Censuses may be public (and cheap) sources of information about population in barracks. Here we will show some examples related with children in barracks from Colombia and Honduras. Graphical methods, statistical tests and confidence intervals for the sex ratio are employed and explained.

1. USING CENSUS INFORMATION TO DETECT
CHILDREN IN BARRACKS
THE CASES OF COLOMBIA, HONDURAS
AND URUGUAY
Carlos Guti´errez
https://cantaaleteo.wordpress.com/
April 2013

2. Introduction
Problem
Methods
Graphical Exploration
Chi square test
Male ratio
Few data
Final remarks

3. Introduction (1)
Usually governments regard information about military as a top
secret issue. It makes difficult for citizens to have control over
their rights and their taxes. However, certain kind of information is
available through:
Politicians who use their charges to obtain data,
Organizations that make lobby before governmental
authorities,
Independent reports that arise data by means of interviews,
surveys, individual cases or...
Population censuses on line!!!!.

4. Introduction (2)
Is census’ information trustworthy? We do not know it, but
what we are sure is that it is official.
In what follows, four examples about the use of censuses to
obtain information about children in barracks are introduced.

5. The problem
It is kown that a census provides information about the whole
population of a country at a given moment.
In some cases, by means of a census it is also possible to
obtain information about the barracks’ population.
Suppose that we find in a census that there are children in
barracks.
Are they recruited or are they just the children of the military
who live with their families in or next to the barrack?

6. The method (1)
Key idea: Assuming that the distribution of children in
barracks has the same characteristics that the distribution of
children who live within their families.
In other words, we are assuming that children in barracks live
with their families.
We only conclude that this assumption is not plausible if we
find enough evidence against it.

7. The method (2)
Together with seminaries, prisons, orphanages and others, barracks
belong to collective housing.
We are going to compare people under 18 years living in Private
housing (families) vrs barracks
Source: Redatam website:
http://www.eclac.cl/redatam/

8. Graphics can be useful!
(Colombia’s census 2005)
Figure : Underaged in families (above) and barracks (below)

9. Graphical approach (2)
By comparing both plots it is clear that at barracks there are
more 17 aged children than expected if they would be family
member from Colombias’ population.
Many times such a disaggregated data is not available and it
makes harder graphical comparisons.
Furthermore, formal test can complement exploratory analysis.
Then, other techniques are required.

10. Chi-square test of goodness-of-fit
(Data from Colombia’s census 2005)
Age group Proportion in families Frequency in barracks
0 - 5 0.27 233
6 - 12 0.34 243
13 - 17 0.39 497
Total 1 973
Table : Distribution of children in families and barracks by age group
This test indicates how probable is to find the age structure of
children from barracks if they were members of a family from
the Colombian population . It compares the expected
distribution (proportion in families × total) against the
observed distribution (frequency in barracks).
In advance a 5% significance level is chosen .

11. Chi-square test (2)
If the probability is larger than 5%, then we conclude that
there is not enough evidence to consider children from the
barracks as different from those of the population who live
with their families.
If the probability is smaller than 5%, we conclude that the age
structure of children in barracks is different from the
population of children living within families. In other words, if
they were not living with their families, then they could be
recruited.
In this case we found that the probability is less than 0.01%.
Most of the free statistical software’s can carry out this test.
There are also available free on-line calculators!!!!: Look for
Chi square goodness of fit on internet.

12. Male ratio (1)
(From Hodura’s census 2001)
Children living in: Sex
Men Women
Families 1508097 1461463
Barracks 239 133
Table : Location of children controlled by sex
Some times it is possible to obtain more than one variable
from the censuses.
Here we are going to use age and sex by comparing children in
barracks and children from Honduras’ families.

13. Male ratio (2)
’Male ratio’ or ’Sex ratio’ is a measurement that summarizes
the most important.
Male ratio = number of men
number of women
Note also that if the number of women and men were the
same, the male ratio would be 1.
The male ratio of Honduras’ families members under 18 years
is 1508097
1461463 = 1.03, which means that there are 3% more men
than women in this age group.
The male ratio of Honduras’ population under 18 years at
barracks is 239
133 = 1.8, in words, there are 80% more men than
women.

