社会统计学习题 第三次
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1、研究 194 个原始社会的基本经济形态（自变项）与家庭组织（因变项）的关系，获得表
1 的频次资料。
（1）试将该表改为条件百分表，并且（2）指出这两个变项有何关系。
表1
原始社会之经济形态与家庭组织之关系
经济形态
家庭组织
狩猎
畜牧
农业
总数
母系
父系
混合
总数
30
18
22
70
1
10
3
14
44
47
19
110
75
75
44
194
2、在某地选取 624 名父亲，研究他们的职业背景会否影响他们对子女的职业期望。表 2 是
获得的资料。
（1）在全部父亲中有百分之几是希望其子女是同业的？（2）计算不对称 Lambda
系数和（3）计算 Tau-Y 系数，并且（4）成立条件百分表和（5）指出哪一类职业的父亲较
多希望其子女从事同类职业。
表2
父亲职业与其对子女职业之期望
父亲职业
子女职业
工
农
总数
工
农
总数
239
44
283
77
264
341
316
308
624
3、研究某地 189 名居民的亲属凝聚程度会否影响他们对异族的态度，获得表 3 的资料。
（1）
计算 Gamma 系数值，和（2）根据 G 值与表 3 的资料，简略地提出研究结论。
表3
亲属凝聚与对异族的态度
亲属凝聚
对异族态度
排斥
不排斥
（总数）
高
低
％
68.1
31.9
（94）
％
33.7
66.3
（95）
（说明：以下题目用英文或中文回答均可，注意理解题意。不要被这些题的形式吓倒，其实
做起来并不难！）
4. The percent of male and female arrestees who tested positive for marijuana use at the time of
their 1995 arrests are reported below. Is there a difference between male and female arrestees? Are
the percentages about the same for both? Calculate the appropriate measures of central tendency
and variability.
City
Male
Female
Atlanta, GA
32
13
Birmingham, AL
36
12
Cleveland, OH
29
11
Dallas, TX
37
21
Denver, CO
33
21
Detroit, MI
42
18
Fort Lauderdale, FL
33
18
Houston, TX
29
18
Indianapolis, IN
38
24
Los Angeles, CA
23
14
Manhattan, NY
28
16
New Orleans, LA
32
16
Omaha, NE
42
24
Philadelphia, PA
34
20
Phoenix, AZ
29
19
Portland, OR
29
16
St. Louis, MO
39
18
San Antonio, TX
34
16
San Diego, CA
35
20
San Jose, CA
27
12
Washington, DC
32
18
Source: Statistical Abstract of the United States, 1997, Table 331
5. Advocates of gay rights often argue that homosexuality is not a “preference” or a choice, but
rather an “orientation” that cannot be changed. Suppose one of your classmates has a close friend
or family member who is gay or lesbian, and he thinks people who don’t have similar
relationships have different beliefs about the origins of homosexuality than people who do have a
gay or lesbian friend or family member. Use the following table to answer the questions.
Has gay or lesbian close
friend or family member?
Homosexuality is
Yes
No
Total
Choice
Can’t change
Don’t know
81
144
29
427
352
121
508
496
150
Total
254
900
1,154
Source: Data based on 1992 New York Times/CBS News poll.
a. What is the dependent variable? the independent variable?
b. What proportion of those polled have a close friend or family member who is gay or lesbian?
c. Are people who have a close relationship with a gay a lesbian more likely to believe that
homosexuality is a choice or that it is something that cannot be changed? (Hint: Calculate
percentages.)
6. Refer to Exercise 5. Suppose another of your classmates says that it can’t be very significant to
know whether a person believes homosexuality is a choice or not, since people are equally split
(44% and 43%, respectively) between the two positions. Your professor presents the following
table based on the same survey.
Should gays and
lesbians be
allowed in the
military?
Is homosexuality a choice
or is it an orientation
that cannot change?
