Statistics Exam
Bachelor of Public Health Science
Jørgen Holm Petersen
Jolene Masters Pedersen
December 2006
Statistics Exam
FSV-Statistics
Introduction
The purpose of the exam is to analyze the association between the social class of the
parents during the child’s childhood and subsequent unemployment by the grown-up
child, taking into consideration possible confounders and effect modifiers. Particular
interest is in understanding the dependence of unemployment on continuously measured
intelligence. This will be accomplished by the use of two different statistical methods,
Mantel Haenszel and multiple logistic regression.
The Data
The data material contains information about a segment of a much larger investigation of
school pupils in 1968. The data was collected by interviewing the same individuals over
almost a 25 year period. The analysis will include the dependant binary variable
unemployment, the primary independent variable social class of the family, and the
secondary variables, sex, intelligence test scores, education, self rated health, education
of parents, type of residence during childhood, and number of serious illnesses.
Descriptive Statistics
The study contains 3151 people. The study population is composed of 70.6% people who
have been unemployed for less than one year, and 29.4% who were unemployed for a
year or more. As illustrated in figure 1, social class I (the highest social class) contains
only 4.6 %( 145) of the study population, and social class V (the lowest social class) has
19.9 %( 628) of the population. The largest percent of people belong to social class III,
37.4% (1179).
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50,0%
Percent
40,0%
30,0%
20,0%
10,0%
0,0%
soc.gr. i
soc.gr. ii
soc.gr. iii
soc.gr. iv
soc.gr. v
Social class of parents
Figure 1: Social Class of Parents
50.4% (1588) of participants were boys and 49.6% (1563) girls, making the population
almost equally distributed among the sexes. A majority of the population, 76.8% never
suffered a serious illness, and19.0% have suffered one serious illness, and only 4.2%
suffered two serious illnesses.. Most of the study participants reported being very content
with their health 70.3%, 22.4% were content, 4.3% were not content, and 3.0 % were
very discontent. Table one shows the participants intelligence test scores. 11.4% (359) of
the people scored -25 on the intelligence test making them the lowest scorers. The highest
scorers on the intelligence test, scoring 41+, made up 32.6% (1027) of the study
population.
Intelligence
-25
26-30
Percent (frequency)
11.4% (359)
13.0% (410)
31-35
36-40
41+
20.2% (635)
22.8%(720)
32.6% (1027)
Table 1: Intelligence Test Scores
Use descriptive statistics specifically for continous variables, e.g. Mean and standard deviation, histograms or
Box-plots.
Both parents and the children reported their level of education. Figure 2 shows the
educational level of the participants. A majority of the people were educated as
craftsmen38.8% (1222), only 6.5% (204) had a long education , and 19.7%(526) had no
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education.
50,0%
Percent
40,0%
30,0%
20,0%
10,0%
0,0%
Long Education
Medium long
education
Short education
crafts man etc.
No education
Education
Figure 2: Education levels of the Participants
Percent
50,0%
40,0%
30,0%
20,0%
10,0%
0,0%
Long education
Medium
education
crafts man
short education
very short
education
No education
Parents Education
Figure 3: Educational level of the Parents
Figure three depicts the educational levels of the parents. The largest percent of the
parents, 41.5% (1089) were crafts men. Many had no education 31.6% (996) and only
6.0% (156) reported a long education.
The number of missing persons in most of the data are around 15% making the number of
people included in the final analysis smaller then if their were no missing people but
there is still a large number of participants remaining
The purpose of the descriptive section is to get an idea of who the studied individuals
are.
Association between Social Class of the Parents during
Childhood and Subsequent Unemployment
Table 2 illustrates the association between the social class of the parents during the
subject’s childhood and subsequent unemployment. In each social class there are more
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people that have been unemployed for <1 yr., than for ≥1 year. Social class V, the lowest
social class, had the largest percentage (35.6%) of persons unemployed for ≥1 year.
