NATIONAL EMPLOYMENT SURVEY
SAMPLE DESIGN
TECHINICAL SUBDIRECTORATE
RESEARCH AND DEVELOPMENT DEPARTMENT
SEPTEMBER 2006
TABLE OF CONTENTS
Pages
1
2
3
4
5
6
7
8
9
10
11
11.1
12
13
14
14.1
14.2
15
16
16.1
16.2
17
Introduction
3
Goals of the survey
4
Target population
4
Sample frame and stratification
4
Estimate levels
6
Sample and analysis units
6
Sample size
6
Average size of dwellings by sections
8
Selection of sampling units
9
Sample distribution
9
Dwellings rotation in the sample
10
Estimation method: factors of expansion
10
Construction of the factor of expansion
11
Total standard estimator
12
Ratio estimator separate from total
13
Variance estimators
14
Estimator of the variance for a total
14
Estimator of the variance for Unemployment Rate
14
Estimator of the standard estimator's variances (not adjusted by population) 15
Sampling error
15
Absolute error of an estimator at 95% confidence
15
Relative error of an estimator at 95% confidence
15
Confidence interval at 95%
15
APPENDICES
APPENDIX 1: Sample by estimate areas and relative error for unemployed
(Base: Oct-Dec 2003)
APPENDIX 2: Procedure for the selection of first- and second-phase units
APPENDIX 3: Areas with difficult access (ADAs), deducted from sample
APPENDIX 4: Comparison between current estimate levels and levels in the
new proposal
APPENDIX 6: Large or big cities
a) Greater Santiago area
b) Greater Valparaíso area
c) Greater Concepción area
d Greater Temuco area
e Greater La Serena area
APPENDIX 7: Estimators of Totals, Ratios, Rates and Variances.
Procedures for calculating estimators used in the National
Employment Survey
BIBLIOGRAPHY
16
16
19
19
21
24
24
25
25
25
25
25
25
29
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NATIONAL STATISTICS INSTITUTE
Introduction
In general terms, the sample selection design for the National Employment Survey
(ENE in Spanish) 2006 is similar to the one used in 19961, that is, a two-stage
probability selection method with geographic stratification by region and urban-rural
area. The estimators associated to the design are not self-weighted and are corrected
by an exogenous forecast of the population, computed using demographic methods
according to the National Statistics Institute (INE) and the Latin American and
Caribbean Demographic Centre (CELADE). Substantially, the new design is identical to
the one in effect. In this sense, the differences are more related to allowing the
measurement of more labour market phenomena than the design in force up to 2005,
as we will show further down this document.
Among the relevant differences, the update of the sample framework SIEH (Spanish
for acronym for Integrated Household Surveys System) with data from the latest
Household and Population Census, carried out in 2002, stands out.
1
National Statistics Institute (1996), NATIONAL EMPLOYMENT SURVEY METHODOLOGY
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1
Goals of the survey
The survey aims to depict Chilean population above 15-year old, laying special
emphasis on the Labour Force. This characterization encompasses several profiles,
including: gender, age, occupation group, activity branch, occupation category,
and education level.
The sample is representative at national level (urban-rural); regional (urbanrural); large urban centres (cities with more than 40,000 habitants); and rest of
urban area.
The sample design takes into account the difference between circumstantial and
structural phenomena in the labour market. Similarly, this was included in the
creation of the new master framework for the SIDEH, with permanent update
being one of its most important improvements.
2
Target population
The target population of the sample for the National Employment Survey - or ENE
- is made up of all the habitants of the country living in occupied private
dwellings. This definition excludes all people living in collective dwellings such as
hospitals, jails, convents, quarters and others, but includes people residing in
private dwellings inside such facilities, such as doorkeepers, janitors and other.
Also, people living in areas of difficult access, known as ADAs, fall outside the
geographic scope.
3
Sample frame and stratification
a)
Sample frame
Given the characteristics of the areas frame, the sample frame development was
based on mapping and base material from the 2001 Pre-census and the 2002
Household and Population Census, made up of region, province, municipality and
district maps including boundaries of urban and rural areas as well as demarcation
of ADAs.
Each and every one of the elements making up the frame has a known, non-zero
probability of being selected.
Structure of the strata in the sample frame: In accordance with geographical
features of the sample frame by areas, the strata to be considered according to
Political-Administrative Division (DPA) are communes, and within them, urban and
rural areas. The frame does not consider difficult access areas (ADA).
Exclusion areas (ADAs): Difficult access areas (ADA) are those that because of
weather conditions, topographic aspects or lack of clear roads or transport (see
Appendix 4) remain isolated during part or the whole year.
Sample frame division into clusters or sections: Considering the
characteristics of the area framework, the construction of the new sample frame
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NATIONAL STATISTICS INSTITUTE
was based on national mapping material, made up of region and municipal maps,
including demarcation of urban and rural areas, and ADA’s.
With this background, a division of the national territory into strata and
geographic areas or clusters, called sections, was undertaken.
Sections were made up considering the population volume and number of
dwellings. The size of each section varies among the different strata making up
the country's provinces or regions.
Table No. 1: Section average size by stratum
Average size of
Stratum
dwellings by section
City
100 - 200 dwellings
Rest of the urban
80 -150 dwellings
area (RUA)
Rural
60 -80 dwellings
For the construction of the sections, stability over time, easy identification on field
(respecting district boundaries both in urban and rural sections), homogeneity 2
and compactness3 were also taken into account.
Coverage or scope: The sample frame for SIEH 2003 used a national geographic
scope taking into account the entire continental territory of Chile, excluding ADAs.
ADAs are determined at a stage prior to the development of the sample frame and
account for 0.53% of occupied private dwellings in the national territory.
b)
Stratification of the master sample frame for ENE:
The master sample frame is divided into communes or municipalities, but for
comparison purposes, this segmentation as attuned with ENE current strata,
adding those resulting from the division of such municipalities. The result was a
total of 158 strata by geographic condition (political-administrative division),
number of dwellings and population contained in the 2002 Housing and Population
Census, according to the following definitions:
Cities or large urban centres (CD): Made up of cities or groups of adjacent
cities with 40,000 or more inhabitants.
Rest of urban area (RUA): Group of dwellings with less than 40,000 habitants
and more than 2,000 inhabitants, or between 1,001 and 2,000 with 50% or more
of the economically active population engaged in secondary or tertiary activities.
Urban areas (R): Group of dwellings, concentrated or scattered, with 1,000 or
fewer inhabitants, or between 1,000 and 2,000 people, with less than 50% of the
economically active population engaged in secondary or tertiary activities.