Choice
Can’t change
Don’t know
Total
Yes
No
Don’t know
162
276
70
268
160
68
66
62
22
496
498
160
Total
508
496
150
1,154
Source: Data based on 1992 New York Times/CBS News poll.
a.
Which is the dependent variable in this table? Which is the independent variable? Discuss
why assigning the variable to these categories is problematic.
b. Is there a relationship between believing that homosexuality is a choice and attitude toward
allowing gays and lesbians in the military? (Use percentages to support your answer.)
7. An organization in your state is lobbying to make pornography illegal because its members
believe that pornography leads to a breakdown in morals. You believe that people with
conservative views about women are more likely to hold such beliefs about pornography and that
people with liberal views about women are more likely to disagree with this view. The GSS has a
question about whether people believe that pornographic materials lead to a breakdown in morals,
and a question about whether people approve or disapprove of women working (the liberal
position is to approve).
a.
Do the GSS data in the following table support your beliefs or not? Why?
Should women work outside the home?
Does pornography
Approve
Disapprove
Total
lead to a
breakdown in
morals?
Yes
251
71
322
No
175
28
203
Total
426
99
525
Source: Data from the 1987 to 1991 GSS
b. Your friend argues that there are gender differences in the effect that attitude about women
working outside the home has on views about pornography. Do the GSS survey data in the
following table support her belief? Why or why not?
Should women work outside the home?
Does
pornography lead
to a breakdown
in morals?
Yes
No
Males
Approve
Disapprove
Females
Approve
Disapprove
86
29
165
42
90
15
85
13
Source: Data from the 1987 to 1991 GSS
c.
What can you conclude about the relationship between views about women working and
attitudes about pornography? Is this an example of a conditional relationship?
8. In the previous exercise you examined the relationship between liberal attitudes about women
and the belief that pornographic materials lead to a breakdown in morals. Do liberal attitudes
about women working have a conditional effect for whites and blacks?
a. Use the following table to answer this question and describe the relationship between race,
attitude toward women working, and attitude toward the effect of pornography. (Hint: Calculate
percentages for White and Black respectively.)
Does
pornography lead
to a breakdown
in morals?
Should women work outside the home?
White
Black
Approve
Disapprove Approve
Disapprove
Yes
157
36
94
35
No
102
14
73
14
Source: Data from the 1987 to 1991 GSS
b. Does race show that the relationship between attitude toward women working and attitude
toward the effect of pornography is spurious? Why or why not?
9. Suicide among older males has drawn increasing public attention. White males 65 years or
older have the highest suicide rate compared to women, younger males, and other ethnic groups.
In 1996 Mark Kaplan, Margaret Adamek, and Olga Geling reported the results of their study based
on 14,887 suicide death records for elderly white males. Based on the following bivariate table,
what can you conclude about the relationship between age and method of suicide?
Age
65-74
75-84
85+
Suicide by firearms
5,687
4,570
1,167
Suicide by other methods
1,647
1,303
513
th
Source: Reprinted with permission of the Gerontological Society of America, 1030 15 street, NW,
Suite 250, Washington, DC 20005. “Sociodemographic Predictors of Firearm Suicide Among
Older White Males”, M. Kaplan, M. Adamek, and O. Geling, The Gerontologist 36(4): 530-533.
Reproduced by permission of the publisher via Copyright Clearance Center, Inc.
10. In Exercise 5, we investigated the relationship between whether someone has a close friend or
family member who is lesbian or gay and whether she or he believes that homosexuality is a
choice. The data form that exercise are displayed again here for convenience.
Has gay or lesbian close
friend or family member?
Homosexuality is
Yes
No
Total
Choice
Can’t change
Don’t know
81
144
29
427
352
121
508
496
150
Total
254
900
1,154
a.