Social group I, the highest social group, had the second highest percentage of
unemployment at 29.5%, but it should be considered that there were very few people in
this social class (145). In general, it seems the tendency is for the lower the social class
the higher the level of unemployment. The significant p value is 0.004. This points to an
association between social class of the parents and subsequent unemployment. The null
hypothesis for the chi squared test is that the effect of interest is zero. This should be
rejected if the p-value is significant. The gamma value is also highly significant
(p=0.002), pointing to an ordinal association in the data. The null hypothesis for gamma
is the same as for chi-squared, that the effect of interest is zero.
Social Class of parents
soc.cl.I
soc.cl.II
Soc.cl.III
Soc.cl.IV
Soc.cl.V
Total
Unemployed <1 yr.
Percent (frequency)
Unemployed ≥1yr.
Percent (frequency)
70.5% (86)
75.7% (193)
72.7% (748)
72.3% (420)
64.4% (331)
71.1% (1778)
29.5% (36)
24.3% (62)
27.3% (281)
27.7% (161)
35.6% (183)
28.9% (723)
Table 2: Association between Social Class of Parents and Unemployment
χ2= 15.538 df(4) p=0.004, , γ=0.103 p=0.002
Note in the above table that a simpler (and better) would exclude the “Unemployed <1 yr”
column as it is redundant. It is desirable to have a table text (or a figure text) contain
also a short description of what is seen. For example:
Table 2: Association between Social Class of Parents and Unemployment. A non-monotone
relationship is seen with social class I and V having higher prevalences of unemployment than the
three other classes. The association between social class and unemployment is statistically
2
significant. (χ = 15.538 df(4) p=0.004, , γ=0.103 p=0.002).
Mantel Haenszel
Recoding
In order to conduct a Mantel Haenszel analysis it is necessary to recode social class of the
parents (the primary independent variable) into a binary variable. To decide the best way
to recode, the homogeneity within the strata of different combinations of variables were
tested by conducting a stratified analysis and using the χ2 test. The variable social class of
the parents was recoded into social classes I-IV and social class V because social classes
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I-IV have around the same risk of being unemployed but that risk sharply increases in
social class V. The χ2 test was insignificant for social classes I-IV (p=0.686) and the null
hypothesis (that the effect of interest is zero) was accepted.
Table 3 illustrates the association between the recoded variable social class of the parents
and subsequent unemployment.
Unemployed <1 yr.
Unemployed ≥1yr.
Total
Percent (frequency)
Percent (frequency)
72.8% (1447)
27.2% (540)
100%(1987)
Soc. class I-IV
64.4% (331)
35.6% (183)
100% (514)
Soc. class V
71.1% (1778)
28.9% (723)
100% (2501)
Total
Table 3: Association between social class of the parents recoded and subsequent unemployment
Social Class of Parents
χ2=14.109, df=1 p=<0.001, OR=1.481 (1.206-1.820)
There is a significant difference between the unemployment rates in social classes’ I-IV
and social class V. As you can see in Table 3, 27.2% (540) of people in social classes IIV were unemployed for one year or more and 35.6%(183) in social class V were
unemployed for one year or more. The significant p-value is <0.001, which indicates that
the null hypothesis (that the effect of interest is zero) should be rejected. Therefore, there
seems to be an association between the social class of the parents and subsequent
unemployment. The odds ratio is 1.481 (1.206-1.820) which means that the risk of
unemployment for one or more years is 48% higher for the people in social class V than
the people in social classes I-IV.
Using the above mentioned method of testing how to recode variables, parents education
was recoded into three variables, long-medium education (χ2=0.009(1),p=0,923), craft,
short or very short education (χ2=1.731(2),p=0,42) and no education. Self rated health
was also recoded into three variables from the original five. The variables are very
content, content and not content-very discontent.
