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Standard error estimation for the EU-SILC indicators of poverty and social exclusion

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  • Institut national de la statistique et des études économiques (STATEC), Luxembourg

Abstract and Figures

Since EU-SILC was launched, much attention has been paid to sampling errors. However, the computation of standard errors for estimates based on EU-SILC is confronted with several challenges. In this article, we propose a simple approach for standard error estimation based upon basic statistical techniques. The proposed estimator is simple and flexible, yet theoretically justified. It can accommodate nearly all the sampling designs and the target indicators used in EU-SILC, no matter their complexity. The proposed approach can be easily implemented with standard statistical software (SAS, SPSS, Stata, R…) and requires minimal computing power. We illustrate the proposed approach by showing preliminary standard error estimates for key EU-SILC indicators of poverty and social exclusion: the new “Europe-2020” indicator of poverty or social exclusion (AROPE indicator) and the persistent at-risk-of-poverty rate, which is the core EU-SILC longitudinal indicator. The change in the AROPE between two years is also considered. It is necessary to estimate the standard error of changes to judge whether the observed differences are statistically significant.
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2013 edition
KS-RA-09-001-EN-C
Methodologies and
Working papers
ISSN 1977-0375
Standard error estimation for the EU–SILC indicators
of poverty and social exclusion
income, expenditures and material deprivation
2013 edition
Methodologies and
Working papers
Standard error estimation for the EU–SILC indicators
of poverty and social exclusion
income, expenditures and material deprivation
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ISBN 978-92-79-30374-6
ISSN 1977-0375
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Theme: Populations and social conditions
Collection: Methodologies & Working papers
© European Union, 2013
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3Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Eurostat is the Statistical Ofce of the European Union (EU). Its mission is to be the leading provider of
high quality statistics on Europe. To that end, it gathers and analyses data from the National Statistical
Institutes (NSIs) across Europe and provides comparable and harmonised data for the EU to use in the
denition, implementation and analysis of EU policies. Its statistical products and services are also of great
value to Europe’s business community, professional organisations, academics, librarians, NGOs, the media
and citizens.
In the eld of income, poverty, social exclusion and living conditions, the EU Statistics on Income and
Living Conditions (EU-SILC) is the main source for statistical data at European level.
Over the last years, important progress has been achieved in EU-SILC as a result of the coordinated work
of Eurostat and NSIs.
In June 2010, the European Council adopted a social inclusion target as part of the Europe 2020 Strategy: to
lift at least 20 million people in the EU from the risk of poverty and exclusion by 2020. To monitor progress
towards this target, the ‘Employment, Social Policy, Health and Consumer Affairs’ (EPSCO) EU Council
of Ministers agreed on an ‘at risk of poverty or social exclusion’ indicator. To reect the multidimensional
nature of poverty and social exclusion, this indicator consists of three sub-indicators: i) at-risk-of-poverty
(i.e. low income); ii) severe material deprivation; and iii) living in very low work intensity households.
In this context, the Second Network for the Analysis of EU-SILC (Net-SILC2) is bringing together National
Statistical Institutes (NSIs) and academic expertise at international level in order to carry out in-depth
methodological work and socio-economic analysis, to develop common production tools for the whole
European Statistical System (ESS) as well as to ensure the overall scientic organisation of the third and
fourth EU-SILC conferences. The current working paper is one of the outputs of the work of Net-SILC2. It
was presented at the third EU-SILC conference (Vienna, December 2012), which was jointly organised by
Eurostat and Net-SILC2 and hosted by Statistics Austria.
It should be stressed that this methodological paper does not in any way represent the views of Eurostat,
the European Commission or the European Union. This is independent research which the authors have
contributed in a strictly personal capacity and not as representatives of any Government or ofcial body.
Thus they have been free to express their own views and to take full responsibility both for the judgments
made about past and current policy and for the recommendations for future policy.
This document is part of Eurostat’s Methodologies and working papers collection, which are technical
publications for statistical experts working in a particular eld. These publications are downloadable free
of charge in PDF format from the Eurostat website:
http://epp.eurostat.ec.europa.eu/portal/page/portal/income_social_inclusion_living_conditions/
publications/methodologies_and_working_papers.
Eurostat databases are also available at this address, as are tables with the most frequently used and
requested short- and long-term indicators.
5Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Table of contents
1. Introduction ................................................................................................
9
2. Variance estimation approach .................................................................... 11
2.1 Case of linear indicators ....................................................................... 12
2.2 Case of non-linear indicators ................................................................ 12
2.3 Interpretation in terms of regression residuals ....................................... 13
2.4 Calibration and imputation ..................................................................... 13
2.5 Extension to estimators of net changes between two waves ................ 14
3. Preliminary results ....................................................................................... 17
3.1 Cross-sectional measures .................................................................... 18
3.2 Longitudinal measures ......................................................................... 18
3.3 Measures of change .............................................................................. 18
4. Design effect estimation .............................................................................. 21
5. The importance of quality design variables ................................................. 23
6. Conclusion and way forward ....................................................................... 25
7. References ................................................................................................ 27
8. Annexes ...................................................................................................... 29
Annex 1: Numerical Results ...................................................................... 29
Annex 2: Proposed changes to ‘Doc065’ which describes the EU-SILC
target variables ............................................................................ 52
7Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Standard error estimation for the EU-SILC
indicators of poverty and social exclusion
Guillaume OSIER, Yves BERGER and Tim GOEDEMÉ(1)
Abstract:
Since EU-SILC was launched, much attention has been paid to sampling errors. However, the
computation of standard errors for estimates based on EU-SILC is confronted with several
challenges. In this article, we propose a simple approach for standard error estimation based
upon basic statistical techniques. The proposed estimator is simple and exible, yet theoretically
justied. It can accommodate nearly all the sampling designs and the target indicators used in
EU-SILC, no matter their complexity. The proposed approach can be easily implemented with
standard statistical software (SAS, SPSS, Stata, R…) and requires minimal computing power.
We illustrate the proposed approach by showing preliminary standard error estimates for key EU-
SILC indicators of poverty and social exclusion: the new “Europe-2020” indicator of poverty or
social exclusion (AROPE indicator) and the persistent at-risk-of-poverty rate, which is the core
EU-SILC longitudinal indicator. The change in the AROPE between two years is also considered.
It is necessary to estimate the standard error of changes to judge whether the observed differences
are statistically signicant.
(1) Guillaume Osier is statistician at the Luxembourg Income Study (LIS) and Luxembourg’s National Statistical Institute (STATEC), Yves Berger is
reader in Statistics at the University of Southampton (UK) and Tim Goedemé is senior researcher and project manager at the University of Antwerp
(Belgium). We would like to thank Emilio Di Meglio and Emanuela Di Falco (Eurostat – Unit F4 “Quality of Life”) for running our programs on the
EU-SILC Production database, which contributed signicantly to this paper. We would also like to thank Tony Atkinson for his review of the paper
presented at the Net-SILC2 Conference in Vienna (6-7th December 2012). This work has been supported by the second Network for the analysis
of EU-SILC (Net-SILC2), funded by Eurostat. The European Commission bears no responsibility for the analyses and conclusions, which are solely
those of the authors. Email addresses for correspondence: Guillaume.osier@statec.etat.lu; Y.G.Berger@soton.ac.uk and tim.goedeme@ua.ac.be.
Introduction 1
9
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
1. Introduction
Over the last years, EU-SILC has developed into a mature project covering all the EU-27 countries as
well as Switzerland, Norway, Iceland, Croatia and Turkey. It is now the main data source for comparative
analysis and indicators on income and living conditions in the EU. Since the launch of the “Europe 2020”
Strategy for smart, sustainable and inclusive growth, the importance of EU-SILC has grown even further.
One of the ve “Europe 2020” headline targets is based on EU-SILC: the social inclusion EU target, which
consists of lifting at least 20 million people in the EU from the risk of poverty or social exclusion by 2020.
Since EU-SILC was launched in 2003, much attention has been paid to sampling errors, mainly because
the EU-SILC data are collected through sample surveys in each participating country. As the indicators
based on EU-SILC are sample estimates, they should be reported along with standard errors estimates
and condence intervals, particularly if they are used for policy purposes. In addition, the Commission
Regulation (EC) n°28/2004 of 5th January 2004 regarding the detailed content of intermediate and nal
EU-SILC Quality Reports requires that standard error estimates be provided by countries along with the
EU-SILC main target indicators.
There exist many approaches for estimating standard errors and condence intervals (e.g. Wolter (2007);
Heeringa et al. (2010)). Estimation methods are usually split into ‘direct’ methods, which rely on analytic
variance formulas, and ‘resampling’ methods, like Jackknife or Boostrap, which consist of drawing
a high number of ‘replications’ from the original sample so to mimic the actual sampling process and
then approximate the sampling distribution of the target statistic. Whichever approach is used, it is highly
desirable that standard error estimates reect as much as possible the sampling process and the estimation
procedure. This means the sample design, the weighting procedure, the imputation schemes and the non-
linear form of survey estimators should be reected in the calculation of standard errors and condence
intervals (Eurostat, 2002; Heeringa et al., 2010; Goedemé, 2013a).
In this paper, we propose a simple approach for standard error estimation based upon basic statistical
techniques (multivariate linear regression). Because of its simplicity, the proposed approach can be easily
used with standard statistical software. Because of its exibility, the proposed approach can handle the
different types of designs used in EU-SILC. The structure of the paper is as follows. In Section 2, we explain
the main challenges of variance estimation in the context of EU-SILC and show how these challenges can be
dealt with using basic statistical techniques. In Section 3, we present some preliminary results on the basis
of these techniques for cross-sectional indicators of poverty and social exclusion, longitudinal indicators,
and estimates of change over time. Subsequently, in Section 4, we propose one common way of estimating
design effects in the context of EU-SILC. Finally, in Section 5 we discuss how sample design information
and the sample design variables in the EU-SILC database could be improved in order to achieve more
accurate variance estimates. We conclude in Section 6.
Variance estimation approach 2
11
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
2. Variance estimation approach
The computation of standard errors for EU-SILC estimates is confronted with several challenges:
• complex sample designs involving stratication, geographical clustering, unequal probabilities of
selection for the sample units and post-survey weighting adjustments (re-weighting for unit non-
response and calibration to external data sources)
• rotating samples
• problems with quality, documentation and availability of sample design variables
• complex non-linear indicators, longitudinal indicators and indicators of net changes
• different methods of imputation used across countries
• condentiality issues
• limited resources in terms of budget, staff and time both at national and EU level
Over the past few years, several projects, working groups, task forces and individual authors have
addressed one or more of these challenges. However, the knowledge remains rather scattered and is not
very accessible for National Statistical Institutes (NSIs) and the wider research community, especially for
the non-statistician researchers.
Standard error estimates should reect as much as possible the sample design, weighting procedures,
imputation and the characteristics of the indicators of interest. Otherwise they may be severely biased.