2
3
Classification of the section within the stratum regarding the Unemployed, by error ρ .
Referring to similarity of sections within a stratum in relation to estimates and errors.
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NATIONAL STATISTICS INSTITUTE
4
Estimate levels
Disaggregation of estimate levels throughout the country is shown bellow:
NATIONAL: Urban areas, large cities and rest of urban areas; Rural.
REGIONAL: Urban and rural.
PROVINCES AND LARGE CITIES (40,000 inhabitants or more).
5
Sample and analysis units
First-phase units are the sections for well-defined geographic clusters or sections
containing approximately 60-200 dwellings each, depending on the strata
selection.
Second-phase units are private dwellings found in each section (first-phase
units). At the same time, the units of analysis are all people making up a
household at selected occupied private dwellings.
6
Sample size
The sample size was determined based on total dwellings, in order to make it
compatible with finding a small-scale sample error for the total estimate of
unemployed, of about 2% as relative error, at a confidence interval of 95%.
The formula used to define the size, in number of sections, corresponds to a
simple random sample adjusted to the design effect (DEFF).
2
⎛ z 0,95 ⎞ S h ⋅ M h
nh = ⎜⎜⎝ ea ⎟⎟⎠ mh ⋅ Deff h
2
Number of sections in the sample in stratum h:
2
158
Resulting on a total size of:
n = ∑ n h = 3,558 sec tions
h =1
Where:
n
e
h
ah
S
4
2
h
: Number of sections by stratum
: Absolute error of the total of Unemployed by stratum h
: Value of quasi-variance estimated by stratum
Mh
: Number of dwellings contained in stratum h as of the 2002 census
Deffh
:
Refers to the “design effect” in stratum h, computed as the quotient
between a standard estimator variance given the design in phases and
the same estimator given a dwellings simple random sample4.
Details of this calculation are provided in Appendix 8 of this document or in INE's Methodology Department
report titled “Cálculo del efecto del diseño en la muestra nacional del empleo en el trimestre Octubre-
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NATIONAL STATISTICS INSTITUTE
The absolute error was computed based in the total number of unemployed people
in each stratum, data obtained and processed from the employment survey
carried out in Oct-Dec 2003. This value was considered fixed in order to define
the resulting sample size at a later stage and therefore to maintain the original
sample errors to guarantee accuracy from a 2% coefficient of variation at national
level.
For sampling allocation at different strata, besides sampling errors5 pyramid
structure, other relative factors from each stratum were taken into account, such
as:
1.
Unemployment rate by stratum
2.
Coefficient of variation
3.
Update and interviewing costs
4.
Population variance, in order to define and analyse margins of error for
different strata and be able to choose an appropriate sample size.
According to design phases, the sample size is disaggregated as follows:
•
First phase units: 3,558 sections
•
Second phase units: 34,511 private dwellings
Table 2 shows the sample sizes at national and regional level by rural urban area.
It should also be noted that in some areas of estimation the relative error is very
high due to a low unemployment rate (for example, in the rural area of region IX).
To narrow error in these cases, with very small rates, it would be necessary to
expand the sample into prohibitive levels6.
5
6
Noviembre –Diciembre 2003” (Calculating the design effect on the national employment sample for
October, November and December 2003).
That is to say, the error is higher as it disaggregates from the structure: National, Urban, Rural; Regional,
Urban, Rural; Communal (Municipalities) and Large Centres, and strata.
In estimate levels with low unemployment rates, it is not necessary to know them exactly. In this case, the
order of magnitude suggested by the estimate and confidence interval is enough to conclude that
unemployment at these levels is not a significant problem compared to other levels where it is urgent to
know if the rate falls from one or two points with appropriate public policies.
B uena
R e g u la r
A c e p ta b le
M a la
B
R
A
M
M e n o r o ig u a l q u e :
E n tre :
E n tre :
M a y o r o ig u a l q u e :
RANGO %
d e E r r o r R e la tiv o a l
95%
10
11
30
31
50
51
c o e fic ie n te d e
v a r ia c ió n
5 ,1
5 ,6
1 5 ,3
1 5 ,8
2 5 ,5
2 6 ,0
-
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NATIONAL STATISTICS INSTITUTE
7
Average size of dwellings by sections
The average size of dwellings by sections at each stratum was defined taking into
account the minimization problem of total unemployment variance, using a cost
function where travel expenses among units are of little importance. Assuming a
fixed number of sections by stratum, the formula is:
mh _ óptimo =
S
S −S
w
2
b
C1 C 2
2
w
Mh
Where:
C = C1 ⋅ n + C 2 ⋅ n ⋅ m .
C: Cost function of surveying in stratum h
c ⋅ n : Proportionate to the number of sample primary units
1
c
⋅ n ⋅ m : Proportionate to total number of second phase units
2
nh
S
2
=
b
∑m
i =1
hi
(Y
n
S
2
w
=
i =1 j =1
n
hij
− Yhi )
∑m − n
h
)
2
: Variance between sections (primary units)
: Variance between dwellings within sections (secondary units)
nh
i =1
M
− Yh
−1
h
n h m hi
∑ ∑ (y
hi
hi
h
: Number of housing dwellings in stratum h
: Number of sections in the sample within stratum h
h
m
h
m
hi
: Number of dwellings in the sample within stratum h
: Number of dwellings in stratum h, section i
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NATIONAL STATISTICS INSTITUTE
As such, the number of dwellings to be included in each section by stratum is set
according to the following table:
Table No. 3: Average number of dwellings to be surveyed, by section and
stratum
8
Stratum
Section average size
Number of dwellings by section
City
Rest of urban area
Rural
100 - 200 dwellings
80 -150 dwellings
60 -80 dwellings
8 (with 1 more as replacement)
12
15
Selection of sampling units
The selection of first phase units was performed at each geographic stratum with
probability proportionate to section sizes, that is to say, according to the number
of dwellings (see Appendix 3).
The probability of inclusion for the i-th primary unit (section), which is
proportionate to the section size, is equal to:
π
hi
= nh ⋅ M hi
M
,
h
Where " h" represents the stratum index CD, RUA/U, R, " M hi " , the total number of
dwellings in section "i" of stratum " h" , as of Census 2002; and " M h " is the total
number of dwellings in stratum " h" as of the same census.
The selection of second phase units (dwellings within each stratum) was
undertaken with equal probability for dwellings in each section, using a systematic
selection with probability
π hij =
m hi
M
´
hi
where
M
'
hi
is the updated number of
dwellings in section i of stratum h, and mhi is the number of dwellings to be
surveyed in section i of stratum h.