Confounding
According to epidemiological principles a variable should be chosen as a confounder if it
is a variable associated with both the outcome and the exposure but does not fall on the
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casual pathway between the associations. In this particular case, in order to check for
confounding first we must explore the relation between the secondary variables (sex,
intelligence test, educational level, self rated health, educational levels of parents, type of
residence during childhood, and number of serious illnesses) and the dependant variable
subsequent unemployment. Then we must do the same for the secondary variables (sex,
intelligence test, educational level, self rated health, educational levels of parents, type of
residence during childhood, and number of serious illnesses) and the primary independent
variable social class of the parents. We test for possible associations by using the chisquared test.
Unemployed
<1 yr.
Percent(freq)
73.7%(1381)
66.8%(399)
52.1%(101)
Unemployed
≥1yr.
Percent(freq)
26.3%(493)
33.2%(198)
47.9%(93)
χ2-value
44.818
v. content
content
not contentv.discontent
64.5% (178)
35.5% (98)
26.837
Intelligence -25
62.7%(215)
37.3%(128)
26-30
69.3% (382)
30.7%(169)
31-35
71.7% (441)
28.3%(174)
36-40
75.6%(667)
24.4%(215)
41+
75.9
%
(390)
24.1%(124)
9.742
Residence
Copenhagen
68.1% (584)
31.9%(274)
in
mid. city
72.0%(157)
28.0%(61)
Childhood
sm. city
71.6%(633)
28.4%(251)
rural
74.0%(151)
26.0%(53)
102.412
Education
Long
81.9%(289)
18.1%(64)
Medium
77.4%(281)
22.6%(82)
Short
71.9%(879)
28.1%(343)
Craftsman
53.9%(283)
46.1%(242)
None
70.1%( 169)
29.9% (72)
5.290
Parent
Long/med.
26.8%(309)
Education
Craft, short, 73.2%(844)
v.short
68.6%(591)
31.4%(271)
None
73.3%(1502)
26.7%(547)
33,913
Serious
0
63.0%(318)
37.0%(187)
Illnesses
1
55.4%(62)
44.6%(50)
2
74.4(974)
25.6%(335)
17.926
Sex
Boy
66.9%(909)
33.1%(449)
Girl
Table 4: Association between secondary variables and Unemployment
Self
Reported
Health
DF
P-Value
2
<0.001
4
<0.001
3
0.021
4
<0.001
2
0.071
2
<0.001
1
<0.001
Table 4 explores if the secondary variables are associated with the dependant variable
unemployment. As you can see, the parents education is not significant (p= 0.071) so it
will not be considered as a confounder. On the other hand, self reported health,
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intelligence, residence in childhood education, sex, and serious illness all have significant
p values which means that the null hypothesis, that the effect of interest is zero can be
rejected. These variables are all associated with unemployment. More specifically, more
girls (33.1%, 449) have been unemployed for one year or more than boys (25.6%, 335).
The more content people are with their health the less likely they are to be unemployed
for one year or more. For example, persons who are very content are unemployed for one
year or more 26.3% (493), where as people who are not content or very discontent have
been unemployed for a year or more 47.9%(93). There is a tendency for the people who
scored higher on the intelligence test to have less incidence of unemployment for 1 or
more years than people who scored lower on the intelligence test. The people who grew
up in Copenhagen have the lowest rate of unemployment for one or more years (24.1%).
The people with no education have the highest percentage of unemployed people for a
year or more (46.1%) and people with a medium length education have the lowest
percentage (18.1%).
Self
Reported
Health
Intelligence
Residence
in
Childhood
Education
Parent
Education
Serious
Illness
Sex
v. content
content
not contentv.discontent
-25
26-30
31-35
36-40
41+
Copenhagen
mid. city
sm. city
rural
Long
Medium
Short
Craftsman
None
Long/med.