14. Confidence interval for the male ratio (1)
Here the results are obvious. Even when it seems that there
are no doubts it is recommendable to report confidence
intervals for the male ratio of children in barracks.
If the confidence interval of the male ratio of children in
barracks contains the male ratio of the population (≈ 1), we
conclude that there is not enough evidence to claim that
children in barracks are different from children living with
their families in the national population.
Otherwise, our conclusion is that children in barracks cannot
be explained by children living with their families.

15. Confidence interval for the male ratio (2)
The confidence interval for the male ratio can be obtained by
using the following formula:
exp log(male ratio) ±
1.96
(women + men) × ˆp × (1 − ˆp)
Where ˆp = men
(women+men)
The expression under the square root is the standard error of
the logarithm of the male ratio.
The number 1.96 is the value of the normal distribution that
corresponds to the 0,025 X 2 = 0,05 = 5% significance level.

16. Confidence interval for the male ratio (3)
In the previous example:
exp log(1.8) ±
1.96
√
372 × 0.64 × 0.36
In this case the confidence interval for the male ratio is
between 1.45 and 2.22, which does not contain the male ratio
of the population of children in families (1.03 ≈ 1).
Despite it seems cumbersome, it can be worked out by means
of paper, pencil and a pocket calculator!!!

17. Small data methods
Uruguay 2011
Age Women Men
0 0 1
1 0 1
5 1 0
11 0 1
13 0 1
15 0 1
Total 1 5
Table : Distribution of underage men and women at barracks in Uruguay
If we calculate the male ratio, it yields 5.
Until now the techniques that has been employed depend on large
data approximations to be reliable. What can we do if there are
few data?

18. Small data methods (2)
Here we are going to estimate the confidence intervals for the male
ratio in two steps
First, we assume that there are even men and women in the
population. We calculate the confidence interval of the
observed data by means by a procedure that performs well
with small datasets:’The Wilson confidence interval for one
proportion’.
Then we estimate the confidence interval for the sex ratio
dividing the boundaries of the confidence interval of the
proportion by their complement.
Finally, we check whether this confidence interval contains 1.

19. Step 1: Confidence interval for one proportion
(Wilson,1927)
midpoint = ˆp +
1.962
2 × n
÷ 1 +
1.962
n
se =
ˆp × (1 − ˆp) +
1.962
4 × n
n
÷ 1 +
1.962
n
The confidence interval are given by midpoint ± 1.96*se.
In our example: n=6 and ˆp = 5
5+1 = 0.83
By replacing those figures in the formules above we get a 95%
confidence interval from 0.44 to 0.97 for the proportion of male
children in barracks.
If there were even men and women in the population, then the
proportion of men would be 0.5 or 50%. As the confidence interval
covers 0.5, we hold the hypothesis that underage men in barracks
come from families population.

20. Step 2: Confidence interval for the male ratio
Now we can obtain the confidence interval for the male ratio by
dividing the boundaries of the confidence interval for the
proportion by their complement.
95%CImale ratio
ˆplow
1 − ˆplow
;
ˆpupper
1 − ˆpupper
In our example:
95%CImale ratio
0.44
1 − 0.44
;
0.97
1 − 0.97
95%CImale ratio [0.79; 32.3]
Which contains 1. Despite the male ratio was 5, there is no
evidence in the direction of recruitment.

21. The more information, the better!!!
Barracks
from:
17 years
old
Women at
barracks
Mothers from
12 to 49
Seventeen agers
Mothers
Colombia 342 1873 468 342
468=0.73
Boyac´a 53 16 5 53
5 =10.6
Boyac´a-
Sogamoso-
Rural zone
48 0 0 48
0 = ???
The table above shows different variables from Sogamoso, a
town in the province of Boyac´a, Colombia (2005).
Data about number of children that were 17 years old, number
of women, number of mothers, detailed by country, province,
town and rural zone provides a lot of meaningful information.
Seventeen year old children in barracks of the rural zone of
Sogamosos cannot be assigned to families.

22. Final remarks
Censuses can be public (and cheap) sources of information
about population in barracks.
They can support individual legal cases of recruitment of
children and neutralize the argument of isolated cases that
authorities like to use.
To check which kind of information is available one can
consult the questionnaires (most are posted on internet).
Not always data about barracks is available.
No census contains information about children in
non-governmental armed groups. Then other sourcers are
nedeed. However, if data is collected, most of the previous
approaches can be applied.

23. Thanks for your time
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