Everybody at each dwelling is surveyed so that there is not a third sampling phase
(see Appendix 2).
9
Sample distribution
The total sample (3,558 sections) is distributed in a quarter and split in three
samples with more or less similar size; each one is assigned to one of the three
months. Therefore, survey on each of these smaller samples lasts one month, and
each one by itself is not representative of estimate levels.
As result, all dwellings surveyed in month "t", are surveyed again in month "t+3"
and each dwelling in the sample is surveyed only once by quarter7.
7
Data from each month is accumulated and included in the entire sample.
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Estimates for period (month) "t" are computed using data from months "t", "t-1",
and "t-2".
10 Dwellings rotation in the sample
Rotation of sections is a procedure aimed at keeping the sample up-to-date and
avoiding overusing the informants.
This procedure involves updating numbering
of the section after a certain
period in order to register changes and possible rises or falls occurred, and to
subsequently make a new dwellings selection, aimed at incorporating the changes
in the estimation of figures provided by the sample and at the same time,
avoiding "overusing" the informants.
To perform the rotation, the sample sections are divided into "shift turns" (Tramos
de Rotación - TR), which are defined considering approximately 1/6 of total urban
sections (CD and RAU) and approximately 1/12 of rural sections from each region
every month. This enables the rotation of the entire sample over an 18-month
period for urban sections and in a 36- month period for rural sections, therefore
reaching the goal of keeping it constantly up to date and valid, by incorporating
relevant changes.
11 Estimation method: weighting factors
Basic population parameters estimated in the ENE are total number of people in
the labour force and unemployed people within it. Therefore the survey's most
significant parameter is the unemployment rate, which is the quotient from
previous totals. This quotient is computed by dividing the respective estimates.
For example to calculate the total number of unemployed within the labour force,
an estimator to “expand” the value of the variable for each person in the sample
to the universe is used, according to the following formula:
YˆSep = ∑ Fhi( 2 ) ⋅ y j
hij
Where:
•
y
j
• The
Number of people in dwelling j
F
( 2)
hi
term is referred to as the expansion factor of section i in stratum h
• These factors are created so as the estimator has suitable statistical features
and they depend on sample size, that is to say, on the sample selection method
and on an adjustment for the projected population.
• The factor of expansion can be construed as the amount of people in the
population represented by one person in the sample.
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NATIONAL STATISTICS INSTITUTE
• To calculate other totals, such as the number of 15 to 24 year old people in the
labour force- only a new “dummy” variable of interest with the required
condition needs to be defined.
11.1 Construction of the factor of expansion
The factor of expansion is defined as:
SE
'
( 2)
h
hi
h
hi
SE
h
hi
hi
h
F
=
M
M
P
⋅
⋅
n ⋅M
m
Pˆ
Where:
Mh
: Number of dwellings in stratum "h" according to the 2002 Household
and Population Census
Mhi
: Number of dwellings in section "i" according to the 2002 census
nh
: Number of sections in the sample of stratum "h"
M 'hi
: Number of dwellings updated in section "i"
m hi
: Number of dwellings in the sample of section "i", stratum h:
PhSE
: Projection of the number of people of gender “S” and age range “E”
according to the 2002 Household and Population Census, in stratum h
PˆhSE
:
Estimated number of people on gender “S” and age range “E”8, in
stratum h, according to a standard estimator, which will be addressed
in detail further down.
To explain the statistical logic of the factor, it is convenient to view it as the
product of two components:
SE
(1)
( 2)
h
hi
hi
SE
h
F
Where:
8
(1)
hi
F
= F
⋅
P
Pˆ
Mh
M hi'
=
⋅
nh ⋅ M hi mhi
Age ranges or groups: E1 = under 15 years old; and E2 = 15 years old o more.
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NATIONAL STATISTICS INSTITUTE
(1)
The factor of expansion Fhi , commonly called theoretic or standard factor,
depends only on the sample design and can be construed as the inverse
probability of inclusion in the sample of person k.
This probability of being selected for the sample is the product of the selection
probabilities in the first phase (sections) by the selection probability in the second
phase (dwellings) by total sections in the stratum:
π hij = π hi ⋅ π j / hi
: Probability of dwelling j, in section i and stratum h
9
of being
selected or included in the sample
π hi =
π j/hi =
n h ⋅ M hi
Mh
m hi
M 'hi
: Probability of i-th section in stratum h
: Conditional probability of being selected for dwelling j,
section i, in stratum h
Where:
Mh
: Number of dwellings in stratum "h" according to the 2002 Household
and Population Census.
Mhi
: Number of dwellings in section "i" according to 2002 census.
nh
: Number of sections in the sample in stratum "h"
M’hi
: Number of updated dwellings in section "i" according to the 2002
Household and Population Census.
mhi
: Number of dwellings in the sample of section "i", stratum "h".
12 Total standard estimator
Component
Fhi(1) defines by itself an expansion factor, which gives way to the
standard estimator
Yˆ
9
10
10
hi
of the total:
=
∑
j , i ∈h
Fhi( 1 ) ⋅ yhi
It is worth noting that the probability changes according to the stratum and section, but it is constant for all
people in each dwelling of a section.
This estimator is called Horvitz-Thompson (1952). For further information about its characteristics, see
Carl-Erik Sarndal, Bengt Swensson, Jan Wretman (1992), Model Assisted Survey Sampling, page 43.
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NATIONAL STATISTICS INSTITUTE
Where yhi is the total number of people with the characteristic of interest
This estimator turns out unbiased and consistent in regard to the variable of
interest total, however its statistical efficiency (average quadratic error) can be
SE
improved by adjusting it to ratio Ph
PˆhSE , resulting into the final estimator used
in ENE to compute totals.
With the definition of the standard estimator, the adjustment factor description
SE
PhSE PˆhSE is complete, since Pˆh =
∑F
j ,i ∈h
(1)
hi
⋅ PhiSE
is the standard estimate of the
SE
number of people in stratum h, gender S and age E, where Phi is the number of
people in section i of stratum h, by gender S and age E.