Craft, short,
v. short
None
0
1
2
Boy
Girl
Social
Classes I-IV
Percent(freq)
80.9%(1426
78.9%(440)
67.4%(122)
)
68.6%(194)
70.6%(271)
76.0%(457)
77.6%(536)
87.0%(853)
85.9%(544)
80.8%(800)
76.1%(191)
72.4%(716)
94.4%(185)
91.5%(311)
86.3%(289)
77.7%(896)
64.3% (308)
99.6%(267)
90.3%(1140)
Social
ClassV
Percent(freq)
19.1%(336)
21.1%(118)
32.6%(59)
χ2-value
DF
P-Value
18.600
2
<0.001
31.4%(89)
29.4%(113)
24.0%(144)
22.4%(155)
13.0%(127)
14.1%(89)
19.2%(190)
23.9%(60)
27.6%(273)
5.6%(11)
8.5%(29)
13.7%(46)
22.3%(257)
35.7% (171)
0.4%(1)
9.7%(123)
76.070
4
<0.001
46.746
3
<0.001
135.957
4
<0.001
398.989
2
<0.001
58.8%(547)
81.2% (1559)
73.2%(350)
75.2%(79)
78.6%(1167)
78.6%(1144)
41.2%(383)
18.8%(360)
26.8% (128)
24.8%(260)
21.4%(317)
21.4%(311)
16.268
2
<0.001
0.000
1
0.993
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Table 5: Association between secondary variables and Social class of parents.
Table 5 explores if the same secondary variables are associated with the primary
independent variable social class of the parents. Sex is not associated with the social class
of the parents p=0.993 (obviously) so it must be ruled out as a confounder. The other
variables have highly significant p values of <0.001. There appears to be a tendency for
people in Social class V (32.6%) to be not content or very discontent with their health
compared with the people from Social classes I-IV (67,4%). There is a tendency for
people with lower intelligence score to be part of social class V compared with the people
with higher intelligence test scores. Of the people with a score of -25 on the test, 31.4%
are part of social class V and of the people with the highest score of 45+, only 13.0%
belong to social class V.
The secondary variables: self reported health, residence in childhood, intelligence,
serious illness and education are all possible confounders because they are associated
with both unemployment and the social class of parents in childhood and they do not fall
on the casual pathway. Therefore, they must be included in the analysis if the relation
between the dependent variable unemployment and the primary independent variable
social class of the parents is to be properly understood.
Mantel Haenszel Analysis
Now the Mantel Haenszel analysis will test the effect of each possible confounder. The
Mantel-Haenszel method is used to control for confounding. The Mantel Haenszel
statistic tests the null hypothesis that the strata are conditional independent. When the
Mantel Haenszel value is insignificant the variable being controlled for is conditional
independent. The Breslow day statistic tests if the odds ratios are the same throughout the
strata, in other words it tests the homogeneity of the odds ratios. The null hypothesis for
the Breslow Day test is that the odds ratios are homogeneous in different strata.
Therefore, if the Breslow Day statistic is insignificant the difference in the different strata
is so small you can calculate the Mantel- Haenszel common odds ratio. If the Breslow
Day test is significant you should stop the analysis there because the strata are most likely
very different and have effect modification.
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Effect Modification
An effect modificator is a variable that modifies the size or the direction of exposure
outcomes on the effect. When you have effect modification the association between
exposure and outcome is different in the different categories of the effect modificator.
They are tested for by using Breslow Day and logistical regression analysis. To check for
effect modification one should stratify and then check the odds ratio for a correlation.
The odds ratio should be closely examined for patterns of odds ratios across the different
strata (how different they look, any trends). If there is effect modification there will be
substantial differences in the association between strata.
Self-rated
Health
v. content
content
notcontentv.discontent
Intelligence
-25
26-30
31-35
36-40
41+
Childhood
Residence
Copenhagen
mid. City
sm. city
rural
Education
Long
Medium
Short
Craftsman
None
Parents
Social Class
Unemployed
<1 yr.
Unemployed
≥1yr.
