtained chi square of 17.56 is significant because it exceeds the critical
Chi square of 3.841 for an alpha of .05 with 2 degrees of freedom. What mistake has been made?
a. neither critical nor obtained Chi squares can have negative values
b. it is impossible to have only 2 degrees of freedom
c. it is impossible for obtained Chi square to exceed 10
d. a one-tailed test should have been used
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9. In a research study conducted to determine if arrests were related to the socioeconomic class of the offender,
the chi square test statistic is 12.2 and has a significance of .000. We can conclude that
a. the variables are independent
b. being in a certain socioeconomic class causes arrests
c. the variables are dependent
d. the probability of getting these results by random chance alone is 0.5.
10. Chi square has been used to test the relationship between gender and support for abortion. The null hypothesis
has been rejected. What may be concluded?
a. support for abortion depends on gender
b. gender and support for abortion are not related
c. females are more supportive of abortion
d. males are more supportive of abortion
11. One limitation of the Chi square test (and all tests of hypothesis) is that they cannot tell us if relationships
between variables are
a. significant
b. random
c. by chance
d. important
12. Tests of significance tell us if our results are non-random. To investigate the strength and direction of
relationships, we must use
a. Chi square tests
b. ANOVA
c. percentages
d. measures of association
13. Measures of association provide the researcher with information that
a. indicates the strength of a relationship between variables
b. assists him or her in making predictions from one variable to another
c. facilitates his or her understanding of causal relationships between variables
d. all of the above
14. If the distribution of the scores of one variable changes across the categories of another variable, the variables
a. are associated to some extent
b. are related in a way that is statistically significant
c. have a cause and effect relationship
d. are perfectly associated
15. The distribution of scores on the dependent variable for a specific category of the independent variable is
called
a. associated categories
b. the distribution correlation
c. the conditional distribution of Y
d. the marginal response category
16. If variables are arranged in a bivariate table, we can see if they are associated by
a. adding their scores vertically
b. subtracting their scores horizontally
c. computing percentages in the direction of the independent variable
d. computing percentages in the direction of the dependent variable
17. In the case of a perfect association, predictions from one variable to another can be made
a. only if variables are measured at the nominal level
b. when at least one variable is ordinal
c. without error
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d. only if the relationship is positive
For variables measured at the ordinal and interval-ratio levels, measures of association will have a lower limit
of ____ and an upper limit of ____.
a. 0 ... 100
b. 0 ... ±1
c. 0 ... 1
d. 1 ... 0
The closer the value of a measure of association is to one,
a. the stronger the relationship
b. the more evenly the scores are distributed
c. the weaker the relationship
d. the more certain we are that the samples are representative
If there is a positive association between two variables,
a. as one variable increases in value, the other also increases
b. as one variable decreases in value, the other increases
c. the researcher can be certain of his conclusions
d. neither variable can decrease
A study was made of marital satisfaction experienced by men and women. A phi of .07 was calculated for the
relationship between gender and satisfaction. This result shows that
a. women experience greater marital satisfaction
b. men experience greater marital satisfaction
c. there is a weak relationship between the variables
d. there is a positive relationship between the variables
For tables larger than 2  2, phi can exceed 1.00. This makes phi
a. useless
b. difficult to interpret
c. the best measure of association
d. preferable to Cramer's V
Cramer's V differs from phi in that it
a. ranges from 0 to  1.00
b. is computed using the expression (minimum of r  1, c  1)
c. can never exceed .80
d. has only one degree of freedom
Proportional reduction in error (PRE) measures of association are based on the logic of
a. percentages
b. inference
c. prediction
d. zero errors
If there is no association between two variables, knowledge of the independent variable
a. causes us to make more prediction errors
b. improves the accuracy of our predictions
c. does not change the number of errors of prediction
d. makes prediction of the dependent variable impossible
For ordinal level variables with only a few categories or values, an appropriate measure of association would
be
a. Spearman's rho
b. Gamma
c. Chi square
d. Cramer's V
____ 27. Gamma ranges from
a. 0 to 1.00
b. 1.00 to 100
c. 0.00 to  1.00
d. 1.00 to + 1.00
____ 28. For a relationship between education and library use, gamma was +0.37. This indicates that
a. library use increases with education
b. the well educated are more likely to purchase books
c. as education goes up, people are less likely to go to the library
d. people with limited funds have greater need for free public libraries
____ 29. A researcher has computed a gamma of 0.45 between marital happiness and number of children. What can
she conclude?