13 Ratio estimator separate from total
The estimator of the total
yˆ h = ∑ Fhi(2) ⋅ yhi
can be expressed more compactly,
i∈h
as the sum of standard estimators by stratum adjusted by the population
projection in the respective stratum:
PhSE ˆ
yˆ h = ∑ SE ⋅ Yhi
ˆ
i∈h P
h
This estimator, called separate ratio estimate, has the following attributes:
1. It is consistent.
2. Average quadratic error is lower than the standard estimator.
3. It is biased, but the bias is negligible compared to benefits of estimation.
4. It allows reducing the non-response bias, since it has the quality that when
estimating total people by gender and above 15 years old in each stratum h, it
matches exactly population projections in stratum h.
( 2)
The final attribute implies that when adding factors Fhi
for all people above 15
years old in the sample, the result is the projection for stratum h. But if factors
Fhi(1)
are added up for all dwellings in the sample within the study domain (1
factor by dwelling), the result is an estimate of the number of dwellings within the
domain.
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14 Variance estimators
The variance or standard error of an estimator allows assessing the quality of an
inference, since by knowing estimators’ variance ranges you can decide with
certainty if a given phenomenon can be observed or not.
The following formulae are inferred considering the two-phase stratified sampling
design. The previous assumption allows simplification of formulae and obtaining
conservative estimators, that is to say, their estimates overestimate true
variances.
14.1
Estimator of the variance for a total
Vˆar ( Yˆh ) =
nh
(1)
⋅ ∑ ⎡ F hi ⋅
n h − 1 i∈h ⎢⎣
y
hi
−R
ˆ
2
⋅ (1)⋅ p hi ⎤⎥⎦
h F hi
Where:
Yhi =
∑y
hij
: Number of people, for example, unemployed in the sample in
Vivienda j
section "i"
phi =
∑
phij
: Number of people above 15 years old in the sample, in section
Vivienda j
"i"
Rˆ h = Yˆh Pˆh :
Ratio between the number of people of the variable of interest and
total people in the stratum, with
14.2
yˆ = ∑ F ⋅ y
(1)
h
hi
i∈h
and
hi
pˆ = ∑ F ⋅ p
(1)
h
hi
i∈h
hi
.
Estimator of the variance for Unemployment Rate
∧
TD h =
ˆ
Y
Estimator of Total Unemployed
h
=
ˆ
Estimator of Total Labour Force
Xh
⎡ (1)
nh
1
⎛ ∧ ⎞
Vˆar ⎜ TD ⎟ = ∑
∑
⎢( Fhi Yhi −
nh
⎝ ⎠ h (nh − 1) i ⎣
∑F
i
∧
Y ) − TD⋅ ( Fhi(1) X hi −
(1)
hi
hi
1
nh
∑F
(1)
hi
i
⎤
X hi ) ⎥ 2
⎦
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NATIONAL STATISTICS INSTITUTE
15 Estimator of
population)
the
(
Vˆar YˆEs tan
standard
)
estimator's
variances
⎛
n
1
= ∑ h ⋅ ∑ ⎜⎜ Fhi(1)Yhi −
nh
h nh − 1
i ⎝
∑
(1)
hi
F
i
(not
⎞
⋅ Yhi ⎟⎟
⎠
adjusted
by
2
Where:
Yhi =
∑y
hij
: Total unemployed people, for example, in the sample in section "i".
Vivienda j
16 Sampling error
Sampling errors of an estimator θˆ in any parameterθ, for instance, from a total
or rate, are the Absolute Error and the Relative Error as defined bellow.
16.1
Absolute error of an estimator at 95% confidence
ea (0,95) = Absolute Error = 1,96 ⋅ Vˆ (θˆ) .
16.2
Relative Error of an estimator at 95% confidence
Relative Error =
AbsoluteError
θˆ
=
ea (0,95)
θˆ
The relative error with a 68% confidence interval is known as “Coefficient of
Variation” of an estimator and is the result from the quotient between the
estimate’s standard deviation (square root of the variance) and the estimate’s
value:
Vˆ (θˆ)
ˆ
ˆ
CV (θ ) =
θˆ
.
17 Confidence interval at 95%
Once the variance of an estimator θˆ has been calculated, it is possible to obtain
the confidence interval for a parameter θ of the total of a variable with 95 %
confidence.
(θˆ − e
a (0,95)
; θˆ + ea (0,95)
)
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NATIONAL STATISTICS INSTITUTE
APPENDIX 1: Sample by estimate areas and relative error for the
unemployed (Base: Oct-Dec 2003).
No. of
sections
FRAME
2002
32,964
No. of
dwellings
FRAME
2002
4,000,403
URBAN
26,279
3,476,817
LARGE CENTRES
18,759
NAME, LEVEL AND
STRATUM
NATIONAL
Unemployed
Unemployment
rate
Sections
sample
Dwellings Coefficient Absolute Relative
sample
of variation
error
error
461,072
0.08
3,551
34,455
1.8
16,399
3.6
432,988
0.09
3,018
26,460
1.9
16,120
3.7
2,808,345
367,021
0.09
2,439
19,512
2.1
15,256
4.2
RURAL URBAN AREA
(RUA)
RURAL
7,520
668,472
65,967
0.07
579
6,948
4.0
5,209
7.9
6,685
523,586
28,084
0.04
533
7,995
5.5
3,011
10.7
REGION I
10.8
1,132
108,142
19,444
0.09
158
1,398
5.5
2,093
ARICA CITY
446
45,409
8,369
0.11
65
520
8.4
1,376
16.4
IQUIQUE CITY
405
41,573
5,904
0.08
60
480
9.8
1,130
19.1
ALTO HOSPICIO CITY
117
12,388
4,815
0.09
10
80
11.2
1,061
22.0
16.6
REGION II
1,012
111,756
13,634
0.08
144
1,317
8.5
2,269
CALAMA CITY
274
28,063
2,351
0.05
60
480
16.7
768
32.7
ANTOFAGASTA CITY
538
68,579
9,806
0.10
48
384
11.0
2,114
21.6
REGION III
778
62,427
10,032