I-IV
V
I-IV
V
I-IV
V
75.7%
67.6%
68.9%
63.6%
53.3%
47.5%
24.3%
32.4%
31.1%
36.4%
46.7%
52.5%
I-IV
V
I-IV
V
I-IV
V
I-IV
V
I-IV
V
68.4%
58.0%
63.6
62.8
70.7
66.1
73.8
63.6
77.1
68.8
31.6%
42.0%
36.4
37.2
29.3
33.9
26.2
36.4
22.9
31.3
I-IV
V
I-IV
V
I-IV
V
I-IV
V
74.7
81.8
71.3
54.5
74.2
62.0
73.4
66.8
25.3
18.2
28.7
45.5
25.8
38.0
26.6
33.2
I-IV
V
I-IV
V
I-IV
V
I-IV
V
I-IV
V
75.7
72.7
82.0
86.2
79.2
69.6
73.3
68.1
54.4
53.2
24.3
27.3
18.0
13.8
20.8
30.4
26.7
31.9
45.6
46.8
Jolene Lee Masters Pedersen
Breslow Day
(df)
0.755 (2)
Mantel
Haenszel
0.001
MH Odds
Ratio (c.i.)
1.409 (1.1441.736)
0.658 (4)
0.003
1.379 (1.1201.699)
0.018 (3)
<0.001
1.487 (1.2041.837)
0.665 (4)
0.112
1.198 (0.9661.485)
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0.199(2)
0.001
1.418 (1.153I-IV
75.6%(1178)
24.4%(380)
1.745)
V
66.7%(240)
33.3%(120)
I-IV
63.3%(221)
36.7%(128)
1
V
62.5%(80)
37.5%(48)
I-IV
59.5%(47)
40.5%(32)
2
V
42.3%(11)
57.7%(15)
Table 6: Mantel Haenszel Test of the secondary confounders, self rated health, intelligence, childhood residence,
education and serious illness.
Serious
Illness
0
In table 6, you can see that childhood residence is an effect modificator because it has a
Breslow Day test of (p=0.018). Therefore, childhood residence can not be considered a
confounder. The effect of family social class is different in the various residences (small,
medium, etc.)The M.H. and common odds ratios can not be commented on because it is
heterogeneous.
Table 6 shows that the Mantel Haenszel test is significant for self rated health,
intelligence, education, and serious illness. This means that there is still an association
between the social class of the parents and subsequent unemployment even when we
have controlled for each confounder individually except when we control for education.
As you can see, the Mantel Haenszel value for education is 0.112. This means that the
association between unemployment and social class can be explained by education. When
we control for education, parent social class and unemployment become independent.
The Mantel Haenszel common odds ratio shows the risk of unemployment based on the
parent’s social class during childhood when each confounder is controlled for. Take self
rated health for example, the Mantel Haenszel common odds ratio tell us that if you are in
social class V you have a 41% greater risk of unemployment than people in social classes
I-IV, when you control for self rated health.
To test the size of the effect of confounding, compare the original odds ratio (from table
4, 1.481 (1.206-1.820)) with the Mantel Haenszel common odds ratio from each strata.
OR  M .H .commonOR
*100
OR
Equation 1:
Using equation one, the effect for the confounder self rated health is -0.61% which means
that controlling for self rated health makes the association between unemployment and
the parents social class only -0.61% stronger. This is a very small difference. The effect
of the confounder intelligence is 6.89%, which means that intelligence explains 6.89% of
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the association between unemployment and the parent’s social class. The effect of the
confounder serious illness is 4.25% which means that serious illness explains 4.25% of
the association between unemployment and the parent’s social class. As you can see in
Table 7 the confidence intervals shown in conjunction with the Mantel Haenszel common
odds ratios are quite broad, and the true value of the common odds ratio falls anywhere
between the two values in the confidence interval. Take serious illness for example,
Common OR=1.418 (1.153-1.745). The confidence interval is very broad and the true
value could be anywhere in between 1.153 – 1.745. A possible reason for the broadness is
that there are relatively few people in some of the strata.