As before, we will treat whether or not someone has a friend or family member who is lesbian
or gay as the independent variable. If we first ignore that variable and try to predict attitude
toward homosexuality, how much errors will we make?
b. If we now take into account the independent variable, how many errors of prediction will we
make for those who have a gay or lesbian friend or family member? for those who don’t?
c. Combine the answers in (a) and (b) to calculate the proportional reduction in error for this
table based on the independent variable. How does this statistic improve our understanding of
the relationship between the two variables?
11. In Exercise 6, we continued the investigation of attitudes toward homosexuality, studying how
belief about whether homosexuality is a choice influenced support for gays or lesbians being
allowed in the military. That table (minus the “Don’t know” responses) is reproduced here.
Should gays and
lesbians be allowed
in the military?
Is homosexuality a choice
or is it an orientation
that cannot change?
Choice
Can’t change
Total
Yes
No
Total
162
276
438
268
160
428
430
436
866
a.
Treating belief about whether homosexuality is a choice as the independent variable, calculate
lambda for the table. How many errors of prediction will be made if the independent variable
is ignored? How many fewer errors will be made if the independent variable is taken into
account? Use lambda to discuss the relationship between these two beliefs. Why is lambda an
appropriate measure of association?
b. Both variables in this table are attitudes, so we could consider belief about whether gays and
lesbians should be allowed in the military as the predictor, or independent, variable. If we do,
then lambda must be recalculated because it is not a symmetrical measure of association.
What is the value for lambda when belief about allowing gays and lesbians in the military is
the independent variable? How does it compare with the lambda calculated in (a)?
12. Women have increasingly been elected to higher political offices in recent years. Given this
fact, is it true that the increasing number of women legislators has, in part, led to a higher
percentage of bills being passed on women’s or family issues? The following table displays data
about the number of bills on women’s and family issues that were introduced and then passed by
the U.S. Congress during two 2-years periods in the early 1990s.
Bills Introduced on
Women’s and Family Issues
Didn’t pass
Did pass
1990/91
1992/93
231
19
437
64
Source: Data from the Congressional Caucus for Women’s Issues
a.
Calculate lambda to assess the strength of the relationship between time period and bill
passage. Be sure to use the appropriate independent variable when calculating lambda.
b. Does the calculated value of lambda seem surprising, given the relationship observed in the
table? Can you explain why lambda has the value that it does?
13. The following table presents data form the 1996 GSS on attitudes toward premarital sex by
age of respondent (grouped into intervals of twenty years).
PREMARSX SEX BEFORE MARRIAGE  CAGE categorical age Crosstabulation
Count
CAGE categorical age
PREMARSX
1 ALWAYS WRONG
1.00 20-39
2.00 40-59
3.00 60+
Total
74
77
74
225
SEX
BEFORE
MARRIAGE
2 ALMST ALWAYS WRG
30
30
32
93
3 SOMETIMES WRONG
88
77
54
219
193
385
170
354
44
204
407
943
4 NOT WRG AT ALL
Total
a.
To calculate a measure of association for ordinal data we need to calculate the number of Ns
and Nd pairs. Calculate these quantities for this table. (Hint: Consider the highest category of
attitude toward premarital sex to be “always wrong”, and reconstruct the table accordingly.)
b. Using Ns and Nd, calculate gamma for this table. Is gamma positive or negative? Using the
value of gamma, interpret the relationship between age and attitude toward premarital sex.
14. Tolerance of premarital sexual activity is associated with several demographic variables. In
this exercise we will explore how well education predicts this attitude. The following table uses
data from the 1996 GSS, with education recoded into the five categories displayed in the columns.