On the other hand, the increased complexity of EU-SILC, the widening of the user community and the
increased reliance on EU-SILC for policy targeting and evaluation have enhanced the need for comparable,
accurate as well as workable solutions for the estimation of standard errors and condence intervals for EU-
SILC based indicators. Therefore, we need an approach making a trade-off between statistical accuracy and
operational efciency. The proposed approach is general enough to be valid under most of the EU-SILC
sampling designs, which is actually a challenge considering the important differences in sampling design
between countries. The approach is also simple and easy to implement using standard statistical software,
such as SAS, SPSS or R, and should require minimal computing power.
Re-sampling methods like Bootstrap or Jackknife are exible enough to be applicable to the sampling
designs and the target indicators used in EU-SILC, no matter their complexity (Verma and Betti, 2011). On
the other hand, the computational effort may be considerable, which is not desirable when standard error
estimates need to be produced quickly for a large number of target indicators, including breakdowns. That
is why we have proposed to use direct variance estimators (Berger, 2004). The main assumption underlying
such estimators is that sample units have been selected with replacement, which considerably simplies
the estimation of the variance. If sample units are selected without replacement, then this approach will
lead to conservative estimates. The overestimation is negligible as long as the sampling fraction is close to
zero. Note that this is nearly always the case with the EU-SILC sampling designs. Furthermore, those direct
estimators can be easily extended to cover multi-stage designs by using the well-known ‘ultimate cluster’
approximation (e.g. Särndal et al., 1992) and to deal with complex non-linear indicators on the basis of
the linearisation procedure (e.g. Deville (1999); Wolter (2007); Osier (2009)). In what follows, we further
explain this approach to variance estimation in some detail. We rst discuss the case of linear indicators
before elaborating on the case of non-linear indicators. Subsequently we explain how multivariate linear
regression offers an easy tool for estimating the variance both of linear and non-linear indicators. Finally,
we elaborate on calibration, imputation and measures of net changes over time.
2Variance estimation approach
12 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
2.1 Case of linear indicators
Linear indicators are means, totals or proportions. The estimation of the variance of linear indicators is
rather straightforward, and is covered in most textbooks on Statistics (e.g., Särndal et al (1992)). Consider a
population U composed of N identiable units (households or individuals). Let s denote a sample of size n
drawn from U using a probabilistic design so that every unit k is having its own, known inclusion probability
πk. For example, in case of simple random sampling without replacement, the inclusion probability is πk =
n / N for each k.
Suppose we wish to estimate the total θ = k U yk , where yk is the value of a study variable y for k. y can
be a continuous variable (e.g., household income), or a dummy variable for a population category (e.g.,
1 if the person is unemployed, 0 otherwise). If y is a dummy, then θ is a count (e.g., the total number of
unemployed in the population). Let
∑∑∑
=
h i j
hijhij
y
ωθ
ˆ
be an estimator of
θ
, for which an estimate of the
standard error is required. We propose the following variance estimator:
V (θ) = ∑ ∑ (yhi• – ӯh••)2, (1)
where yhi• = ωhij yhij and ӯh•• = yhi• /nh
h is the stratum label, with a total of H strata. If no stratication, the whole target population U can
be regarded as one large stratum (H = 1)
i is the label of the primary sampling unit (PSU) within stratum h, with a total of nh PSUs
j is the household label within PSU i of stratum h, with a total of mhi households. In case of a one-
stage sampling design, each household is regarded as a PSU
• ωhij is the sampling weight for household j in PSU i of stratum h. The weights ωhij are used to make
inference about the population. They are usually adjusted for unit non-response and calibration
yhij is the value of the study variable y for household j in PSU i of stratum h
If nh = 1 for some strata, the estimator (1) cannot be used. A solution is to collapse strata to create “pseudo-
strata” so that each pseudo-stratum has at least two PSUs. Common practice is to collapse a stratum with
another one that is similar with regard to the target variables of the survey (Rust and Kalton (1987); Ardilly
and Osier (2007)).
2.2 Case of non-linear indicators
The estimator (1) is valid for linear indicators, i.e. means, totals and proportions. However, most of the EU-
SILC indicators are non-linear (e.g., the at-risk-of-poverty threshold, the at-risk-of-poverty rate, the income
quintile share ratio or the Gini coefcient). In order to estimate the variance of non-linear indicators, the
linearisation approach may be used (Kovacevic and Binder 1997, Deville 1999, Demnati and Rao 2004,
Wolter 2007, Osier 2009). The principle is to approximate a non-linear indicator by a linear form by
retaining only the rst-order term of a Taylor expansion. The variance of the linear approximation can be
used as an approximation of the variance of the non-linear indicator considered. The linearisation procedure
is justied on the basis of asymptotic properties of large samples and populations (Verma and Betti, 2005).
h=1
H
^ ^ nh
nh - 1
j=1
mhi
i=1
nh
()
Variance estimation approach 2
13
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Suppose
θ
is a complex non-linear indicator. The variance of an estimator
θ
ˆ
of
θ
is estimated by:
V (θ) = (zhi• – zh••)2 . (2)
This is exactly the same formula as (1), except that the study variable y is replaced by the “linearised”
variable z. For example, if
( )( )
1
1
==
XYxy
Uk k
Uk k
θ
is the ratio of two population totals, then the
“linearised” variable is:
( )
kkk xyXz =
θ
1
for all k. More examples can be found in Osier (2009).
2.3 Interpretation in terms of regression residuals
The differences (yhi• – ӯh••) in (1) and (zhi• – zh••) in (2) can be seen as the residuals of the linear regression
of the PSU aggregates yhi• and zhi• on the dummy variables for each stratum category (Berger, 2004). These
dummy variables are equal to 1 if the i-th PSU belongs to the stratum h, 0 otherwise. This provides a
quick and easy way to compute the variance of both cross-sectional and longitudinal measures using basic
statistical techniques (multivariate linear regression).
2.4 Calibration and imputation
The approach proposed here reects survey design features such as stratication, multi-stage selection,
unequal probabilities of inclusion for the sample units and post-survey weighting adjustments for unit non-
response. On the other hand, a specic approach is needed to measure how calibration weighting (Deville
and Särndal 1992) affects the variance. The effect of calibration on variance is expected to be signicant
in the “Nordic” countries like Denmark or Finland in which powerful auxiliary information from income
registers is used for calibration. As shown by Deville and Särndal (1992), the effect of re-weighting for
calibration on variance estimation can be allowed for by replacing the study variable by the residuals of the
regression on the calibration variables, and by calculating the variance assuming no calibration. Such an
approach is easy to implement as long as the calibration variables are available as well as the initial weights
before calibration or, equivalently, the calibration adjustment factors (also called g-weights). Up to now, the
EU-SILC database does not contain this information.
A major shortcoming of the proposed approach is that it does not take the imputation variance into account.
Actually, the EU-SILC income variables have been heavily imputed, with different imputation methods
used across countries, as well as across different income components. For the sake of simplicity, imputed
values have been treated as true values. Such an assumption may lead to severely under-estimating the
variance, particularly when the proportion of imputed values is important (Rao and Shao, 1992). However,
variance estimation under imputation is not an easy task. Direct estimation formulas are very complex
(Deville and Särndal, 1994) and method-specic. Thus, though signicant, it does not seem realistic to
try to estimate the imputation variance on a streamline basis, even more so that the imputation methods
used in the EU-SILC vary greatly from one country to another. Nevertheless, the imputation variance
might be estimated occasionally using for instance the SAS software SEVANI developed by Statistics
Canada (Beaumont and Bissonnette, 2011). For hot-deck imputation, Berger and Escobar (2012) proposed
an approach to estimate the variance of change in the presence of imputed values.
h=1
H
^ ^ nh
nh-1
2Variance estimation approach
14 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
2.5 Extension to estimators of net changes between two waves
Monitoring changes or trends in indicators over time is of key importance in many areas of economic and
social sciences. For example, since the launch of the “Europe 2020” Strategy for smart, sustainable and
inclusive growth, EU-SILC has been increasingly used for policy targeting, as one of the ve Europe 2020
headline targets is based on EU-SILC data. For example, the social inclusion EU target consists of lifting at
least 20 million people in the EU from the risk of poverty and exclusion by 2020.
Interpreting differences between cross-sectional estimates calculated from different waves may be
misleading however. It is therefore necessary to estimate the standard error for these differences in order to
judge whether or not the observed differences are statistically signicant. As the EU-SILC survey is time-
dependent, temporal correlations between indicators have to be taken into account.
In order to meet both the cross-sectional and longitudinal requirements, Eurostat has recommended
a rotational design based on four rotation groups. At the rst wave of EU-SILC, four sub-samples of
individuals are drawn. Each subsequent wave, one sub-sample (25% of the whole sample) is dropped out
and a new one is substituted for. Nearly all the EU-SILC countries have adopted this rotating structure.
Figure 1: The EU-SILC four-year rotating structure
Sub-sample 1
Sub-sample 2
Sub-sample 3
Sub-sample 4
Cross-sectional
sample at t
Cross-sectional
sample at t+1
Cross-sectional
sample at t+2
Variance estimation approach 2
15
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
(2) Please note that for most countries the correlation is zero if two estimates are compared with more than 4 years difference (the two samples do not
contain the same respondents in this case and can be considered independent). However, in some countries (e.g. Belgium) the primary sampling
units have been selected for the entire duration of EU-SILC and rotation is implemented only at the within PSU level. As a consequence, also when
all households are rotated out, there still remains some correlation that has to be estimated.
Let
( )
=
Uk kl
l
y
;
θ
denote the total of a study variable
y
measured at wave l. Let
( )
l
θ
ˆ
be an estimator of
( )
l
θ
based on the cross-sectional sample at wave l. Suppose we wish to estimate the absolute difference
( ) ( )
12
θθ
=
where
( )
1
θ
and
( )
2
θ
are calculated from wave 1 and 2, respectively. The difference
is
estimated by
( ) ( )
12 ˆˆ
ˆ
θθ
=
. Furthermore, the variance of
ˆ
is given by
( )
( )
( )
( )
( )
( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( )
( )
212121
2121
ˆ
,
ˆˆˆ
2
ˆˆ
ˆ
,
ˆ
2
ˆˆ
ˆ
θθρθθθθ
θθθθ
VVVV
CovVVV
×+=
×+=
, (3)
where
( ) ( )
( )
21
ˆ
,
ˆ
θθρ
is the correlation coefcient between
( )
1
ˆ
θ
and
( )
2
ˆ
θ
. As these estimators are calculated
from rotating samples,
( ) ( )
( )
21
ˆ
,
ˆ
θθρ
is generally strictly positive. As a result, if condence intervals of the
estimate in wave 1 would be simply compared with the estimate in wave 2, one is overly conservative.
However,
( ) ( )
( )
21
ˆ
,
ˆ
θθρ
is also the most difcult part to estimate(2).
The regression-based approach introduced in the previous sections can be easily extended to cope with
estimators of changes between two waves (Berger and Priam (2010, 2013); Berger and Oguz Alper (2013)).
