Critical Thinking
Using a Control Variable and Spuriousness
Let’s look at the relationship between the strength of a person’s religious affiliation and how a person feels
about the distribution of pornography. One of the variables in the General Social Survey is PORNLAW. This
question asks respondents what type of laws they think we ought to have regulating the distribution of
pornography. Should pornography be illegal to everyone or should it be illegal only to those under the age of 18
or should it be legal to everyone? We can draw a parallel to laws governing the distribution of drugs such as
cocaine (illegal to everyone) and laws governing the distribution of alcohol and tobacco (illegal only to those
under a certain age).
We’ll start by developing a hypothesis. The stronger a person’s religious affiliation, the more likely they are to
feel that pornography ought to be illegal for everyone regardless of their age. However, the weaker the person’s
religious affiliation, the more likely they are to feel that pornography ought to be illegal only for those under the
age of 18. Imagine that you have told your hypothesis to a friend and your friend asks “Why?” You need to
develop an argument to explain why you think your hypothesis is true. What is the link between a person’s
religious feelings and their opinion about pornography? Why should more religious individuals be more likely
to think that pornography should be illegal for everyone?
Once you have developed your argument, then you need to construct a dummy table showing what the
relationship between RELITEN and PORNLAW should look like if your hypothesis is true. Use “Tables” in
Word to construct a table like the following table.
PORNLAW
Strong
Illegal to all
Illegal under
18
Legal
a>
e<
i
Somewhat
strong
b>
f<
j
Religiosity
Not very
strong
c>
g<
k
No religion
d
h
l
Notice that the dummy table shows that as the strength of a person’s attachment to their religion decreases (i.e.,
goes from left to right), the percent who feel that pornography ought to be illegal to everyone gets smaller. But
as a person’s attachment to their religion decreases, the percent who feel that pornography ought to be illegal
only to those under the age of 18 gets larger. Also notice that the hypothesis says nothing about people feeling
that pornography ought to be legal for everyone so that row is left blank. In fact, very few people feel that
pornography ought to be legal for all.
Now that you have constructed your dummy table, it’s time to find out what the relationship actually looks like.
To do this you will need to run Crosstabs in SPSS. Crosstabs is found under Analyze/Descriptive
Statistics/Crosstabs. Your independent variable should always be the column variable and your dependent
variable should be the row variable. You also need to be sure to include the appropriate percents. Since the
independent variable is the column variable, you want the column percents. Here’s the table that you should get
to test this hypothesis.
FEELINGS ABOUT PORNOGRAPHY LAWS * S TRENGTH OF RELIGIOUS AFFILIATION Crosstabulation
STRENGTH OF RELIGIOUS AFFILIATION
FEELINGS ABOUT
PORNOGRAPHY
LAWS
ILLEGAL TO ALL
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
ILLEGAL UNDER 18
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
LEGAL
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
Total
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
STRONG
376
SOMEWHAT
STRONG
88
NOT VERY
STRONG
238
NO RELIGION
62
Total
764
54.0%
39.8%
31.9%
19.7%
38.6%
296
122
493
240
1151
42.5%
55.2%
66.2%
76.2%
58.2%
24
11
14
13
62
3.4%
5.0%
1.9%
4.1%
3.1%
696
221
745
315
1977
100.0%
100.0%
100.0%
100.0%
100.0%
All that is left is to interpret the table. Since the independent variable is the column variable, we had SPSS
compute the column percents. It’s important to compare the percents across. It’s clear that the more religious
people are, the more likely they are to think that pornography ought to illegal to all. But the less religious they
are, the more likely they are to think that pornography ought to be illegal only to those under 18. For example,
54% of those who are strongly religious think pornography ought to be illegal to all, while only 20% of those
who have no religion think that it should be illegal to everyone. But 76% of those who have no religion think
pornography ought to be illegal only to those under 18, while 43% of the strongly religious feel this way.
Does this support your hypothesis? Compare the dummy table with the table you got from SPSS. The pattern is
exactly what you expected to find if the hypothesis was true. So the data support the hypothesis. Remember not
to make too much out of small differences. The reason we don’t want to make too much out of small
differences is because of sampling error. No sample is a perfect representation of the population from which the
sample was selected. There is always some error present. Small differences could just be sampling error. So
we don’t want to make too much out of small differences.
We can also use the Chi Square test to determine whether the relationship could be due to sampling error. In the
Chi Square test, the null hypothesis that we are testing is that there is no relationship between RELITEN and
PORNLAW. In other words, any differences that we see in the table are just due to sampling error. To test the
null hypothesis, we click on the statistics button in crosstabs and check the Chi Square box. This produces the
table below. We look at the significance value which in this table is .000. This actually means less than .0005
since it is a rounded value. If this value is less than .05, then we reject the null hypothesis and say Chi Square is
significant. If it is .05 or larger, then we don’t reject the null hypothesis and say that Chi Square is not
significant. In this case, the probability that we would be wrong if we rejected the null hypothesis is less than
.0005. The Chi Square test tells us there probably is a relationship between RELITEN and PORNLAW in the
population.