0.09
145
1,371
5.8
1,138
11.3
COPIAPO CITY
338
28,959
3,276
0.08
60
480
10.7
687
21.0
VALLENAR CITY
133
11,481
3,075
0.13
42
336
10.4
627
20.4
REGION IV
1,701
164,615
15,208
0.07
211
2,185
8.1
2,408
15.8
URBAN
1,219
126,752
14,401
0.09
164
1,480
8.4
2,365
16.4
COQUIMBO CITY
314
39,951
5,533
0.10
38
304
15.0
1,625
29.4
LA SERENA CITY
302
39,249
5,575
0.11
37
296
13.7
1,494
26.8
OVALLE CITY
217
17,742
1,362
0.08
47
376
17.4
464
34.0
ELQUI PROVINCE
852
98,380
11,563
0.09
104
1,011
9.8
2,223
19.2
LIMARI PROVINCE
535
43,527
1,871
0.04
72
724
16.2
595
31.8
CHOAPA PROVINCE
314
22,708
1,773
0.06
35
450
20.4
710
40.0
RURAL
482
37,863
807
0.02
47
705
28.7
454
56.2
REGION V
4,065
449,301
63,176
0.11
400
3,822
4.8
5,944
9.4
URBAN
3,590
415,291
61,076
0.11
358
3,192
4.9
5,897
9.7
RURAL
475
34,010
2,100
0.04
42
630
18.0
742
35.3
PETORCA PROVINCE
LOS ANDES
PROVINCE
LOS ANDES CITY
SAN FELIPE
PROVINCE
QUILLOTA
PROVINCE
VALPARAISO
PROVINCE
VALPARAISO CITY
261
18,867
3,147
0.10
31
402
12.1
747
23.8
313
24,831
1,590
0.05
43
424
18.7
583
36.6
185
15,246
1,058
0.05
29
232
22.5
467
44.1
460
36,312
3,611
0.07
40
504
13.3
943
26.1
536
47,233
2,962
0.06
46
482
18.3
1,063
35.9
1,795
258,227
43,676
0.13
160
1,325
6.4
5,490
12.6
488
76,355
15,884
0.15
54
432
9.1
2,841
17.9
VIÑA DEL MAR CITY
663
102,724
12,973
0.19
66
528
11.4
2,899
22.3
QUILPUE CITY
248
37,495
7,497
0.16
22
176
14.8
2,172
29.0
VILLA ALEMANA CITY
SAN ANTONIO
PROVINCE
186
28,965
5,578
0.17
16
128
21.9
2,389
42.8
497
39,891
6,054
0.12
51
453
10.0
1,184
19.6
_____________________________________________________________________________________ 16
NATIONAL STATISTICS INSTITUTE
GRAN VALPARAISO
No. of
sections
FRAME
2002
1,531
No. of
dwellings
FRAME
2002
236,936
SAN ANTONIO CITY
285
22,620
QUILL-CAL-CR
CITIES
322
33,253
NAME, LEVEL AND
STRATUM
Unemployed
Unemployment
rate
Sections
sample
Dwellings
sample
Coefficient Absolute Relative
of variation
error
error
40,850
0.13
151
1,208
6.4
5,133
12.6
4,627
0.14
42
336
9.6
866
18.7
2,289
0.18
47
376
18.3
821
35.9
REGION VI
2,323
207,603
7,440
0.03
218
2,372
11.3
1,654
22.2
URBAN
1,542
148,272
5,414
0.04
158
1,472
14.2
1,507
27.8
RURAL
781
59,331
2,026
0.02
60
900
17.2
681
33.6
RANCAGUA CITY
SAN FERNANDO
CITY
CACHAPOAL
PROVINCE
COLCHAGUA
PROVINCE
CARDENAL CARO
PROVINCE
458
57,026
1,619
0.05
65
520
21.2
673
41.6
159
13,592
852
0.05
41
328
18.3
306
35.9
1,496
145,051
5,617
0.04
109
1,120
14.2
1,567
27.9
618
51,386
1,591
0.02
78
832
16.3
507
31.9
209
11,166
233
0.02
31
420
32.3
147
63.2
REGION VII
2,815
248,150
33,300
0.09
278
3,025
5.4
3,510
10.5
URBAN
1,813
167,355
26,114
0.11
195
1,780
6.2
3,157
12.1
RURAL
1,002
80,795
7,187
0.06
83
1,245
10.9
1,532
21.3
CURICO CITY
311
25,472
5,586
0.14
40
320
10.0
1,091
19.5
TALCA CITY
426
53,504
8,386
0.11
57
456
10.2
1,678
20.0
LINARES CITY
209
17,621
1,762
0.08
43
344
15.4
531
30.2
TALCA PROVINCE
LINARES
PROVINCE
CAUQUENES
PROVINCE
CURICO PROVINCE
958
97,024
13,028
0.10
85
849
9.3
2,380
18.3
829
68,812
7,207
0.08
87
959
12.2
1,719
23.9
232
16,498
762
0.04
35
468
22.1
329
43.2
796
65,816
12,304
0.12
71
749
7.9
1,894
15.4
REGION VIII
4,573
483,336
50,945
0.08
496
4,820
4.5
4,465
8.8
URBAN
3,452
397,465
44,843
0.08
424
3,740
4.8
4,196
9.4
RURAL
1,121
85,871
6,102
0.05
72
1,080
12.8
1,525
25.0
CHILLAN CITY
357
44,017
4,925
0.17
62
496
13.2
1,271
25.8
LOTA CITY
107
12,539
2,276
0.13
44
352
15.1
672
29.5
CORONEL CITY
191
23,550
3,347
0.12
44
352
14.0
919
27.5
LOS ANGELES CITY
2,402
311,251
37,716
0.28
305
2,672
5.6
4,151
11.0
ÑUBLE PROVINCE
CONCEPCION
PROVINCE
CONCEPCION CITY
1,221
112,371
8,270
0.06
98
1,071
11.3
1,833
22.2
1,797
237,308
30,097
0.09
247
2,092
6.1
3,616
12.0
TALCAHUANO CITY
ARAUCO
PROVINCE
BIO-BIO PROVINCE
GREATER
CONCEPCION
AREA
655
100,237
11,184
0.24
66
528
11.8
2,576
23.0
409
61,730
8,945
0.20
44
352
11.2
1,964
22.0
485
37,365
4,014
0.07
45
570
11.0
862
21.5
1,349
130,499
12,391
0.07
140
1,359
8.4
2,050
16.5
1,139
173,380
22,196
0.09
119
952
7.6
3,325
15.0
REGION IX
2,543
234,996
14,406
0.05
212
2,252
7.7
2,186
15.2
URBAN
1,609
159,098
13,202
0.07
160
1,472
7.7
1,994
15.1
RURAL
934
75,898
1,205
0.01
52
780
37.9
894
74.2
ANGOL CITY
141
11,703
1,089
0.08
40
320
17.7
378
34.8
TEMUCO CITY
MALLECO
PROVINCE
CAUTIN PROVINCE
558
70,462
6,887
0.15
72
576
11.5
1,554
22.6
1,008
104,609
8,681
0.05
100
1,018
9.7
1,644
18.9
1,460
121,075
4,815
0.05
99
1,130
14.4
1,359
28.2
_____________________________________________________________________________________ 17
NATIONAL STATISTICS INSTITUTE
No. of
sections
FRAME
2002
3,084
No. of
dwellings
FRAME
2002
276,360
21,822
0.06
295
3,196
URBAN
2,038
191,644
17,618
0.07
211
1,936
RURAL
1,046
84,716
4,204
0.03
84
VALDIVIA CITY
316
33,400
2,973
0.07
OSORNO CITY
359
36,638
2,873
0.07
NAME, LEVEL AND
STRATUM
REGION X
Unemploy
ed
Unemploym
ent rate