a. families with more children are happier. This is a moderate relationship
b. children have a strong, positive influence on levels of marital happiness
c. there is a moderate, negative relationship between number of children and marital
happiness
d. there is a weak, negative relationship between the variables
____ 30. The table below shows a relationship between education and support for a policy to restrict immigration to the
United States. The relationship between education and opposition is
EDUCATION
Less than High School
High School
SUPPORT:
Low
Neutral
High
Totals
60
20
10
100%
30
30
40
100%
College
10
20
70
100%
a. positive
b. negative
c. neither a positive nor negative relationship since the variables are measured at the nominal
level
d. none of the above
____ 31. Two ordinal level scales measuring religiosity and personal happiness have scores that range from 0 to 100.
Which measure of association would be most appropriate to assess the relationship between these two
variables?
a. chi square
b. phi
c. gamma
d. Spearman's rho
____ 32. Spearman's rho is appropriate for ordinal level variables because it is computed from
a. raw scores
b. the square root of gamma
c. ranks, not scores
d. percentiles, not ranks
____ 33. Many studies have explored the relationship between smoking and health problems. If one of these studies
found a Spearman's rho of +0.78 between amount of smoking and seriousness of health problems, this would
indicate
____ 34.
____ 35.
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____ 37.
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____ 39.
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____ 41.
____ 42.
a. that smoking causes health problems
b. a positive, causal relationship between these variables
c. a positive, strong relationship between these variables
d. a positive, statistically significant relationship between these variables
When referring to interval-ratio variables, a commonly used synonym for association is
a. probability
b. predictability
c. correlation
d. causation
A perfect association between variables can be seen on a scattergram when
a. all dots lie an equal distance from the regression line
b. all dots lie on the regression line
c. the regression line forms a right angle at its intersection with the X axis
d. the regression line is parallel to the X axis
There is no linear relationship between two interval-ratio variables when the regression line on a scattergram
a. is parallel to the horizontal axis
b. does not touch all of the scores
c. is not an equal distance from all of the scores
d. is bimodal
One key assumption of correlation analysis is that the variables have an essentially ____ relationship.
a. linear
b. non-linear
c. curvilinear
d. circular
In a scattergram, the point of minimized variation for scores of Y for a given value of X (the
independent variable) is
a. the sum of the conditional Y scores
b. the standard deviation of the conditional Y scores
c. the mean of the conditional Y scores
d. the predicted Y score
For summarizing the relationship between X and Y, the points of minimized variation for the conditional
distributions of Y provide us with
a. several regression lines to choose from
b. the best fitting regression line
c. a regression line that touches all of the dots
d. regression lines with negative slopes
The Y intercept is the point where
a. the horizontal axis connects to the vertical axis
b. the regression line crosses the horizontal axis of the scattergram
c. the regression line meets the conditional mean of Y
d. the regression line crosses the vertical axis of the scattergram
If the slope of a regression line is 1.5, then
a. for every unit of change in X there is a change of 1.5 units in Y
b. for every unit of change in Y there is a change of 1.5 in X
c. the score of each case is 1.5 times higher on Y than on X
d. Y causes X
If a regression line is parallel to the horizontal axis of the scattergram, the slope (b) will be
a. 1.00
b. 1.00
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____ 50.
c. 0.00
d. 0.45
If a = 2 and b = 4, for the regression line y=a+bx what would the value of Y be when X = 1?
a. 4
b. 6
c. 2
d. 1
A researcher wants to measure the strength of the association between income (measured in dollars per year)
and education (measured in number of years of formal schooling). Which of the following would be the most
appropriate measure of association?
a. the slope (b)
b. gamma
c. chi square
d. Pearson's r
If we calculate an r of .60, the proportion of the variation of Y that is explained by X is
a. .36
b. .40
c. .60
d. .64
Partial and multiple correlation require data which is
a. nominal in level of measurement
b. ordinal in level of measurement
c. inferential and bivariate
d. interval-ratio in level of measurement
Which of the following describes a direct relationship between X and Y?