Logistic Regression Analysis
From logistical regression we can determine which explanatory variables influence the
outcome as well as evaluate the probability of a particular outcome. The dependant
variable can only be binary and the independent variables can be of any kind. Logistic
regression gives us information from the estimated logistic regression coefficient,
estimated odds ratio with the 95% confidence interval and the Wald test statistic with an
associated p-value. The Wald Test statistic tests the null hypothesis that the relevant
logistic regression coefficient (beta) is equal to zero. The higher the Wald test (it depends
on the degrees of freedom), the more significant the p-value will be , because a high
Wald Test means that the SE is low compared to the difference between the two Beta
parameters. The overall Wald test is a weight, an average of the Wald tests in between
categories. The information from the logistical regression analysis is used to determine
whether each variable is related to the outcome and to quantify how much this is so.
Model seeking
In order to test the connection between the various explaining variables and
unemployment, backwards model seeking was preformed. It’s important to keep
in mind the hierarchical principle that one must not remove variables if there was still a
remaining interaction with that variable. First the model included each variable and
combination of variables: [sex, social class, intelligence, education, self rated health,
parents education, childhood residence, serious illness, sex*social class, sex*intelligence,
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sex*education, sex*self health, sex*parent education, sex*childhood residence,
sex*serious illness, social class*intelligence, social class*education, social class*self
health, social class*parents education, social class*childhood residence, social
class*serious illness, intelligence*education, intelligence*self health, intelligence*parent
education, intelligence*childhood residence, intelligence*serious illness, education*self
health, education*parents education, education*childhood residence, education*serious
illness, self health*parent education, self health*childhood residence, self health*serious
illness, parent education*childhood residence, parent education*serious illness, childhood
residence*serious illness] .The least significant variable was removed and the logistical
regression analysis was preformed again, repeating the process until only significant
interactions and variables remained. The order in which the variables were excluded and
their corresponding p-values are depicted in table 7.
Variable
1.family social class*family education
2.family education*child residence
3. family social class*sex
4.sex*serious illness
5.family social class*self rated health
6.serious illness*intelligence
7.self reported health*child residence
8.family education*sex
9.self rated health*serious illness
10.family social class*intelligence
11.sex*child residence
12.self rated health*intelligence
13.family social class*education
14.family education*intelligence
15.family education*self rated health
16.child residence*intelligence
p-value
0.943
0.852
0.779
0.668
0.653
0.590
0.538
0.480
0.432
0.437
0.449
0.409
0.348
0.229
0.417
0.304
Variable
17. education* child residence
18.self rated health*education
19.education*intelligence
20.serious illness*education
21.serious illness*child residence
22.family social class*child residence
23.family social class*serious illness
24.family social class
25.family education*serious illness
26.family education*education
27.family education
28.self rated health*sex
29.sex*intelligence
30.sex*education
31.intelligence
p-value
0.308
0.248
0.330
0.372
0.243
0.220
0.158
0.725
0.154
0.197
0.244
0.492
0.395
0.189
0.172
Table 7: Order in which variables were removed from logistic regression model
Before presenting the final logistic regression model it should be explained that the
variable intelligence coded into five categories was included in the model opposed to the
linear variable intelligence. An original model seeking was performed with the linear
variable and it was found that intelligence is not linear. This was found by including
different combinations of intelligence variables (one at a time) and seeing which p-value
was the highest compared with the linear value. The p-values follow: intelligence linear
(0.500) intelligence squared (0.892); intelligence linear (0.547) intelligence cubed
(0.547); Intelligence in 5 categories(0.053, intelligence linear (0.598); only linear (0.057)
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only intelligence in 5 categories (0.008). As you can see, intelligence in 5 categories was
the most significant of all the variables and combinations of variables tested. Therefore
the logistic regression analysis was made again including intelligence in five categories
as a variable and leaving the linear variable out.
The section on linearity is confusing. Testing whether the effect of intelligence is linear
can be done in two ways. Either by including also higher order terms, e.g. intelligence
squared, followed by testing whether the higher order term is statistically significant. One
does not involve the p-value for the linear term in a model that includes also intelligence
squared. In the second approach, the linear term is included as well as a categorical
version of intelligence. Again, only the p-value for one of the two – here the categorical
version – is relevant.