Berger and Priam (2013) proposed to use the residual variance matrix of a multivariate model. This residual
variance matrix is used to produce estimates of correlation which are used in the variance of the net
change between indicators. The multivariate model includes covariates which specify the stratication and
interactions which specify the rotation of the sampling designs.
Now, we describe briey the approach proposed by Berger & Priam (2010, 2013) in the case when
( )
1
ˆ
θ
and
( )
2
ˆ
θ
are two estimator of totals; that is, when
( )
=
i
il
l
y
;
ˆ(
θ
, where
ўl;i = ωhij yl;hij if i slh ,
0 otherwise
where slh is the wave l sample of PSUs of stratum h. The stratum h is such that the i-th PSU belongs to the
stratum h. Berger and Priam (2013) proposed to use the residual covariance of the following multivariate
(or general) linear regression model
= + εi , (5)
where
( ) ( )
hhhh
sssssi
2121
==
. The covariates
ih
z;1
and
ih
z
;2
are a set of (dummy) design
variables which species the stratication. These variables are dened by
. (6)
(4)
j=1
mhi
{
h=1
H
ўl;i
ў2;i
( )
β(1)
z1h;i + β(1) z2h;i + β(1) z1h;i z2h;i
β(2)
z1h;i + β(2) z2h;i + β(2) z1h;i z2h;i
1h
1h
2h
2h
12h
12h
()
z1h;i =
{
1 if i slh
0 otherwise
2Variance estimation approach
16 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
The parameters and are regression parameters that need to be included into the
model.
Let
V
ˆ
be the ordinary least squares estimate of the covariance matrix of the model (5). The correlation can
be estimated by
ρ ( , ) = V12 (V11V22)-1/2 , (7)
Where Vkl is the component (k,l) of the ordinary least squares residual matrix of the model (5).
Suppose that
( )
1
ˆ
θ
and
( )
2
ˆ
θ
are two functions of totals. For example, this is the case for the EU-SILC
indicators. In this case,
ˆ
is a also a function of totals; that is,
( )
τ
ˆ
ˆf=
where
( )
'
21
ˆ
,
ˆ
,
ˆ
,
ˆˆ
Pp
τττττ
LL=
and
P is the number of totals. The quantity
p
τ
ˆ
is the the estimator of the p-th (PSU level) variable ўpl:i; where p
= 1,…Q, Q+1,…P, l = 1 if pQ and l = 2 if p > Q. The constant Q is the number of totals calculated from
the rst wave.
Using the delta method (Taylor linearisation), we have that an approximation of
ˆ
in the neighbourhood
of
τ
is given by
( )
( )
τττ
ˆ
ˆ
'
; where
( )
τ
is the gradient of
( )
τ
f
at
τ
. Therefore, the linearisation
estimator for the variance is
( )
( ) ( ) ( )
''
ˆˆ
ra
ˆ
v
ˆ
ˆ
ra
ˆ
v
τττ
=
. (8)
Berger and Priam (2013) showed how a multivariate model similar to (5) and including more dependent
variables can be used to estimate the covariance matrix
( )
τ
ˆ
ra
ˆ
v
. In Section 3.3, we used this generalised
approach for the estimation of change between the EU-SILC indicators.
12h
β(2)
1h
β(1)
2h
β(1)
12h
β(1)
1h
β(2)
2h
β(2)
, , , ,
^
V
ˆ
( )
1
ˆ
θ
( )
2
ˆ
θ
^ ^ ^
Preliminary results 3
17
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
3. Preliminary results
In this section, we use the proposed variance estimation approach to produce standard error estimates for
cross-sectional measures, longitudinal measures and measures of change based on EU-SILC. The reference
cross-sectional measure is the AROPE (At-risk-of-poverty or social exclusion) indicator, which is the
“Europe 2020” headline indicator on poverty and social exclusion. It counts the number of individuals living
in households which are at-risk-of-poverty, severely materially deprived or with very low work intensity;
the individuals present in several sub-indicators being counted only once. In what follows we rst present
standard errors of the cross-sectional AROPE estimates. Subsequently we discuss preliminary variance
estimates of the persistent at-risk-of-poverty rate, which is the core EU-SILC longitudinal indicator. The
persistent risk of poverty is dened as having an equivalised disposable income below the at-risk-of-
poverty threshold in the current year and in at least two of the preceding three years’. In the last subsection,
the change in the AROPE between two years is considered.
Figure 2: The ‘Europe 2020’ headline indicator on poverty or social exclusion (at-risk-
of-poverty or social exclusion - AROPE)
Individuals living in households at-risk-
of-poverty
Individuals living in households
suffering from severe material
deprivation
Individuals aged less than 60 living
in households with very low work
intensity
The calculations rely on the anonymised EU-SILC micro-data les that are provided by Eurostat for
statistical/research purposes only. Since the research les do not include any stratum label or any calibration
information, we had to use NUTS2 region as a proxy for the stratum label and ignore the impact of calibration
on variance. These assumptions will incur higher variance estimates, as it is well-known that stratication
usually reduces variance, and so does calibration.
All the results shown in this section are still preliminary. Given the lack of sampling design
information in the EU-SILC user data les and potential quality problems with the current sample
design variables, the variance gures should be read with caution. Eurostat, in collaboration with
Net-SILC2, is currently working to improve this situation.
3Preliminary results
18 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
3.1 Cross-sectional measures
In the Annex 1 (tables 1a-1d), we have standard error estimates for the at-risk-of-poverty rate (POV), the
severe material deprivation rate (DEP), the share of individuals aged less than 60 living in households with
very low work intensity (LWI) and the AROPE. We also calculate condence intervals and relative margins
of error(3) based upon the normality assumption. In 2011, the standard error estimates for the AROPE lies
between 0.5 and 1 percentage point in most of the countries, which means that the length of a condence
interval (at 95% condence) for the indicator lies between ±1 and ±2 percentage points. The standard error
is greater than 1 point in Bulgaria, Lithuania and Romania; while it is lower than 0.5 point in Germany,
Finland, Sweden and Slovenia. For Finland and Sweden, it seems that the impact of weight calibration on
variance has been taken into account somehow. Standard error estimates for the male/female populations
appear to be higher than for the total population. The reason is that the number of sample units which fall
into each subpopulation is lower than the number of sample units in the total population.
As far as the AROPE’s three sub-indicators are concerned (POV, DEP, LWI), the standard error estimates
appear lower than those calculated for the AROPE. These results make sense because, by denition, the
AROPE indicator reaches higher values than its three components. For example, the estimated standard
error for the severe material deprivation rate is relatively low for some countries (0.2 percentage point for
Luxembourg).
3.2 Longitudinal measures
In the Annex 1 (tables 2a-2c), we have standard error estimates for the persistent risk of poverty. For the
four-year period 2007-2010, the relative margin of error of the persistent at-risk-of-poverty rate ranges from
13% in France and 15% in Spain to 54% in Hungary and 63% in Iceland. The precision of the persistent
at-risk-of-poverty rate appears to be lower than the precision of the AROPE. There are several possible
reasons for this. For the longitudinal component of EU-SILC, the achieved sample size is lower than for
the cross-sectional component: the longitudinal sample sizes range from about 1000 individuals in Iceland
to more than 12000 in France. This is caused mainly by the rotating design used in most of the countries
(25% of the sample is refreshed every year with new individuals), but also by losses to follow-up and
attrition. Another explanation is that the persistent at-risk-of-poverty rate generally takes lower value than
the cross-sectional at-risk-of poverty rate (POV) or the AROPE indicator. Finally, the higher dispersion of
the longitudinal sampling weights, which are adjusted at each wave for attrition and calibration to external
data sources, is likely to reduce the precision of the persistent risk of poverty.
3.3 Measures of change
In the Annex 1 (tables 3a-3d), we have the standard error estimates and condence intervals (based on
normality assumption) for changes in the AROPE between 2007 and 2011, 2008 and 2011, 2009 and 2011
and between 2010 and 2011. The computations were made within Eurostat premises using the EU-SILC
Production Data Base(4). If a condence interval does not include 0, we can say the difference is statistically
signicant (at a given level of condence).
Remark: Standard condence intervals based upon the normality assumption can perform poorly when the
sampling distribution is skewed (e.g., domain estimation). For example, the lower bounds of a condence
interval can be negative even when the parameter of interest is positive. The coverage and the tail errors
(3) By denition, the relative margin of error is the half-length of the condence interval (‘absolute’ margin of error) expressed as a percentage of the
indicator value. Like condence intervals, the relative margin of error can be dened for any desired condence level, but usually a level of 90 %,
95 %, 99 % or 99.9 % is chosen (typically 95 %).
(4) We would like to thank Emilio Di Meglio and Emanuela Di Falco (Eurostat – Unit F4 “Quality of Life”) for running our programs on the EU-SILC
Production database, which contributed signicantly to this paper. However, the results published in this paper are still provisional.
Preliminary results 3
19
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Figure 3: Condence Intervals for the persistent at-risk-of-poverty rate based upon the
normality assumption (N) and the empirical likelihood approach (EL)
can be also lower than their intended levels. On the other hand, empirical likelihood condence intervals
(Berger and De La Riva Torres, 2012) may be better in this situation, as empirical likelihood condence
intervals are determined by the distribution of the data and the range of the parameter space is preserved.
Figure 4: Condence Intervals for the persistent at-risk-of-poverty rate based upon
the normality assumption (N) and the empirical likelihood approach (EL), males born
between 1965 and 1984
Source: authors’ calculations based on the anonymised EU-SILC micro-data les provided by Eurostat for statistical/research purposes only
(Version 01-03-12)
Source: authors’ calculations based on the anonymised EU-SILC micro-data les provided by Eurostat for statistical/research purposes only
(Version 01-03-12)
Design effect estimation 4
21
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
4. Design effect estimation
The EU-SILC Framework Regulation has formulated precision requirements in terms of minimum effective
sample sizes to be achieved by the participating countries(5). The effective sample size is calculated as the
achieved sample size divided by the design effect. Therefore, it is important to apply a common denition
of the design effect across EU-SILC countries.
By denition, the design effect factor Deff of an estimator
θ
ˆ
of
θ
is the ratio of the variance of
θ
ˆ
under
the actual sampling design (P) to the variance that would be obtained from a hypothetical simple random
sample (SRS) of the same size, without replacement:
( )
( )
SRSSRS
P
V
V
Deff
θ
θ
ˆ
ˆ
=
, (9)
where
SRS
θ
ˆ
is the estimator of
θ
under simple random sampling without replacement.
Calculating the design effect is important in EU-SILC:
1. The complex structure of the EU-SILC samples suggests not to use the naive variance formula
running under the assumption that sample observations are independently and identically (iid)
distributed random variables, but rather to go beyond this elemental variability by taking into
account complex design features such as stratication, clustering, unequal selection probabilities,
re-weighting for unit non-response and calibration to external data sources. If we do not take
account of these features, the standard errors will be under-estimated, thus resulting in over-
optimistic interpretations of differences calculated between two estimators (see above)..