a. X causes Z, which causes Y
b. Y causes Z, which causes X
c. both Z and Y cause Z
d. X causes Y
The partial correlation coefficient will reveal an interactive relationship between three variables when
a. the partial correlation coefficients drops to zero
b. the partial is greater in value than the zero-order correlation coefficient
c. the partial correlation coefficient is negative
d. none of the above. partial correlation will not detect interaction
A Pearson's r calculated for the bivariate relationship between X and Y is .50. After controlling for Z, the
partial correlation coefficient is .49. This outcome would be evidence of a(n) ____ relationship between X
and Y.
a. direct
b. spurious
c. interactive
d. negative
The partial correlation coefficient between X and Y after controlling for Z shows a much weaker relationship
than the Pearson's r computed for X and Y. This would be taken as evidence of a(n) ____ relationship
between X and Y.
a. direct
b. spurious or intervening
c. interactive
d. positive
____ 51. A Pearson's r calculated for a bivariate relationship is .50. After controlling for Z, the partial correlation
coefficient is .07. This outcome would be evidence of a(n) ____ relationship between X and Y.
a. direct
b. spurious or intervening
c. interactive
d. positive
____ 52. In the least-squares multiple regression equation, the unstandardized partial slopes show
a. the point where the line crosses the Y axis
b. the combined effects of all independents on the dependent variable
c. the amount of change in Y for a unit change in one independent variable while
controlling for all other independent variables
d. the residual effects of the independent after partialling out the effect of the
dependent variable
____ 53. If a = 1, b1 = 10, b2 = 10, X1= 2, and X2 = 3, what would the predicted Y score be?
a. 51
b. 26
c. 5
d. 0
____ 54. Under what condition could the coefficient of multiple determination (R2) be lower in value than the zeroorder correlation coefficients?
a. under no condition. This is mathematically impossible
b. only when all bivariate relationships are negative
c. only when all bivariate relationships are zero
d. only when the relationships are spurious
____ 55. Which of the following is not a prerequisite for the use of the techniques of multiple regression and
correlation
a. interval-ratio level of measurement
b. linear relationships
c. no interaction among the variables
d. partial slopes less than zero
____ 56. To the extent that the variables do not meet the assumptions of regression analysis, coefficients and
slopes become
a. greater in value
b. lower in value
c. less trustworthy
d. less representative of the population
Problem
57. Is support for the proposed anti-smoking law related to political party affiliation? Write a sentence or two
interpreting your results. Don't forget to compute and interpret column percentages and the value of chisquared.
Support:
In Favor
Neutral
Opposed
Democrat
36
20
10
66
Party
Independent
23
17
18
58
Republican
17
16
36
69
76
53
64
193
SPSS Output #1
Answer the following questions for the output below.
58. What is the null hypothesis?
59. What is the alternative hypothesis?
60. Should you reject the null hypothesis?
61. Write a conclusion statement.
62. What measure of association would be appropriate to use if there is sufficient evidence of a relationship?
SPSS Output #2
Answer the following questions for the output below.
63. Is the output below for the bivariate or partial correlation?
64. What is the null hypothesis for the circled square?
64. What is the alternative hypothesis?
65. Should you reject the null hypothesis?
66. Write a conclusion statement.
67. What combinations of variables shown below do not have sufficient evidence of a relationship?
SPSS Output #3
Answer the following questions for the output below.
68. Which variable is the x and which is the y?
69. In the output below, what is the linear regression equation?
70. Give the interpretation of the constant.
71. Give the interpretation of the slope.
72. Make a prediction for the variable of preference for staying home if they answer yes to the binary variable I am an
extravert which has a value of 1 for yes and 0 for no.
PS 225! Exam 3 Multiple Choice and Hand Calculations Only
Answer Section
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PROBLEM
57. ANS:
Support:
In Favor
Neutral
Opposed
Democrat
54.55%
30.30%
15.15%
100.00%
Party
Independent
39.66%
29.31%
31.03%
100.00%
Republican
24.64%
23.19%
52.17%
100.00%
Chi square = 22.45
Democrats are most in favor of the ban, followed by Independents. Republicans are the least supportive
group.
PTS: 1
OBJ: Test Problems