Equation 2 shows the final logistic regression model that was chosen.
0.686 0.146 x
P(unemployment | sex, education, selhealth , childresid ence, seriousill .)
sexgirl
e
 0.686 0.146 x sexgirl
1 e
 0.694 x edulo 1.294 x edume 1.070 x edush  0.748 0.209 x shc  0.555 x shnc  0.802 x shvd  0.201x crcp  0.259 x crmc  0.013x crsc  0.233x si
 0.694 x edulo 1.294 x edume 1.070 x edush  0.748 0.209 x shc  0.555 x shnc  0.802 x shvd  0.201x crcp  0.259 x crmc  0.013x crsc  0.233x si
Where:
X
assumed value is 1, if the person is a girl.
assumed value is 1, if the person had a long education.
X
edume, assumed value is 1, if the person had a medium education.
X
edush, assumed value is 1, if the person had a short education.
X
educr, assumed value is 1, if the person was educated as a craftsman.
X
shc, assumed value is 1, if the person was content with self health.
X
shnc, assumed value is 1 if the person was not content with self health.
X
shvd, assumed value is 1 if the person is very discontent with self health.
X
crcp, assumed value is 1, if the person grew up in Copenhagen.
X
crmc, the assumed value is 1, if the person grew up in a medium sized city.
X
chsc, assumed value is 1, if the person grew up in a small city.
X
si, assumed value is 1, for each serious illness.
X
sexgirl
edulo,
Equation2: Logistic Regression Equation
Sex
Boy
Girl
Education
None
Craftsman
Short
Medium
Long
Beta
Wald
P-value
OR(95% c.i.)
0
0.416
23.957
78.004
40.892
42.115
56.655
12.492
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
1
1.586(1.319-1.908)
0
-0.748
-1.070
-1.294
-0.694
Jolene Lee Masters Pedersen
1
0.473(0.376-0.595)
0.343(0.248-0.474)
0.274(0.196-0.384)
0.500(0.340-0.734)
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Statistics Exam
Self-Rated Health
Very content
Content
Not content
Very discontent
Child-residence
Rural
Small city
Medium city
Copenhagen
Serious Illnesses
0
Per illness
Constant
N
FSV-Statistics
0
0.209
0.555
0.802
0
-0.013
0.259
-0.201
0
0.233
-0.686
3151
12.040
3.150
5.998
8.125
13.668
0.005
5.675
2.321-
0.007
0.076
0.014
0.004
0.003
0.943
0.017
0.128-
5.370
0.020
1
1.233(0.978-1.553)
1.741(1.117-2.714)
2.229(1.285-3.869)
1
0.988(0.701-1.391)
1.296(1.047-1.605)
0.818(0.632-1.059)
1
1.262(1.037-1.537)
Table 8: Final Logistic Regression Model
It is imperative that social class is included in the model – it is the whole purpose of the
analysis!
Table 8 reports the final logistic regression model with the following as the reference
group; boy, no education, very content with self rated health, grew-up in rural Denmark,
and 0 serious illnesses. According to the model, sex, education, self rated health, child
residence and serious illness all have an effect on subsequent unemployment. It seems
that girls are 59% more likely than boys to have subsequent unemployment. There is a
tendency for people who are very content with their health to suffer less unemployment
compared to people who are just content (23% higher risk), not content (74% higher
risk) and very discontent (123% greater risk). People who live in medium sized cities
have 29% greater risk of being unemployed then people who live in rural areas. People
who live in Copenhagen have only 82% of the risk that people who live in rural areas of
being unemployed. Not surprisingly with each additional serious illness that a person
suffers their risk of unemployment increases by 26%.
Jolene Lee Masters Pedersen
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1,0
Upper 95% c.i.
Lower 95%c.i.