Sections
sample
Dwellings Coefficient
sample
of variation
Absolute
error
Relative
error
6.0
2,573
11.8
6.5
2,228
12.6
1,260
15.6
1,288
30.6
54
432
14.3
836
28.1
48
384
17.6
993
34.6
PUERTO MONTT CITY
369
38,892
3,194
0.07
47
376
15.2
952
29.8
VALDIVIA PROVINCE
1,064
94,405
7,321
0.06
99
1,044
11.1
1,596
21.8
OSORNO PROVINCE
LLANQUIHUE
PROVINCE
CHILOE-PALENA
PROVINCE
REGION XI
667
61,953
3,978
0.06
72
723
14.5
1,134
28.5
866
79,676
4,379
0.04
83
874
12.8
1,099
25.1
487
40,326
6,144
0.09
41
555
10.4
1,258
20.5
384
24,886
1,926
0.05
106
954
12.3
465
24.1
COIHAIQUE CITY
168
12,473
1,221
0.08
52
416
17.2
411
33.7
PUERTO AISEN CITY
68
4,338
214
0.03
35
280
33.1
139
64.8
REGION XII
546
43,190
4,289
0.07
94
860
9.9
828
19.3
PUNTA ARENAS CITY
408
34,710
3,628
0.07
73
584
11.2
798
22.0
8,008
1,585,641
205,449
0.09
794
6,883
3.2
13,027
6.3
7,618
METROPOLITAN
REGION
URBAN
1,549,965
203,479
0.09
764
6,356
3.3
13,016
6.4
RURAL
GREATER SANTIAGO
AREA
PUENTE ALTO CITY
432
44,303
2,950
0.04
41
615
13.2
761
25.8
6,993
1,425,287
185,820
0.09
630
5,040
3.5
12,726
6.8
629
127,753
15,283
0.10
63
504
12.0
3,591
23.5
SAN BERNARDO CITY
292
60,770
11,549
0.10
56
448
8.9
2,022
17.5
MELIPILLA CITY
71
14,640
1,560
0.06
38
304
24.0
735
47.1
COLINA CITY
CHACABUCO
PROVINCE
CORDILLERA
PROVINCE
MAIPO PROVINCE
72
14,717
2,908
0.12
24
192
14.4
818
28.1
200
32,910
5,572
0.05
36
354
12.5
1,364
24.5
692
135,481
16,852
0.10
72
627
10.9
3,599
21.4
515
95,990
15,933
0.09
77
730
8.4
2,628
16.5
265
37,754
2,908
0.05
54
529
20.5
1,169
40.2
306
55,369
6,178
0.07
55
643
11.5
1,393
22.5
MELIPILLA PROVINCE
TALAGANTE
PROVINCE
_____________________________________________________________________________________ 18
NATIONAL STATISTICS INSTITUTE
APPENDIX 2: Procedure for the selection of first- and second-phase units
First-phase units (sections) will be selected with probability proportionate to size,
based on the number of dwellings, following the systematic procedure below.
Intervals “N” (= number of sections in the stratum) are constructed as follows:
Section No. of Dwellings
1
2
3
Intervals
M1
M2
M3
M
1 and M1
M1 + 1 and M1 + M2
M1 + M2 + 1 and M1 + M2 + M3
M
N
MN
M1 +...+ MN-1 + 1
and
M
M1 + ...+ MN = M
Next, a random number “A” is generated between 1 and k = M/n, then, selected
sections are determined by the interval to which the amounts belong:
A, A + k, A + 2k, ... , A + (n - 1)k.
The previous procedure does not enable repetitions and can be demostrated that
selection probability of a unit with “Mi” dwellings is “n Mi/M”.
APPENDIX 3: Areas with difficult access (ADAs), deducted from the
sample
Region
I
Location
Valle de Lluta (P)
II
Entity
Situation
Difficult access; bad, sandy road, dangerous dunes
and brook zone. Sora is a hamlet with difficult
Sora
access, where the road crosses a fast-flowing river,
with no bridge.
The entire municipality of Ollagüe.
The entire district No.19 in Copiapó is considered
Campo Marte
ADA, since it is a very remote, Andean area.
III
Ciénaga Redonda
IV
Caldera y Damas
V
Alta Montaña
VI
Chancón (P)
Anita
VII
El Baúl
El Baúl
VIII
Puerto Sur
IX
Chilpaco (P)
Ex Colonia
Penal
Chilpaco (P)
X
Hueyusca (P)
El Mirador
XI
Las Bandurrias (P)
XII
XIII
Entre Vientos
El Ingenio (P)
La Sombría
Los
Libertadores
Las
Bandurrias
Monte Bello
El Ingenio
Difficult access
Only in winter-time.
Access only possible from January to March.
Classification as ADA was ratified with CD.
The sector remains classified as ADA, since access
is very difficult; a 4WD vehicle is required, on top of
good weather condition. Very far away from urban
centres.
Area of high cost all DC 10 corresponds to Isla
Santa María
ADA. Chilpaco (P) is considered entity.
DC7 Hueyusca hamlet, El Mirador (Cs) entity is an
area with difficult access.
EXCLUSION AREA
AE (MILITAR ZONE)
Difficult access
_____________________________________________________________________________________ 19
NATIONAL STATISTICS INSTITUTE
In the following regions, entire communes/municipalities have been excluded from
the sample:
•
Region II (Ollagüe commune is excluded)
•
Region V (Isla de Pascua and Juan Fernández are excluded)
•
Region X (Cochamó, Futaleufú, Hualaihué and Palena have been excluded)
•
Region XI (Guaitecas, O'Higgins and Tortel are excluded)
•
Region XII (Cabo de Hornos and the Antarctica are excluded)
_____________________________________________________________________________________ 20
NATIONAL STATISTICS INSTITUTE
APPENDIX 4: Comparison between current estimate levels and levels in
the new proposal
Estimate levels used in the National Employment Survey 1996 versus estimate
levels proposed for the new ENE, based on Census 2002. Emphasis is put on
additional levels in the new proposal for ENE 2006 and levels of the current
sample from ENE 96 that would no longer be included.