2. The design effects are needed to determine the effective sample sizes for each country. Given that
the effective sample size is dened as the achieved sample size divided by the design effect, it
can be interpreted as an indicator of the loss of precision due to the use of a complex design, as
compared to using simple random sampling: the stronger the design effect, the smaller the effective
sample size. The EU-SILC Framework Regulation has set out minimum effective sample sizes
to be achieved by the countries. Thus, correct estimation of the design effect is a very important
business in the planning stage of EU-SILC, which must be taken with utmost seriousness. Over-
estimating the design effect leads to selecting more units than necessary and, as a result, will incur
increased survey costs. On the other hand, under-estimating it results in a lower effective sample
size, which can make the survey non-compliant with the minimum requirements (cf. Osier, 2012).
Design-based estimation of the Deff consists of individually estimating each variance term and then making
the ratio between the two estimators. The numerator of Deff, that is, the variance under the actual sampling
design, can be estimated using the proposed variance estimation approach. As regards the variance that
would be obtained under simple random sampling without replacement and of the same size, we propose to
use the following estimator (Ardilly and Tillé (2005); Ardilly and Osier (2007)):
, (10)
where
(5) EP and Council Regulation N°1177/2003 of 16 June 2003. In the Framework Regulation, the design effect refers to the at-risk-of-poverty rate.
( )
( ) ( )
1
1
1
ˆ
ˆ
2
2
2
2
==
si
i
si
si
i
SRSSRS
yy
n
f
N
n
s
fNV
ω
ω
θ
ω
4Design effect estimation
22 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
( )
s
ii
ωω
=
is the sampling weight for household
i
in the sample
s
( )
2
2
1
=
si
i
i
si
i
yy
s
ω
ω
ω
ω
is the weighted dispersion of the study variable
y
(6) in the sample
=
si
i
si
ii
y
y
ω
ω
ω
is the weighted sample mean of
y
Nnf /= is the sampling fraction
The estimator (10) provides a nearly unbiased variance estimator under simple random sampling. On the
other hand, (10) may not be stable, especially if the distribution of the sampling weights is skewed. An
alternative is to use a non-weighted formula.
(6) If θ is non-linear, y is the “linearized” variable
The importance of quality design variables 5
23
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
5. The importance of quality design variables
As the sample design often has a strong effect on the sampling variance, it cannot be ignored when
estimating the sampling variance. As a result, accurate variables for identifying strata and sampling clusters
in the dataset are necessary for estimating standard errors, condence intervals, design effects and effective
sample sizes. As documented by Goedemé (2010, 2013a, 2013b), currently, for many countries, sample
design variables are (partially) lacking, inaccurate and/or not very well documented – even though the
situation has improved somewhat with the latest releases of EU-SILC.
If we assume that the ultimate cluster method can be applied in the case of EU-SILC, only variables for
identifying the rst stage of the sample design are needed. Three different steps in the recording of sample
design variables can be identied: (1) the construction of the ‘original’ sample design variables, (2) the
construction of ‘computational’ sample design variables and (3) the construction of ‘public’ sample design
variables. It is important to stress that if a mistake is made in an earlier step, this mistake will be carried on
to the other steps. Here we summarize the main recommendations as formulated in Goedemé (2013b). We
limit the discussion to the identication of strata and sampling clusters. As stressed above, also other sample
design variables may be important, such as variables referring to the sampling fraction and calibration. In
terms of EU-SILC variables, we limit the discussion to variables DB050 (primary strata), DB060 (PSUs),
DB062 (Secondary Sampling Units, SSUs) and DB070 (order of selection at the rst stage of the sample
design) in the EU-SILC data les.
As far as the ‘original’ sample design variables are concerned:
1. It is highly recommended that the sample design variables are accurate, also for earlier waves of
EU-SILC. There are still countries for which no information, or only partial information on the
sample design is available in the data les available to Eurostat and/or the EU-SILC UDB. This is
especially the case for earlier waves of EU-SILC.
2. All sample design variables should reect the situation at the time of selection. In other words,
when households move from one region to another, DB060 should remain the same. In addition,
for these households DB040 (region at moment of interview) cannot be used as a stratication
variable. With DB050 it should be possible to identify all strata at the rst stage of the sample
design.
3. Each selected PSU should receive a unique identier, also in the case of multiple hits (a separate
code for every ‘hit’). In addition, sample design variable codes (DB050, DB060, DB062 and
DB070, as well as household identiers if households are the PSUs) should remain consistent
across (rotational) panels and waves, for the entire duration of EU-SILC. Otherwise, it is impossible
to estimate the variance of changes from one EU-SILC wave to another (cf. Section 2.5).
4. Self-representing PSUs should be clearly identiable and in the case of these PSUs information
on the second stage of the sample design (stratication, clustering, order of selection) should be
included in the dataset. Special care is needed in the case of unequal probability systematic samples.
5. Strata which contain only one PSU should be clearly identiable, and an indication of similar
strata on the basis of information on the sampling frame should be included in the ag variable. In
addition, national quality reports should contain detailed information on the nature of strata which
contain only one PSU.
There are three other recommendations, which are of a somewhat different nature, but are equally important
to take into account:
6. It is necessary that the coding of sample design variables is clearly documented in the national
quality reports, in relation to a description of the implemented sample design.
7. Further research is necessary with regard to the necessity of taking account of the order of selection
in the case of systematic samples with unequal probabilities of selection.
8. Sample designs should be as simple as possible and changes in the sample design over time should
5The importance of quality design variables
24 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
be avoided. If (changes in) sample designs are so complex that the variance of point estimates
cannot be accurately estimated, the usefulness of the sample is strongly reduced.
In many cases, original sample design variables cannot be directly used for the estimation of the sampling
variance. Special care is needed in the case of strata which contain only one PSU and in the case of
systematic samples. On the basis of the original sample design variables, ‘computational strata and PSU
variables’ should be constructed. For doing so, primary strata should be carefully grouped in the case of
non-self-representing single PSUs and systematic samples and secondary strata and secondary sampling
units should be integrated in the Primary Stratum and PSU variables in the case of self-representing PSUs.
It is strongly recommended that NSIs and Eurostat agree on a concrete list of specications about
how the sample design variables should be recorded in the EU-SILC data les and about how sample
design variables should be described in the national quality reports. There should be a clear link
between the sampling variables in the dataset and the description of the EU-SILC sample design in
the national quality report. Special attention should be paid to who is responsible for constructing the
‘computational strata and PSU variables’, which should be kept distinct from the task of accurately
recording the ‘original’ sample design variables. We formulate a concrete proposal in Annex 2.
Apart from the problems related to the sample design variables available to Eurostat (i.e. the ‘original’
sample design variables), there are currently three problems which the EU-SILC UDB users have to face.
First, the stratication variable is missing (i.e. DB050). Consequently, standard errors are likely to be over-
estimated. Second, the lack of DB050 in the UDB is an issue for some countries. That is, in some cases
DB070 (the order of selection) and DB060 (PSUs) are not uniquely dened across strata. This is especially
the case for DB060. This leads to problems, as PSUs with a similar code are collapsed across strata. This
problem is worsened by the fact that UDB users have no idea about the direction and degree of bias in the
variance estimates obtained by using the available information in the UDB. Third, UDB users are not able
to merge various waves of EU-SILC. Therefore, they cannot accurately estimate changes over time using
the EU-SILC UDB.
Given the importance of sample design effects on estimated standard errors and the additional burden
on Eurostat and/or NSIs to make alternatives available, any deviation from providing the original
or computational strata and PSUs in the EU-SILC UDB should be based on a scientic analysis
of the real disclosure risk which would be associated with the provision of the complete original
computational strata and PSU variables in the UDB.
Alternative strategies consist in collapsing strata and PSUs or in constructing replicate weights as public
sample design variables. Each of these two approaches has its strengths and weaknesses. In any case, they
presuppose sufcient time and resources available to Eurostat and NSIs as the implementation of these
approaches requires sufcient knowledge, care and time to test and check the accuracy of the newly created
variables. In any case, it is crucial that the quality of the current sample design variables available to both
Eurostat and the EU-SILC user community is improved such that the variance of EU-SILC estimates can
be estimated with a sufcient degree of accuracy.
Conclusion and way forward 6
25
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
6. Conclusion and way forward
The proposed variance estimator is simple and exible, yet theoretically sound. It can accommodate a wide
class of sampling designs and estimators using standard statistical techniques. The approach does not rely
on any specialised computer package and can be implemented with standard statistical software such as
SAS, SPSS, Stata or R. It can also be extended to complex estimators through linearisation. However, as
the latter procedure is justied on the basis of asymptotic properties, variance estimates may not be reliable
if the sample size is not sufciently large.
The numerical results obtained using this approach are sound, although they still be read with caution given
the lack of sampling design information in the EU-SILC user data les and potential quality problems with
the current design variables. Eurostat is currently working with Net-SILC2 to improve the situation. In this
paper, we propose several concrete recommendations for better recording sample design variables in EU-
SILC.
Finally, computer programs for standard error estimation under the proposed approach (for cross-sectional,
longitudinal and measures of change between two years) are currently being developed by Net-SILC2.
References 7
27
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion 27
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
7. References
ARDILLY, P. & OSIER, G. (2007). Cross-sectional variance estimation for the French “Labour Force
Survey”. Survey Research Methods, vol. 1, no. 2, pp. 75-83.
Available at: http://w4.ub.uni-konstanz.de/srm/article/viewPDFInterstitial/77/55.
ARDILLY, P. & TILLE, Y. (2005). Sampling Methods: Exercises and Solutions. New York: Springer.
BEAUMONT, J.-F. & BISSONNETTE, J. (2011). Variance Estimation under Composite Imputation: The
Methodology Behind SEVANI. Survey Methodology, vol. 37, pp. 171-179.
BERGER, Y. G. (2004). A Simple Variance Estimator for Unequal Probability Sampling Without
Replacement. Journal of Applied Statistics, no. 3, pp. 305-315.
BERGER, Y. G. & DE LA RIVA TORRES, O. (2012). An Unied Theory of Empirical Likelihood Condence
Intervals under Unequal Probability Sampling from a Finite Population. Southampton, GB, Southampton
Statistical Sciences Research Institute, 31pp. (S3RI Methodology Working Papers). (Submitted)
BERGER, Y. G. & ESCOBAR, E. L. (2012). Variance estimation of imputed estimators of change over
time from repeated surveys. In Journées de Méthodologie Statistiques 2012, Paris, FR, 24-26 Jan 2012. 8pp.
BERGER, Y. G. & OGUZ ALPER, M. (2013). Variance estimation of change of poverty based upon the
Turkish EU-SILC survey. Paper presented at the NTTS (New Techniques and Technologies for Statistics)
Conference, Brussels, 5-7 March 2013.
BERGER, Y. G. & PRIAM, R. (2010). Estimation of Correlations between Cross-Sectional Estimates from
Repeated Surveys – an Application to the Variance of Change. Proceedings of the 2010 Statistics Canada
Symposium.