PREMARSX SEX BEFORE MARRIAGE  DEGREE RS HIGHEST DEGREE Crosstabulation
DEGREE RS HIGHEST DEGREE
PREMARSX
1 ALWAYS WRONG
SEX
% within DEGREE RS
BEFORE
MARRIAGE
Count
0 LT HIGH
1 HIGH
2 JUNIOR
3
4
SCHOOL
SCHOLL
COLLEGE
BACHELOR
GRADUATE
Total
49
129
12
28
8
226
37.1%
23.9%
21.1%
19.4%
9.9%
23.7%
9
61
8
11
5
94
6.8%
11.3%
14.0%
7.6%
6.2%
9.9%
28
122
15
32
24
221
21.2%
22.6%
26.3%
22.2%
29.6%
23.2%
46
228
22
73
44
413
34.8%
42.2%
38.6%
50.7%
54.3%
43.3%
132
540
57
144
81
954
100.0%
100.0%
100.0%
100.0%
100.0%
100.0
HIGHTST DEGREE
2 ALMST ALWAYS WRG
Count
% within DEGREE RS
HIGHTST DEGREE
3 SOMETIMES WRONG
Count
% within DEGREE RS
HIGHTST DEGREE
4 NOT WRG AT ALL
Count
% within DEGREE RS
HIGHTST DEGREE
Total
Count
% within DEGREE RS
%
HIGHTST DEGREE
Directional Measures
Asymp.
Value
Ordinal by Ordinal
Somers’ d
Symmetric
Std. Error
Approx.
a
Approx. T
b
Sig.
.119
.027
4.318
.000
.125
.029
4.318
.000
PREMARSX SEX
BEFORE MARRIAGE
Dependent
.113
DEGREE RS HIGHEST
.026
4.318
.000
DEGREE Dependent
a.
Not assuming the null hypothesis.
b.
Using the asymptotic standard error assuming the null hypothesis.
Symmetric Measures
Asymp. Std.
Value
Ordinal by Ordinal
Gamma
N of Valid Cases
Error
.181
Approx.
a
Approx. T
.042
b
Sig.
4.318
.000
954
a.
Not assuming the null hypothesis.
b.
Using the asymptotic standard error assuming the null hypothesis.
Notice that gamma and Somers’ d have been calculated. Use these two statistics to discuss the
relationship between education and attitude toward premarital sex.
b. Why is Somers’ d smaller than gamma?
a.
15. Gun ownership is quite common in the United States, but those who own a gun are not
necessarily a cross-section of Americans. One possibility is that there might be a difference in gun
ownership by marital status (perhaps married individuals are more likely to own a gun to protect
their family). Using the GSS1996 data, you construct the following table.
OWNGUN HAVE GUN IN HOME  MARITAL MARITAL STATUS Crosstabulation
MARITAL MARITAL STATUS
OWNGUN
1 YES
HAVE GUN
Count
% within MARITAL
IN HOME
1
2
3
4
5 NEVER
MARRIED
WIDOWED
DIVORCED
SEPARATED
MARRIED
237
31
51
10
53
52.2％
29.5％
34.7％
28.6％
26.1％
217
74
96
25
150
47.8％
70.5％
65.3％
71.4％
73.9％
454
105
147
35
203
100.0％
100.0％
100.0％
100.0％
100.0％
4
MARITAL STATUS
2 NO
Count
% within MARITAL
5
MARITAL STATUS
Total
Count
% within MARITAL
MARITAL STATUS
a. What measure of association is appropriate for this table?
b. Without doing any calculations, you should be able to study this table and provide one
possible value for the proper measure of association. What is that value, and why?
10
16. A company tests applicants for a job by giving writing and software proficiency tests. The
means and standard deviations for each exam follow, along with the scores for two applicants, Bill
and Ted. Assume test scores are normally distributed.
a.
Exam
Mean
Standard
deviation
Bill
Ted
Writing
56.4
9.3
65
67
Software use
68.7
5.6
70
75
On which test did Bill do better, relative to the other applicants? Calculate appropriate
statistics to answer this question.
b. On which test did Ted do better, relative to the other applicants? Calculate statistics to answer
this question.
c. What proportion of applicants scored below Bill’s Software Use test score?
d. What is the percentile rank of Ted’s Writing score of 67?