The following table shows the levels in both samples (current and the new
proposal):
CURRENT LEVELS
NEW LEVELS
NATIONAL TOTAL
URBAN
LARGE URBAN CENTRES
NATIONAL RURAL-URBAN AREA (RUA)
NATIONAL
URBAN
LARGE CENTRES
RUA
RURAL
RURAL
REGION I, TARAPACA
ARICA CITY
IQUIQUE CITY
REGION I
ARICA CITY
IQUIQUE CITY
ALTO HOSPICIO CITY
REGION II, ANTOFAGASTA
CALAMA CITY
CHUQUICAMATA CITY
ANTOFAGASTA CITY
REGION II
CALAMA CITY
REGION III, ATACAMA
COPIAPO CITY
REGION III
COPIAPO CITY
VALLENAR CITY
VALLENAR CITY
REGION IV, COQUIMBO
URBAN
RURAL
COQUIMBO CITY
LA SERENA CITY
OVALLE CITY
ELQUI PROVINCE
LIMARI PROVINCE
CHOAPA PROVINCE
ANTOFAGASTA CITY
REGION IV
URBAN
RURAL
COQUIMBO CITY
LA SERENA CITY
OVALLE CITY
ELQUI PROVINCE
LIMARI PROVINCE
CHOAPA PROVINCE
_____________________________________________________________________________________ 21
NATIONAL STATISTICS INSTITUTE
CURRENT LEVELS
NEW LEVELS
REGION V, VALPARAISO
URBAN
RURAL
PETORCA PROVINCE
LOS ANDES PROVINCE
V REGION
URBAN
RURAL
PETORCA PROVINCE
LOS ANDES PROVINCE
LOS ANDES CITY
SAN FELIPE PROVINCE
QUILLOTA PROVINCE
VALPARAISO PROVINCE
GREATER VALPARAISO AREA
VALLENAR CITY
VIÑA DEL MAR CITY
QUILPUE CITY
VILLA ALEMANA CITY
SAN ANTONIO PROVINCE
SAN ANTONIO CITY
QUILL-CAL-CR CITIES
SAN FELIPE PROVINCE
QUILLOTA PROVINCE
VALPARAISO PROVINCE
GREATER VALPARAISO AREA
VALPARAÍSO CITY
VIÑA DEL MAR CITY
SAN ANTONIO PROVINCE
SAN ANTONIO CITY
GROUP: QUILLOTA CALERA - LA CRUZ
REGION VI, DEL LIBERTADOR
GENERAL BERNARDO O'HIGGINS
URBAN
RURAL
RANCAGUA CITY
SAN FERNANDO CITY
CACHAPOAL PROVINCE
COLCHAGUA PROVINCE
CARDENAL CARO PROVINCE
REGION VII, DEL MAULE
URBAN
RURAL
CURICO PROVINCE
CURICO CITY
TALCA PROVINCE
TALCA CITY
LINARES PROVINCE
LINARES CITY
CAUQUENES PROVINCE
REGION VI
URBAN
RURAL
RANCAGUA CITY
SAN FERNANDO CITY
CACHAPOAL PROVINCE
COLCHAGUA PROVINCE
CARDENAL CARO PROVINCE
REGION VII
URBAN
RURAL
CURICO PROVINCE
CURICO CITY
TALCA PROVINCE
TALCA CITY
LINARES PROVINCE
LINARES CITY
CAUQUENES PROVINCE
_____________________________________________________________________________________ 22
NATIONAL STATISTICS INSTITUTE
CURRENT LEVELS
NEW LEVELS
REGION VIII, BIOBIO
URBAN
RURAL
ÑUBLE PROVINCE
CHILLAN CITY
CONCEPCION PROVINCE
GREATER CONCEPCION AREA
CONCEPCION CITY
TALCAHUANO CITY
LOTA CITY
CORONEL CITY
ARAUCO PROVINCE
BIO-BIO PROVINCE
LOS ANGELES CITY
REGION VIII
URBAN
RURAL
ÑUBLE PROVINCE
CHILLAN CITY
CONCEPCION PROVINCE
GREATER CONCEPCION AREA
CONCEPCION CITY
TALCAHUANO CITY
LOTA CITY
CORONEL CITY
ARAUCO PROVINCE
BIO-BIO PROVINCE
LOS ANGELES CITY
REGION IX, DE LA ARAUCANIA
URBAN
RURAL
MALLECO PROVINCE
ANGOL CITY
TEMUCO CITY
CAUTIN PROVINCE
REGION IX
URBAN
RURAL
MALLECO PROVINCE
ANGOL CITY
TEMUCO CITY
CAUTIN PROVINCE
REGION X, LOS LAGOS
URBAN
RURAL
VALDIVIA PROVINCE
VALDIVIA CITY
OSORNO PROVINCE
OSORNO CITY
LLANQUIHUE PROVINCE
PUERTO MONTT CITY
CHILOE-PALENA PROVINCE
REGION X
URBAN
RURAL
VALDIVIA PROVINCE
VALDIVIA CITY
OSORNO PROVINCE
OSORNO CITY
LLANQUIHUE PROVINCE
PUERTO MONTT CITY
CHILOE-PALENA PROVINCE
REGION XI, AISEN DEL
GENERAL CARLOS IBANEZ DEL CAMPO
COIHAIQUE CITY
PUERTO AISEN CITY
REGION XI
COIHAIQUE CITY
PUERTO AISEN CITY
REGION XII, MAGALLANES
Y DE LA ANTARTICA CHILENA
REGION XII
PUNTA ARENAS CITY
PUNTA ARENAS CITY
_____________________________________________________________________________________ 23
NATIONAL STATISTICS INSTITUTE
CURRENT LEVELS
NEW LEVELS
METROPOLITAN REGION, SANTIAGO
URBAN
RURAL
SANTIAGO PROVINCE
GREATER SANTIAGO AREA
PUENTE ALTO CITY
SAN BERNARDO CITY
MELIPILLA CITY
MR
URBAN
RURAL
CHACABUCO PROVINCE
CORDILLERA PROVINCE
MAIPO PROVINCE
MELIPILLA PROVINCE
TALAGANTE PROVINCE
SANTIAGO PROVINCE
GREATER SANTIAGO AREA
PUENTE ALTO CITY
SAN BERNARDO CITY
MELIPILLA CITY
COLINA CITY
CHACABUCO PROVINCE
CORDILLERA PROVINCE
MAIPO PROVINCE
MELIPILLA PROVINCE
TALAGANTE PROVINCE
APPENDIX 6: Large/big cities
As detailed in the classification of Urban Centres, the Metropolis is a country's
largest urban representation; it concentrates more than 1,000,000 inhabitants
and accounts for a high percentage of the total population. The Metropolis is made
up of the urban area of a set of communes or municipalities that have come
together as result of “conurbation” processes.
a. Greater Santiago area
Following the above-described scheme, the Greater Santiago area went “from
the level of Large Urban Area defined at the 1992 Census to the level of
Metropolis in 2002, due to its high population scale; this level -“Gran Santiago”
in Spanish- is subject to different treatment.