BERGER, Y. G. & PRIAM, R. (2013). A simple variance estimator of change for rotating repeated surveys:
an application to the EU-SILC household surveys. University of Southampton, Statistical Sciences Research
Institute. Available at: URL = http://eprints.soton.ac.uk/347142.
DEMNATI, A. & RAO, J. N. K. (2004). Linearization variance estimators for survey data. Survey
Methodology, vol. 30, pp. 17-26.
DEVILLE, J-C. (1999). Variance estimation for complex statistics and estimators: Linearization and
residual techniques. Survey Methodology, December 1999, vol. 25, no. 2, pp. 193-203.
DEVILLE, J-C. & SÄRNDAL, C-E. (1992). Calibration estimators in survey sampling. Journal of the
American Statistical Association, vol. 87, no. 418, pp. 376-382.
DEVILLE, J-C. & SÄRNDAL, C-E. (1994). Variance Estimation for the Regression Imputed Horvitz-
Thompson Estimator. Journal of Ofcial Statistics, vol. 10, no. 4, pp. 381–394.
EUROSTAT (2002). Monographs of ofcial statistics. Variance estimation methods in the European Union,
Luxembourg: Ofce for Ofcial Publications of the European Communities, 63p.
GOEDEMÉ, T. (2010). The construction and use of sample design variables in EU-SILC. A user’s
perspective. Report prepared for Eurostat. Available at: http://www.centrumvoorsociaalbeleid.be/index.
php?q=node/2157/en.
GOEDEMÉ, T. (2013a). How much Condence can we have in EU-SILC? Complex Sample Designs and
7References
28 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
the Standard Error of the Europe 2020 Poverty Indicators. Social Indicators Research, vol. 110, no. 1, pp.
89-110
GOEDEMÉ, T. (2013b). The EU-SILC sample design variables: critical review and recommendations.
CSB Working paper 13/02, Antwerp: Herman Deleeck Centre for Social Policy – University of Antwerp.
Available at: http://www.centrumvoorsociaalbeleid.be/index.php?q=node/3891.
HEERINGA, S. G.; WEST, B. T. & BERGLUND, P. A. (2010). Applied Survey Data Analysis, Boca Raton:
Chapman & Hall/CRC, 467p.
KOVACEVIC, M. & BINDER, D.A. (1997). Variance Estimation for Measures of Income Inequality and
Polarization – The Estimating Equations Approach. Journal of Ofcial Statistics, vol. 13, no. 1, pp. 41-58.
OSIER, G. (2009). Variance estimation for complex indicators of poverty and inequality using linearization
techniques. Survey Research Methods, vol. 3, no. 3, pp. 167-195. Available at: http://w4.ub.uni-konstanz.
de/srm/article/view/369.
OSIER, G. (2012). Design effect (Deff) estimation. Paper prepared for the Net-SILC2 workshop on standard
error estimation and other related sampling issues (Eurostat, 29-30 March 2012). Available at: http://www.
cros-portal.eu/content/workshop-2930-march-2012.
RAO, J. N. K. & SHAO, A. J. (1992). Jackknife variance estimation with survey data under hotdeck
imputation. Biometrika, 79, pp. 811-822.
RUST, K. & KALTON, G. (1987). Strategies for collapsing strata for variance estimation. Journal of
Ofcial Statistics, vol. 3, no. 1, pp. 69-81.
SÄRNDAL, C-E. ; SWENSSON, B. & WRETMAN, J. (1992). Model Assisted Survey Sampling. New
York: Springer.
VERMA, V. & BETTI, G. (2005). Sampling errors and design effects for poverty measures and other
complex statistics. University of Siena, working paper n°53. Available at: http://www.econ-pol.unisi.it/
dmq/pdf/dMQ_WP_53.pdf.
VERMA, V. & BETTI, G. (2011). Taylor linearization sampling errors and design effects for poverty
measures and other complex statistics. Journal of Applied Statistics, vol. 38, no. 8, pp. 1549-1576.
WOLTER, K. M. (2007). Introduction to Variance Estimation. 2nd ed. New York: Springer.
Annexes 8
29
Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
8. Annexes
Annex 1: Numerical Results
8Annexes
30 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-ri sk-of -pove rty r ate (POV ) Severe m ateri al depr ivati on rate ( DEP) % of indiv idual s aged l ess tha n 60 livin g in hous e-
holds w ith ver y low work inten sity (LW I) At- risk-of- pover ty or soc ial excl usion (A ROPE)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval at
95% -
upper
bound
Relative
margin
of error
(%)
Austri a
Total 12,4 0,58 11,3 13,5 9,2 6,4 0,52 5,4 7,4 15,9 7,8 0,50 6,8 8,8 12,6 18,6 0,71 17,2 20,0 7,5
Males 11,2 0,63 10,0 12,4 11,0 6,0 0,53 5,0 7,0 17,3 6,6 0,53 5,6 7,6 15,7 16,8 0,76 15,3 18,3 8,9
Females 13,5 0,66 12,2 14,8 9,6 6,7 0,60 5,5 7,9 17,6 9,0 0,62 7,8 10,2 13,5 20,3 0,80 18,7 21,9 7,7
Belgiu m
Total 14,7 0,71 13,3 16,1 9,5 5,6 0,58 4,5 6,7 20,3 11,7 0,69 10,3 13,1 11,6 20,8 0,84 19,2 22,4 7,9
Males 13,6 0,73 12,2 15,0 10,5 5,2 0,65 3,9 6,5 24,5 10,2 0,69 8,8 11,6 13,3 19,1 0,89 17,4 20,8 9,1
Females 15,9 0,79 14,4 17,4 9,7 6,0 0,58 4,9 7,1 18,9 13,2 0,79 11,7 14,7 11,7 22,4 0,90 20,6 24,2 7,9
Bulgar ia
Total 21,3 1,10 19,1 23,5 10,1 41,2 1,22 38,8 43,6 5,8 8,1 0,79 6,6 9,6 19,1 44,7 1,24 42,3 47,1 5,4
Males 19,7 1,15 17,4 22,0 11,4 39,6 1,26 37,1 42,1 6,2 7,8 0,86 6,1 9,5 21,6 43,0 1,30 40,5 45,5 5,9
Females 22,8 1,12 20,6 25,0 9,6 42,7 1,27 40,2 45,2 5,8 8,3 0,81 6,7 9,9 19,1 46,4 1,28 43,9 48,9 5,4
Cyprus
Total 16,2 0,73 14,8 17,6 8,8 8,2 0,58 7,1 9,3 13,9 4,1 0,41 3,3 4,9 19,6 22,2 0,84 20,6 23,8 7,4
Males 14,0 0,76 12,5 15,5 10,6 8,0 0,64 6,7 9,3 15,7 3,5 0,46 2,6 4,4 25,8 19,7 0,89 18,0 21,4 8,9
Females 18,3 0,81 16,7 19,9 8,7 8,4 0,62 7,2 9,6 14,5 4,7 0,47 3,8 5,6 19,6 24,6 0,93 22,8 26,4 7,4
Czech
Republi c
Total 9,0 0,46 8,1 9,9 10,0 6,8 0,39 6,0 7,6 11,2 7,2 0,43 6,4 8,0 11,7 15,3 0,53 14,3 16,3 6,8
Males 8,0 0,49 7,0 9,0 12,0 6,3 0,42 5,5 7,1 13,1 6,2 0,46 5,3 7,1 14,5 13,3 0,55 12,2 14,4 8,1
Females 10,1 0,51 9,1 11,1 9,9 7,3 0,42 6,5 8,1 11,3 8,2 0,49 7,2 9,2 11,7 17,2 0,58 16,1 18,3 6,6
Germa ny
Total 15,2 0,37 14,5 15,9 4,8 5,5 0,24 5,0 6,0 8,6 11,6 0,36 10,9 12,3 6,1 20,1 0,40 19,3 20,9 3,9
Males 14,2 0,43 13,4 15,0 5,9 5,3 0,30 4,7 5,9 11,1 10,8 0,44 9,9 11,7 8,0 18,5 0,47 17,6 19,4 5,0
Females 16,2 0,42 15,4 17,0 5,1 5,6 0,26 5,1 6,1 9,1 12,3 0,41 11,5 13,1 6,5 21,6 0,46 20,7 22,5 4,2
Denmar k
Total 11,8 0,63 10,6 13,0 10,5 2,0 0,28 1,5 2,5 27,4 8,3 0,57 7,2 9,4 13,5 16,3 0,68 15,0 17,6 8,2
Males 11,7 0,78 10,2 13,2 13,1 1,5 0,30 0,9 2,1 39,2 8,2 0,73 6,8 9,6 17,4 15,7 0,84 14,1 17,3 10,5
Females 12,0 0,73 10,6 13,4 11,9 2,4 0,40 1,6 3,2 32,7 8,3 0,71 6,9 9,7 16,8 17,0 0,82 15,4 18,6 9,5
Estoni a
Total 19,5 0,63 18,3 20,7 6,3 4,9 0,35 4,2 5,6 14,0 5,3 0,39 4,5 6,1 14,4 21,8 0,67 20,5 23,1 6,0