Chi-Square Tes ts
6
As ymp . Sig .
(2-sided)
.000
146.967
6
.000
102.039
1
.000
Pearso n Ch i-Squ are
Value
143.325 a
Likeliho od Ratio
Lin ear-by-Linear As sociation
N of Valid Cases
df
1977
a. 0 cells (.0%) hav e expect ed co unt less than 5. The minimum
exp ected co unt is 6.93.
At this point we have only considered two variables. We need to consider other variables. For
example, sex is related to both these variables. Women are more likely to feel that they are strong in
their religion and women are also more likely to feel that pornography ought to be illegal for all
regardless of age. (We’ll run the tables in class to confirm this.) This raises the possibility that the
relationship between self-reported strength of religion and how one feels about pornography laws
might be due to gender. How are we going to check on the possibility that the relationship between
strength of religion and pornography laws is due to the effect of sex on the relationship? What we can
do is to separate males and females into two tables and look at the relationship between strength of
religion and pornography laws separately for men and for women. We can do that in SPSS by putting
RELITEN in the column box (our independent variable), putting PORNLAW in the row box (our
dependent variable), and putting SEX in the third box in SPSS. In this case, sex is the variable we are
holding constant and is often called the control variable. Here’s what you would get.
FEELINGS ABOUT PORNOGRAPHY LAWS * S TRENGTH OF RELIGIOUS AFFILIATION * RES PONDENTS SEX Crosstabulation
STRENGTH OF RELIGIOUS AFFILIATION
RESPONDENTS SEX
M ALE
FEELINGS ABOUT
PORNOGRAPHY
LAWS
ILLEGAL TO ALL
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
ILLEGAL UNDER 18
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
LEGAL
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
Total
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
FEMALE
FEELINGS ABOUT
PORNOGRAPHY
LAWS
ILLEGAL TO ALL
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
ILLEGAL UNDER 18
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
LEGAL
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
Total
Count
% within STRENGTH
OF RELIGIOUS
AFFILIATION
STRONG
113
SOMEWHAT
STRONG
30
NOT VERY
STRONG
73
NO RELIGION
24
Total
240
43.0%
32.6%
22.0%
13.3%
27.6%
137
58
250
148
593
52.1%
63.0%
75.3%
81.8%
68.3%
13
4
9
9
35
4.9%
4.3%
2.7%
5.0%
4.0%
263
92
332
181
868
100.0%
100.0%
100.0%
100.0%
100.0%
263
58
165
38
524
60.7%
45.0%
40.0%
28.4%
47.2%
159
63
243
92
557
36.7%
48.8%
58.8%
68.7%
50.2%
11
8
5
4
28
2.5%
6.2%
1.2%
3.0%
2.5%
433
129
413
134
1109
100.0%
100.0%
100.0%
100.0%
100.0%
Chi-Square Tes ts
RESPONDENTS SEX
MA LE
Pearson Ch i-Squ are
6
As ymp . Sig .
(2-sided )
.000
df
Likeliho od Ratio
61.545
6
.000
Lin ear-by-Linear Ass ociation
40.235
1
.000
N o f Valid Cases
FEMALE
Value
60.607a
868
Pearson Ch i-Squ are
72.375b
6
.000
Likeliho od Ratio
71.985
6
.000
Lin ear-by-Linear Ass ociation
46.050
1
.000
N o f Valid Cases
1109
a. 1 cells (8.3%) have expect ed count less than 5. The minimum expected coun t is 3.71.
b. 2 cells (16.7%) h ave expected coun t les s than 5. The minimum expected cou nt is 3.26.
Let’s see what happens to the relationship between strength of religion and opinion on pornography
laws when we hold sex constant. We’ll start by looking at only the males (i.e., the top half of the
table). The numbers are different from our two-variable table, but the pattern is the same. Men who
feel that they are strong in their religion are more likely than men who feel they are less strong in their
religion to think that pornography ought to be illegal to everyone regardless of age. The Chi Square
value is significant, so you can reject the null hypothesis and conclude that there probably is a
relationship between these two variables in the population.
Now we’ll do the same thing for the females (i.e., the bottom half of the table). Again, the numbers
are different from the two-variable table, but the pattern is the same. Women who feel that they are
strong in their religion are more likely than women who feel less strong in their religion to think that
pornography ought to be illegal to everyone regardless of age. Again, the Chi Square value is
significant, so you can reject the null hypothesis and conclude that there probably is a relationship
between these two variables in the population.
What does this mean? If the relationship had been due to sex, then the relationship between strength of
religion and opinion on pornography laws would have disappeared or decreased when we took out the
effect of sex by holding it constant. However, the relationship did not disappear. Therefore, the
relationship between strength of religion and opinion about pornography laws is not due to sex. It is
not spurious when we hold sex constant. Spurious means that there is a statistical relationship, but not
a causal relationship. We know that the relationship is not spurious due to sex, but it might be spurious
due to some other variable.