Santiago Metropolis (2002)
Gran Santiago (1992)
32 communes of the Santiago province
32 communes of the Santiago province
Puente Alto Municipality
Puente Alto Municipality
San Bernardo Municipality
San Bernardo Municipality
Padre Hurtado Municipality
Padre Hurtado Municipality
Pirque city (Pirque Municipality) *
La Obra-Las Vertientes (San José de Maipo Municipality) *
* Both City of Pirque with 4,855 inh. and City of La ObraLas Vertientes with (2,477) inh. belong to the Cordillera
Province RUA stratum in the new ENE Sample.
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b. Greater Valparaíso area
The Greater Valparaíso area is made up of the cities of Valparaíso, Quilpue,
Villa Alemana and Viña del Mar.
c. Greater Concepción area
The Greater Concepción area comprises the cities of Concepción, Chiguayante,
Penco, San Pedro de la Paz and Talcahuano.
d. Greater Temuco area
The Greater Temuco area comprises the cities of Temuco and Padre Las Casas.
e. Greater La Serena area
Gran Serena comprises the cities of Coquimbo and la Serena.
The following estimate levels are to be taken into account for the New 2006
National Employment Survey:
-
Alto Hospicio City
Los Andes City
Quilpue City
Villa Alemana City
Colina City.
Chuquicamata City was an estimate level in the 96 ENE and is not included in
the new proposal for 2006 ENE.
APPENDIX 7: Estimators of totals, ratios, rates and variances.
Procedures for calculating estimators used in the National Employment
Survey
The sample base must contain the survey data and parameters used for the
Expansion Factor definition, as well as the formulae required for calculating
Averages, Rates and Ratios.
This base containing the employment survey data to be projected for the
population calls for procedures connected to the sample design.
For this purpose, technical algorithms used to expand the selected sample to the
universe must be included. And this will be fed into computing programs.
Sample factors of expansion
The factor of expansion is expressed as the times represented by a selected unit
in relation to the universe.
Factors used for the National Employment Survey expansion according to design
is expressed as follows:
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Theoretical expansion factor in dwelling j of the section, within stratum h
FE
(1)
hi
Mh
M hi'
=
⋅
nh ⋅ M hi mhi
Mh
= Number of dwellings in stratum h according to the 2002 Household
and Population Census
Mhi
= Number of dwellings in section "i" of stratum h according to the 2002
Census
nh
= Number of sections in the stratum h sample
M 'hi
= Number of updated dwellings in section i of stratum h
m hi
= Number of dwellings in the sample, section i and stratum h.
Adjusted expansion factor in dwelling i of section j and stratum h
FE
( 2)
hi
Mh
M hi' PhSE
=
⋅
⋅ SE
nh ⋅ M hi mhi Pˆh
,
Where:
P
SE
h
PˆhSE
= Forecasted number of people on gender “S” and age group “E” (15
years old or more and below 15 years old) according to the 2002
Household and Population Census, in stratum h
= Estimated number of people on gender “S” and age group “E” in
stratum h
SE
PˆhSE = ∑ FE (1)
hi ⋅ Phij
= Standard estimate of people in stratum h, on gender
j
“S” and age range “E” (15 years old or more and below 15 years old).
PhijSE
= Number of people in dwelling j, section i and stratum h, on gender “S”
and age range “E” (above or equal to 15 years old and below 15
years old) in the labour force.
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Estimators
Estimators connected to this design are not self-weighted due to the set number
of dwellings selected by section.
Estimates are conducted taking into account the entire sample and based on
mobile quarters, which include the ongoing month and two previous months.
Exogenous data on population projections used for calculations refers to the
central month.
The estimate of a given total for a variable is firstly obtained with the
multiplication of the variable's value for each person by his factor of expansion
and then added up on all the people in the sample.
The estimated population by stratum, gender and age group is obtained by
weighting each person by the theoretical expansion factor and then adding up all
the people in the sample within the stratum, by gender and age range.
Total estimator of people with condition c
[ ]
Pˆc = ∑∑∑ FEhi(1) ⋅ Phijc
h
i
j
Phijc = Total people in dwelling j, section i of stratum h with condition c
Estimated rate (average) of condition b, by person with condition c
Tˆbc =
Pˆb
Pˆc
;
Pˆb
= Total estimate o people with condition b
Total estimated variance
Vˆar ( Pˆc ) =
nh
⋅∑
n h − 1 i∈h
[F
(1)
i
⋅
p
ic
−R
ˆ
c
⋅ F i(1)⋅ p
ic
]
2
Sampling error
Sampling errors defined below are the Coefficient of Variation, Absolute Error and
Relative Error.
An estimate variation coefficient is obtained from the quotient between the
estimate standard deviation (square root of the variance) and the estimate value.
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Coefficient of vriation:
Absolute eror:
Relative eror:
V ( Pc )
CVˆ ( Pc ) =
Pˆc
.
AbsoluteError = 1,96 ⋅ V ( Pˆc ) .
Re lativeError =
AbsoluteError
Pˆ
Statistical confidence interval for estimator between 2 periods (mobile quarters)
Once you know the estimator variance, it is possible to obtain the confidence
interval for the total people, in the population, with condition “c” at a 95 %
confidence level.
Confidence interval at 95%
( Pˆ
c
− 1,96 × V(Pc ) ; Pˆc + 1,96 × V(Pc )
)
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BIBLIOGRAPHY

Des Raj (1968), “Sampling Theory”.
Cochran W. G. (1998), “Sampling Techniques”.
Carl-Erik Sarndal, Bengt Swensson, Jan Wretman (1992), “Model Assisted
Survey Sampling”.
C. J. Skinner, D. Holt and T. M. Smith (1989), “Analysis of Complex Surveys”.
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