Males 16,5 0,73 15,1 17,9 8,7 4,8 0,41 4,0 5,6 16,7 5,9 0,51 4,9 6,9 16,9 18,9 0,77 17,4 20,4 8,0
Females 22,0 0,75 20,5 23,5 6,7 4,9 0,39 4,1 5,7 15,6 4,7 0,44 3,8 5,6 18,3 24,3 0,78 22,8 25,8 6,3
Greece
Total 20,1 0,72 18,7 21,5 7,0 11,2 0,61 10,0 12,4 10,7 7,4 0,43 6,6 8,2 11,4 28,1 0,78 26,6 29,6 5,4
Males 19,6 0,77 18,1 21,1 7,7 10,1 0,62 8,9 11,3 12,0 6,0 0,46 5,1 6,9 15,0 26,3 0,83 24,7 27,9 6,2
Females 20,7 0,76 19,2 22,2 7,2 12,2 0,66 10,9 13,5 10,6 8,8 0,53 7,8 9,8 11,8 29,8 0,84 28,2 31,4 5,5
Spain
Total 19,6 0,55 18,5 20,7 5,5 2,5 0,23 2,0 3,0 18,0 6,2 0,32 5,6 6,8 10,1 22,9 0,58 21,8 24,0 5,0
Males 18,3 0,57 17,2 19,4 6,1 2,6 0,25 2,1 3,1 18,8 5,7 0,34 5,0 6,4 11,7 21,6 0,61 20,4 22,8 5,5
Females 21,0 0,58 19,9 22,1 5,4 2,5 0,24 2,0 3,0 18,8 6,7 0,37 6,0 7,4 10,8 24,2 0,61 23,0 25,4 4,9
Table 1a: Standard error estimates for the at-risk-of-poverty or social exclusion indicator (AROPE) and its three sub-indicators, 2008
Annexes 8
31Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-ri sk-of -pove rty r ate (POV ) Severe ma teri al depr ivati on rate ( DEP) % of indiv idual s aged l ess tha n 60 livin g in hous e-
holds w ith ver y low work inten sity (LW I) At- risk-of- pover ty or soc ial excl usion (A ROPE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Finland
Total 13,6 0,44 12,7 14,5 6,3 3,5 0,25 3,0 4,0 14,0 7,3 0,36 6,6 8,0 9,7 17,4 0,49 16,4 18,4 5,5
Males 12,7 0,50 11,7 13,7 7,7 3,2 0,28 2,7 3,7 17,2 7,2 0,43 6,4 8,0 11,7 15,9 0,55 14,8 17,0 6,8
Females 14,5 0,54 13,4 15,6 7,3 3,8 0,31 3,2 4,4 16,0 7,5 0,45 6,6 8,4 11,8 18,9 0,59 17,7 20,1 6,1
France
Total 12,7 0,49 11,7 13,7 7,6 5,4 0,41 4,6 6,2 14,9 8,8 0,41 8,0 9,6 9,1 18,6 0,55 17,5 19,7 5,8
Males 11,9 0,52 10,9 12,9 8,6 5,1 0,45 4,2 6,0 17,3 8,0 0,48 7,1 8,9 11,8 17,5 0,58 16,4 18,6 6,5
Females 13,4 0,54 12,3 14,5 7,9 5,7 0,43 4,9 6,5 14,8 9,5 0,44 8,6 10,4 9,1 19,7 0,60 18,5 20,9 6,0
Hungar y
Total 12,4 0,59 11,2 13,6 9,3 17,9 0,65 16,6 19,2 7,1 12,0 0,58 10,9 13,1 9,5 28,2 0,76 26,7 29,7 5,3
Males 12,4 0,65 11,1 13,7 10,3 17,3 0,69 15,9 18,7 7,8 11,1 0,61 9,9 12,3 10,8 27,3 0,84 25,7 28,9 6,0
Females 12,4 0,60 11,2 13,6 9,5 18,4 0,68 17,1 19,7 7,2 12,8 0,62 11,6 14,0 9,5 29,0 0,78 27,5 30,5 5,3
Irelan d
Total 15,5 0,87 13,8 17,2 11,0 5,5 0,65 4,2 6,8 23,2 13,6 1,10 11,4 15,8 15,9 23,7 1,18 21,4 26,0 9,8
Males 14,5 0,94 12,7 16,3 12,7 5,3 0,70 3,9 6,7 25,9 13,0 1,24 10,6 15,4 18,7 22,7 1,32 20,1 25,3 11,4
Females 16,4 0,97 14,5 18,3 11,6 5,8 0,74 4,3 7,3 25,0 14,3 1,16 12,0 16,6 15,9 24,7 1,24 22,3 27,1 9,8
Icelan d
Total 10,1 0,62 8,9 11,3 12,0 0,8 0,20 0,4 1,2 49,0 2,6 0,35 1,9 3,3 26,4 11,8 0,66 10,5 13,1 11,0
Males 9,5 0,68 8,2 10,8 14,0 0,7 0,20 0,3 1,1 56,0 2,3 0,39 1,5 3,1 33,2 11,0 0,73 9,6 12,4 13,0
Females 10,7 0,75 9,2 12,2 13,7 0,9 0,26 0,4 1,4 56,6 3,0 0,48 2,1 3,9 31,4 12,6 0,80 11,0 14,2 12,4
Italy
Total 18,7 0,69 17,3 20,1 7,2 7,5 0,56 6,4 8,6 14,6 9,8 0,35 9,1 10,5 7,0 25,3 0,79 23,8 26,8 6,1
Males 17,1 0,69 15,7 18,5 7,9 7,2 0,57 6,1 8,3 15,5 8,3 0,35 7,6 9,0 8,3 23,2 0,82 21,6 24,8 6,9
Females 20,1 0,74 18,6 21,6 7,2 7,8 0,56 6,7 8,9 14,1 11,3 0,41 10,5 12,1 7,1 27,2 0,81 25,6 28,8 5,8
Lithua nia
Total 20,0 1,00 18,0 22,0 9,8 12,3 1,07 10,2 14,4 17,1 5,1 0,45 4,2 6,0 17,3 27,6 1,25 25,2 30,1 8,9
Males 17,6 1,11 15,4 19,8 12,4 11,7 1,23 9,3 14,1 20,6 5,1 0,54 4,0 6,2 20,8 25,3 1,45 22,5 28,1 11,2
Females 22,0 1,07 19,9 24,1 9,5 12,9 1,16 10,6 15,2 17,6 5,0 0,49 4,0 6,0 19,2 29,7 1,32 27,1 32,3 8,7
Luxembo urg
Total 13,4 0,96 11,5 15,3 14,0 0,7 0,13 0,4 1,0 36,4 4,7 0,52 3,7 5,7 21,7 15,5 0,99 13,6 17,4 12,5
Males 12,5 1,02 10,5 14,5 16,0 0,6 0,15 0,3 0,9 49,0 3,8 0,50 2,8 4,8 25,8 14,2 1,05 12,1 16,3 14,5
Females 14,3 1,08 12,2 16,4 14,8 0,7 0,15 0,4 1,0 42,0 5,5 0,70 4,1 6,9 24,9 16,7 1,13 14,5 18,9 13,3
Latvi a
Total 25,6 0,96 23,7 27,5 7,4 19,0 0,81 17,4 20,6 8,4 5,1 0,39 4,3 5,9 15,0 33,8 1,01 31,8 35,8 5,9
Males 23,1 1,05 21,0 25,2 8,9 17,3 0,87 15,6 19,0 9,9 5,5 0,50 4,5 6,5 17,8 31,0 1,11 28,8 33,2 7,0
Females 27,7 0,98 25,8 29,6 6,9 20,4 0,85 18,7 22,1 8,2 4,8 0,40 4,0 5,6 16,3 36,2 1,03 34,2 38,2 5,6
Nether lands
Total 10,5 0,76 9,0 12,0 14,2 1,5 0,23 1,0 2,0 30,1 8,1 0,59 6,9 9,3 14,3 14,9 0,81 13,3 16,5 10,7
Males 10,5 0,90 8,7 12,3 16,8 1,5 0,24 1,0 2,0 31,4 6,9 0,65 5,6 8,2 18,5 14,3 0,99 12,4 16,2 13,6
Females 10,4 0,76 8,9 11,9 14,3 1,6 0,27 1,1 2,1 33,1 9,3 0,62 8,1 10,5 13,1 15,5 0,80 13,9 17,1 10,1
Norway
Total 11,6 0,48 10,7 12,5 8,1 2,0 0,22 1,6 2,4 21,6 6,3 0,40 5,5 7,1 12,4 15,1 0,53 14,1 16,1 6,9
Males 10,0 0,52 9,0 11,0 10,2 2,0 0,24 1,5 2,5 23,5 5,4 0,42 4,6 6,2 15,2 13,2 0,58 12,1 14,3 8,6
Females 13,0 0,63 11,8 14,2 9,5 1,9 0,28 1,4 2,4 28,9 7,3 0,56 6,2 8,4 15,0 16,8 0,69 15,4 18,2 8,1
8Annexes
32 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-risk-of-poverty rate (POV) Severe material deprivation rate (DEP) % of individuals aged less than 60 living in households with
very low work intensity (LWI) At-risk-of-poverty or social exclusion (AROPE)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval at
95% - upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval
at 95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval
at 95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval
at 95%
- upper
bound
Relative
margin
of error
(%)
Poland
Total 16,9 0,50 15,9 17,9 5,8 17,7 0,44 16,8 18,6 4,9 7,9 0,28 7,4 8,4 6,9 30,5 0,54 29,4 31,6 3,5
Males 17,0 0,53 16,0 18,0 6,1 17,6 0,50 16,6 18,6 5,6 7,3 0,30 6,7 7,9 8,1 29,9 0,59 28,7 31,1 3,9
Females 16,7 0,52 15,7 17,7 6,1 17,9 0,45 17,0 18,8 4,9 8,6 0,31 8,0 9,2 7,1 31,2 0,56 30,1 32,3 3,5
Portug al
Total 18,5 0,94 16,7 20,3 10,0 9,7 0,81 8,1 11,3 16,4 6,3 0,55 5,2 7,4 17,1 26,0 1,10 23,8 28,2 8,3
Males 17,9 1,02 15,9 19,9 11,2 9,5 0,87 7,8 11,2 17,9 5,8 0,63 4,6 7,0 21,3 25,0 1,19 22,7 27,3 9,3
Females 19,1 0,96 17,2 21,0 9,9 9,9 0,85 8,2 11,6 16,8 6,8 0,60 5,6 8,0 17,3 26,8 1,14 24,6 29,0 8,3
Romania
Total 23,3 1,12 21,1 25,5 9,4 32,8 1,21 30,4 35,2 7,2 8,2 0,65 6,9 9,5 15,5 44,0 1,27 41,5 46,5 5,7
Males 22,3 1,15 20,0 24,6 10,1 32,3 1,25 29,9 34,8 7,6 7,2 0,69 5,8 8,6 18,8 42,8 1,32 40,2 45,4 6,0
Females 24,2 1,17 21,9 26,5 9,5 33,3 1,25 30,9 35,8 7,4 9,2 0,68 7,9 10,5 14,5 45,1 1,30 42,6 47,6 5,6
Sweden
Total 12,2 0,42 11,4 13,0 6,7 1,4 0,16 1,1 1,7 22,4 5,4 0,32 4,8 6,0 11,6 14,9 0,45 14,0 15,8 5,9
Males 11,3 0,48 10,4 12,2 8,3 1,3 0,16 1,0 1,6 24,1 5,0 0,36 4,3 5,7 14,1 13,7 0,51 12,7 14,7 7,3