Odds Ratio
0,8
0,6
0,4
0,2
none
craftsman
short
medium
long
Education Level
Figure 4: Education Level and Risk of Unemployment
Figure 4 explores the relationship between education level and risk of subsequent
unemployment. In both the Mantel Haenszel analysis and the logistic regression model
education is an important variable that has an effect on unemployment. As you can see,
the risk of unemployment has a tendency to decrease as the amount of education
increases with the exception of a long education. A possible reason for this is that there
are relatively few people (6%) who have a long education. It could also be that people
with a long education lack social skills to work or that their education was long, but the
field provides few jobs. It could also be explained by the 95% confidence intervals
themselves. All of the confidence intervals surround 0.346-0.384. This indicates that the
true values of the numbers could be the same, and the amount of education does not make
a difference on the subsequent unemployment. It’s interesting that none of the confidence
intervals surround one. This explains that some education is better than no education at
preventing unemployment.
Discussion
There are advantages and disadvantages of using both models to analyze the data. A draw
back of using the Mantel-Haenszel is that the number of strata rapidly increases when
attempting to control for the effects of more confounding variables so it makes it
impossible to estimate stratum specific odds ratios. An increased number of strata leave a
very small number of persons in each strata causing statistical uncertainty. Another
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problem with Mantel Haenszel is that you have to dichotomize the primary variables, for
example social class of the family, which causes information to be lost. With these
considerations in mind the logistic regression gave more information. Table 6 and table 8
show that both models identify self rated health, education and serious illness as
confounders. Differences are that Mantel Haenszel identifies childhood residence as an
effect modificator and logistic regression sees it as a confounder. Mantel Haenszel rules
out sex as a possible confounder because it is not associated with social class of the
parents but the logistic regression model (which does not consider social class of the
family to be associated with subsequent unemployment) shows that it has an effect of
unemployment. Finally, Mantel Haenszel shows that intelligence is a confounder between
social class of the family and unemployment but logistic regression does not include
intelligence in the final model. Both models show that education is more important than
intelligence in explaining subsequent unemployment.
Possible Errors
Possible errors in the analysis are type I and type II errors. Type I errors are made when a
significant result is obtained, and the null hypothesis is rejected when it is in fact true.
Type I errors are usually estimated to occur 5% of the time. Type II errors occur when a
non-significant result is obtained when the null hypothesis is true. A possible type II error
in this analysis could have occurred because the Wald Test does not look at the order of
categories, therefore variables could have been taken from the logistic regression model
that should have been there.
Conclusion
This analysis used Mantel Haenszel and multiple logistic regression to explore the
association between the social class of the parents during the child’s childhood and
subsequent unemployment by the grown-up child, taking into consideration possible
confounders and effect modifiers. The Mantel Haenszel analysis identified self rated
health, intelligence, serious illness and education as confounders and childhood residence
as an effect modificator. It was also discovered that education explains the association
between social class and unemployment. The logistic regression model identifies sex,
education, self-rated health, childhood residence and serious illness as possible
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confounders. This analysis did not show that unemployment is dependent on
continuously measured intelligence, but rather that unemployment is influenced by the
above measured confounders and effect modificator and in particular education.
This is a good paper with reflections that show considerable understanding of quantitative
methods.
Include a sentence or a section with your research hypotheses, that is what you in
advance think the association between social class and unemployment will be. This
correspond to the situation you will be in when analyzing data for research purposes, and
makes it more realistic when discussing the finding relative to the prior expectations.
There are some shortcomings.
An important use of the descriptive statistics section is to be able to discuss to what
extent the later results can be generalized. It would have improved the paper if it had had
a table of descriptive statistics for all relevant variables (i.e. not including the response:
unemployment).
The primary variables of interest – here social class and intelligence – should always be
included in the final model irrespective of whether they are statistically significant or not.
The results of the different analyses should be compared and its should be made clear
how different conclusions can be reached depending on which variables that are
controlled for.
Grade: 7 (12 point scale)
Jolene Lee Masters Pedersen
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