Females 13,0 0,51 12,0 14,0 7,7 1,6 0,20 1,2 2,0 24,5 5,8 0,40 5,0 6,6 13,5 16,1 0,55 15,0 17,2 6,7
Slovenia
Total 12,3 0,42 11,5 13,1 6,7 6,7 0,34 6,0 7,4 9,9 6,7 0,33 6,1 7,3 9,7 18,5 0,49 17,5 19,5 5,2
Males 11,0 0,45 10,1 11,9 8,0 6,4 0,37 5,7 7,1 11,3 6,2 0,38 5,5 6,9 12,0 16,6 0,53 15,6 17,6 6,3
Females 13,6 0,48 12,7 14,5 6,9 6,9 0,37 6,2 7,6 10,5 7,3 0,40 6,5 8,1 10,7 20,3 0,56 19,2 21,4 5,4
Slovakia
Total 10,9 0,49 9,9 11,9 8,8 11,8 0,48 10,9 12,7 8,0 5,2 0,35 4,5 5,9 13,2 20,6 0,61 19,4 21,8 5,8
Males 10,1 0,54 9,0 11,2 10,5 11,1 0,54 10,0 12,2 9,5 4,5 0,38 3,8 5,2 16,6 18,9 0,67 17,6 20,2 6,9
Females 11,5 0,52 10,5 12,5 8,9 12,3 0,51 11,3 13,3 8,1 5,9 0,39 5,1 6,7 13,0 22,0 0,65 20,7 23,3 5,8
United
Kingdo m
Total 18,7 0,59 17,5 19,9 6,2 4,5 0,41 3,7 5,3 17,9 10,4 0,58 9,3 11,5 10,9 23,2 0,67 21,9 24,5 5,7
Males 17,4 0,62 16,2 18,6 7,0 4,3 0,48 3,4 5,2 21,9 9,7 0,67 8,4 11,0 13,5 21,7 0,72 20,3 23,1 6,5
Females 19,9 0,63 18,7 21,1 6,2 4,8 0,41 4,0 5,6 16,7 11,1 0,60 9,9 12,3 10,6 24,7 0,71 23,3 26,1 5,6
Source: authors’ c alculations based on the anony mised EU-SILC mic ro- data les provided by Eu rostat for statistical/re search purposes only (Vers ion 01-03-13)
Annexes 8
33Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Table 1b: Standard error estimates for the at-risk-of-poverty or social exclusion indicator (AROPE) and its three sub-indicators, 2009
At-risk-of-poverty rate (POV) Severe material deprivation rate (DEP) % of individuals aged less than 60 living in households with
very low work intensity (LWI) At-risk-of-poverty or social exclusion (AROPE)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval
at 95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval
at 95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points)
Condence
interval at
95%
- lower
bound
Condence
interval
at 95%
- upper
bound
Relative
margin
of error
(%)
Austri a
Total 12,0 0,54 10,9 13,1 8,8 4,8 0,39 4,0 5,6 15,9 7,2 0,47 6,3 8,1 12,8 17,0 0,62 15,8 18,2 7,1
Males 10,7 0,59 9,5 11,9 10,8 4,4 0,42 3,6 5,2 18,7 5,6 0,44 4,7 6,5 15,4 15,0 0,68 13,7 16,3 8,9
Females 13,2 0,63 12,0 14,4 9,4 5,1 0,47 4,2 6,0 18,1 8,7 0,64 7,4 10,0 14,4 18,9 0,71 17,5 20,3 7,4
Belgiu m
Total 14,6 0,77 13,1 16,1 10,3 5,2 0,50 4,2 6,2 18,8 12,3 0,71 10,9 13,7 11,3 20,2 0,87 18,5 21,9 8,4
Males 13,4 0,78 11,9 14,9 11,4 4,9 0,52 3,9 5,9 20,8 11,0 0,71 9,6 12,4 12,7 18,5 0,88 16,8 20,2 9,3
Females 15,7 0,85 14,0 17,4 10,6 5,5 0,53 4,5 6,5 18,9 13,6 0,82 12,0 15,2 11,8 21,8 0,94 20,0 23,6 8,5
Bulgar ia
Total 21,7 0,88 20,0 23,4 7,9 41,7 1,08 39,6 43,8 5,1 6,9 0,61 5,7 8,1 17,3 46,0 1,08 43,9 48,1 4,6
Males 19,7 0,92 17,9 21,5 9,2 39,9 1,14 37,7 42,1 5,6 7,0 0,67 5,7 8,3 18,8 43,9 1,14 41,7 46,1 5,1
Females 23,6 0,91 21,8 25,4 7,6 43,3 1,12 41,1 45,5 5,1 6,8 0,63 5,6 8,0 18,2 47,9 1,11 45,7 50,1 4,5
Cyprus
Total 15,3 0,78 13,8 16,8 10,0 9,5 0,84 7,9 11,1 17,3 3,8 0,40 3,0 4,6 20,6 22,9 1,03 20,9 24,9 8,8
Males 13,4 0,84 11,8 15,0 12,3 9,3 0,93 7,5 11,1 19,6 3,1 0,43 2,3 3,9 27,2 20,9 1,12 18,7 23,1 10,5
Females 17,1 0,83 15,5 18,7 9,5 9,6 0,90 7,8 11,4 18,4 4,5 0,48 3,6 5,4 20,9 25,0 1,09 22,9 27,1 8,5
Czech
Republi c
Total 8,6 0,46 7,7 9,5 10,5 6,1 0,41 5,3 6,9 13,2 6,0 0,37 5,3 6,7 12,1 14,0 0,54 12,9 15,1 7,6
Males 7,5 0,51 6,5 8,5 13,3 5,8 0,45 4,9 6,7 15,2 4,8 0,38 4,1 5,5 15,5 12,3 0,59 11,1 13,5 9,4
Females 9,5 0,49 8,5 10,5 10,1 6,5 0,44 5,6 7,4 13,3 7,1 0,44 6,2 8,0 12,1 15,7 0,58 14,6 16,8 7,2
Germa ny
Total 15,5 0,38 14,8 16,2 4,8 5,4 0,25 4,9 5,9 9,1 10,8 0,36 10,1 11,5 6,5 20,0 0,42 19,2 20,8 4,1
Males 14,7 0,44 13,8 15,6 5,9 5,3 0,30 4,7 5,9 11,1 10,4 0,44 9,5 11,3 8,3 18,8 0,49 17,8 19,8 5,1
Females 16,3 0,43 15,5 17,1 5,2 5,4 0,28 4,9 5,9 10,2 11,2 0,40 10,4 12,0 7,0 21,2 0,47 20,3 22,1 4,3
Denmar k
Total 13,1 0,63 11,9 14,3 9,4 2,3 0,28 1,8 2,8 23,9 8,5 0,60 7,3 9,7 13,8 17,6 0,68 16,3 18,9 7,6
Males 12,8 0,78 11,3 14,3 11,9 2,2 0,35 1,5 2,9 31,2 8,0 0,71 6,6 9,4 17,4 17,0 0,84 15,4 18,6 9,7
Females 13,4 0,76 11,9 14,9 11,1 2,4 0,33 1,8 3,0 27,0 9,1 0,74 7,6 10,6 15,9 18,2 0,81 16,6 19,8 8,7
Estoni a
Total 19,7 0,68 18,4 21,0 6,8 6,2 0,41 5,4 7,0 13,0 5,6 0,43 4,8 6,4 15,1 23,4 0,73 22,0 24,8 6,1
Males 17,5 0,80 15,9 19,1 9,0 6,2 0,48 5,3 7,1 15,2 6,4 0,54 5,3 7,5 16,5 21,1 0,85 19,4 22,8 7,9
Females 21,6 0,77 20,1 23,1 7,0 6,3 0,47 5,4 7,2 14,6 4,7 0,48 3,8 5,6 20,0 25,5 0,83 23,9 27,1 6,4
Greece
Total 19,7 0,79 18,2 21,2 7,9 11,0 0,64 9,7 12,3 11,4 6,5 0,42 5,7 7,3 12,7 27,6 0,87 25,9 29,3 6,2
Males 19,1 0,83 17,5 20,7 8,5 10,2 0,68 8,9 11,5 13,1 5,2 0,43 4,4 6,0 16,2 26,1 0,93 24,3 27,9 7,0
Females 20,2 0,85 18,5 21,9 8,2 11,7 0,70 10,3 13,1 11,7 7,8 0,57 6,7 8,9 14,3 29,0 0,95 27,1 30,9 6,4
Spain
Total 19,5 0,52 18,5 20,5 5,2 3,5 0,26 3,0 4,0 14,6 7,0 0,35 6,3 7,7 9,8 23,4 0,54 22,3 24,5 4,5
Males 18,3 0,56 17,2 19,4 6,0 3,5 0,30 2,9 4,1 16,8 6,5 0,38 5,8 7,2 11,5 22,3 0,58 21,2 23,4 5,1
Females 20,6 0,55 19,5 21,7 5,2 3,4 0,25 2,9 3,9 14,4 7,5 0,40 6,7 8,3 10,5 24,4 0,57 23,3 25,5 4,6
8Annexes
34 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-risk-of-poverty rate (POV) Severe material deprivation rate (DEP) % of individuals aged less than 60 living in households with
very low work intensity (LWI) At-risk-of-poverty or social exclusion (AROPE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Finland
Total 13,8 0,46 12,9 14,7 6,5 2,8 0,25 2,3 3,3 17,5 8,2 0,42 7,4 9,0 10,0 (%) 0,48 16,0 17,8 5,6
Males 12,9 0,54 11,8 14,0 8,2 2,9 0,35 2,2 3,6 23,7 8,5 0,52 7,5 9,5 12,0 15,8 0,56 14,7 16,9 6,9
Females 14,7 0,53 13,7 15,7 7,1 2,7 0,24 2,2 3,2 17,4 7,9 0,45 7,0 8,8 11,2 17,9 0,56 16,8 19,0 6,1
France
Total 12,9 0,51 11,9 13,9 7,7 5,6 0,34 4,9 6,3 11,9 8,3 0,51 7,3 9,3 12,0 18,5 0,55 17,4 19,6 5,8
Males 11,9 0,54 10,8 13,0 8,9 5,2 0,40 4,4 6,0 15,1 7,6 0,53 6,6 8,6 13,7 17,1 0,59 15,9 18,3 6,8
Females 13,8 0,53 12,8 14,8 7,5 5,9 0,35 5,2 6,6 11,6 9,1 0,55 8,0 10,2 11,8 19,7 0,58 18,6 20,8 5,8
Hungar y
Total 12,4 0,53 11,4 13,4 8,4 20,3 0,64 19,0 21,6 6,2 11,3 0,52 10,3 12,3 9,0 29,6 0,69 28,2 31,0 4,6
Males 12,8 0,59 11,6 14,0 9,0 20,2 0,69 18,8 21,6 6,7 10,6 0,55 9,5 11,7 10,2 29,1 0,76 27,6 30,6 5,1
Females 12,1 0,53 11,1 13,1 8,6 20,4 0,65 19,1 21,7 6,2 11,9 0,56 10,8 13,0 9,2 30,0 0,71 28,6 31,4 4,6
Irelan d
Total 15,0 0,98 13,1 16,9 12,8 6,1 0,66 4,8 7,4 21,2 19,8 1,29 17,3 22,3 12,8 25,7 1,23 23,3 28,1 9,4
Males 14,9 1,15 12,6 17,2 15,1 5,5 0,69 4,1 6,9 24,6 18,6 1,35 16,0 21,2 14,2 25,0 1,35 22,4 27,6 10,6
Females 15,1 1,02 13,1 17,1 13,2 6,8 0,83 5,2 8,4 23,9 21,0 1,48 18,1 23,9 13,8 26,4 1,36 23,7 29,1 10,1
Icelan d
Total 10,1 0,59 8,9 11,3 11,4 0,8 0,17 0,5 1,1 41,7 2,1 0,29 1,5 2,7 27,1 11,6 0,63 10,4 12,8 10,6
Males 9,2 0,66 7,9 10,5 14,1 1,0 0,24 0,5 1,5 47,0 2,2 0,36 1,5 2,9 32,1 10,7 0,69 9,3 12,1 12,6
Females 11,0 0,74 9,5 12,5 13,2 0,6 0,19 0,2 1,0 62,1 2,0 0,36 1,3 2,7 35,3 12,6 0,78 11,1 14,1 12,1
Italy
Total 18,4 0,66 17,1 19,7 7,0 7,0 0,46 6,1 7,9 12,9 8,8 0,38 8,1 9,5 8,5 24,7 0,77 23,2 26,2 6,1
Males 17,0 0,70 15,6 18,4 8,1 6,7 0,46 5,8 7,6 13,5 7,4 0,38 6,7 8,1 10,1 22,8 0,80 21,2 24,4 6,9
Females 19,8 0,67 18,5 21,1 6,6 7,3 0,48 6,4 8,2 12,9 10,3 0,45 9,4 11,2 8,6 26,4 0,80 24,8 28,0 5,9
Lithua nia
Total 20,6 0,94 18,8 22,4 8,9 15,1 0,85 13,4 16,8 11,0 6,9 0,60 5,7 8,1 17,0 29,5 1,07 27,4 31,6 7,1
Males 19,1 1,08 17,0 21,2 11,1 14,3 0,96 12,4 16,2 13,2 7,3 0,74 5,8 8,8 19,9 27,3 1,21 24,9 29,7 8,7
Females 21,9 1,00 19,9 23,9 8,9 15,7 0,92 13,9 17,5 11,5 6,6 0,62 5,4 7,8 18,4 31,4 1,14 29,2 33,6 7,1
Luxembo urg
Total 14,9 0,93 13,1 16,7 12,2 1,1 0,21 0,7 1,5 37,4 6,3 0,58 5,2 7,4 18,0 17,8 0,97 15,9 19,7 10,7
Males 13,8 0,98 11,9 15,7 13,9 0,9 0,22 0,5 1,3 47,9 4,9 0,58 3,8 6,0 23,2 16,0 1,02 14,0 18,0 12,5
Females 16,0 1,05 13,9 18,1 12,9 1,3 0,26 0,8 1,8 39,2 7,8 0,76 6,3 9,3 19,1 19,6 1,11 17,4 21,8 11,1
Latvi a
Total 25,7 0,89 24,0 27,4 6,8 21,9 0,87 20,2 23,6 7,8 6,7 0,42 5,9 7,5 12,3 37,4 1,01 35,4 39,4 5,3
Males 24,2 1,01 22,2 26,2 8,2 21,3 0,97 19,4 23,2 8,9 7,2 0,52 6,2 8,2 14,2 35,9 1,15 33,6 38,2 6,3
Females 27,0 0,88 25,3 28,7 6,4 22,5 0,88 20,8 24,2 7,7 6,2 0,45 5,3 7,1 14,2 38,7 1,01 36,7 40,7 5,1
Malta
Total 15,3 0,67 14,0 16,6 8,6 4,7 0,43 3,9 5,5 17,9 8,3 0,53 7,3 9,3 12,5 20,2 0,76 18,7 21,7 7,4
Males 14,7 0,71 13,3 16,1 9,5 4,5 0,50 3,5 5,5 21,8 6,4 0,53 5,4 7,4 16,2 19,0 0,82 17,4 20,6 8,5
Females 15,9 0,72 14,5 17,3 8,9 4,9 0,45 4,0 5,8 18,0 10,2 0,66 8,9 11,5 12,7 21,4 0,83 19,8 23,0 7,6
Nether lands
Total 11,1 0,74 9,6 12,6 13,1 1,4 0,20 1,0 1,8 28,0 8,3 0,68 7,0 9,6 16,1 15,1 0,83 13,5 16,7 10,8
Males 10,8 0,82 9,2 12,4 14,9 1,4 0,25 0,9 1,9 35,0 7,5 0,75 6,0 9,0 19,6 14,3 0,92 12,5 16,1 12,6
Females 11,3 0,81 9,7 12,9 14,0 1,5 0,21 1,1 1,9 27,4 9,2 0,74 7,7 10,7 15,8 15,9 0,88 14,2 17,6 10,8
Annexes 8
35Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-risk-of-poverty rate (POV) Severe material deprivation rate (DEP) % of individuals aged less than 60 living in households with
very low work intensity (LWI) At-risk-of-poverty or social exclusion (AROPE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Norway
Total 11,7 0,51 10,7 12,7 8,5 2,2 0,24 1,7 2,7 21,4 6,8 0,43 6,0 7,6 12,4 15,2 0,56 14,1 16,3 7,2
Males 10,1 0,55 9,0 11,2 10,7 2,4 0,29 1,8 3,0 23,7 6,5 0,48 5,6 7,4 14,5 13,7 0,62 12,5 14,9 8,9
Females 13,2 0,67 11,9 14,5 9,9 2,0 0,28 1,5 2,5 27,4 7,0 0,56 5,9 8,1 15,7 16,8 0,72 15,4 18,2 8,4
Poland
Total 17,1 0,48 16,2 18,0 5,5 15,0 0,45 14,1 15,9 5,9 6,9 0,27 6,4 7,4 7,7 27,8 0,57 26,7 28,9 4,0
Males 16,9 0,53 15,9 17,9 6,1 14,6 0,49 13,6 15,6 6,6 6,4 0,30 5,8 7,0 9,2 27,0 0,62 25,8 28,2 4,5
Females 17,4 0,49 16,4 18,4 5,5 15,3 0,48 14,4 16,2 6,1 7,4 0,29 6,8 8,0 7,7 28,6 0,59 27,4 29,8 4,0
Portug al
Total 17,9 0,91 16,1 19,7 10,0 9,1 0,80 7,5 10,7 17,2 6,9 0,54 5,8 8,0 15,3 24,9 1,04 22,9 26,9 8,2
Males 17,3 1,01 15,3 19,3 11,4 8,9 0,83 7,3 10,5 18,3 6,6 0,59 5,4 7,8 17,5 24,0 1,11 21,8 26,2 9,1
Females 18,4 0,91 16,6 20,2 9,7 9,2 0,83 7,6 10,8 17,7 7,3 0,60 6,1 8,5 16,1 25,8 1,08 23,7 27,9 8,2
Romania
Total 22,4 1,17 20,1 24,7 10,2 32,1 1,27 29,6 34,6 7,8 7,7 0,59 6,5 8,9 15,0 42,9 1,30 40,4 45,4 5,9
Males 21,4 1,18 19,1 23,7 10,8 31,7 1,32 29,1 34,3 8,2 6,5 0,57 5,4 7,6 17,2 41,7 1,34 39,1 44,3 6,3
Females 23,3 1,23 20,9 25,7 10,3 32,5 1,29 30,0 35,0 7,8 8,9 0,66 7,6 10,2 14,5 44,1 1,34 41,5 46,7 6,0
Sweden
Total 13,3 0,48 12,4 14,2 7,1 1,6 0,16 1,3 1,9 19,6 6,2 0,37 5,5 6,9 11,7 15,9 0,50 14,9 16,9 6,2
Males 12,0 0,56 10,9 13,1 9,1 1,5 0,19 1,1 1,9 24,8 5,9 0,41 5,1 6,7 13,6 14,4 0,58 13,3 15,5 7,9
Females 14,5 0,57 13,4 15,6 7,7 1,6 0,20 1,2 2,0 24,5 6,6 0,48 5,7 7,5 14,3 17,5 0,60 16,3 18,7 6,7
Slovenia
Total 11,3 0,39 10,5 12,1 6,8 6,1 0,29 5,5 6,7 9,3 5,6 0,29 5,0 6,2 10,2 17,1 0,45 16,2 18,0 5,2
Males 9,8 0,42 9,0 10,6 8,4 5,9 0,32 5,3 6,5 10,6 4,8 0,32 4,2 5,4 13,1 15,1 0,50 14,1 16,1 6,5
Females 12,8 0,45 11,9 13,7 6,9 6,3 0,31 5,7 6,9 9,6 6,5 0,34 5,8 7,2 10,3 19,1 0,51 18,1 20,1 5,2
Slovakia
Total 11,0 0,50 10,0 12,0 8,9 11,1 0,49 10,1 12,1 8,7 5,6 0,38 4,9 6,3 13,3 19,6 0,60 18,4 20,8 6,0
Males 10,1 0,56 9,0 11,2 10,9 10,5 0,54 9,4 11,6 10,1 5,1 0,42 4,3 5,9 16,1 18,0 0,68 16,7 19,3 7,4
Females 11,8 0,52 10,8 12,8 8,6 11,6 0,51 10,6 12,6 8,6 6,0 0,41 5,2 6,8 13,4 21,1 0,63 19,9 22,3 5,9
United
Kingdo m
Total 17,3 0,66 16,0 18,6 7,5 3,3 0,29 2,7 3,9 17,2 12,6 0,62 11,4 13,8 9,6 22,0 0,70 20,6 23,4 6,2
Males 16,7 0,73 15,3 18,1 8,6 3,4 0,33 2,8 4,0 19,0 12,0 0,66 10,7 13,3 10,8 21,1 0,77 19,6 22,6 7,2
Females 17,8 0,68 16,5 19,1 7,5 3,3 0,30 2,7 3,9 17,8 13,3 0,69 11,9 14,7 10,2 22,9 0,73 21,5 24,3 6,2
Source: authors’ c alculations based on the anony mised EU-SILC mic ro- data les provided by Eu rostat for statistical/re search purposes only (Vers ion 01-03-13)
8Annexes
36 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Table 1c: Standard error estimates for the at-risk-of-poverty or social exclusion indicator (AROPE) and its three sub-indicators, 2010
At-ri sk-of -pove rty r ate (POV ) Severe mate rial de priva tion ra te (DEP) % of in dividu als ag ed less t han 60 li ving in ho use-
holds w ith ver y low work inten sity (LW I) At-risk- of-povert y or social exclus ion (ARO PE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Austri a
Total 12,1 0,55 11,0 13,2 8,9 4,3 0,36 3,6 5,0 16,4 7,7 0,47 6,8 8,6 12,0 16,6 0,62 15,4 17,8 7,3
Males 10,7 0,59 9,5 11,9 10,8 3,9 0,41 3,1 4,7 20,6 6,7 0,54 5,6 7,8 15,8 14,7 0,69 13,3 16,1 9,2
Females 13,5 0,63 12,3 14,7 9,1 4,6 0,38 3,9 5,3 16,2 8,8 0,56 7,7 9,9 12,5 18,4 0,69 17,0 19,8 7,4
Belgiu m
Total 14,6 0,75 13,1 16,1 10,1 5,9 0,57 4,8 7,0 18,9 12,6 0,73 11,2 14,0 11,4 20,8 0,94 19,0 22,6 8,9
Males 13,9 0,79 12,4 15,4 11,1 5,7 0,60 4,5 6,9 20,6 11,8 0,75 10,3 13,3 12,5 20,0 1,00 18,0 22,0 9,8
Females 15,2 0,80 13,6 16,8 10,3 6,0 0,58 4,9 7,1 18,9 13,5 0,85 11,8 15,2 12,3 21,7 0,98 19,8 23,6 8,9
Bulgar ia
Total 20,6 0,88 18,9 22,3 8,4 45,6 1,06 43,5 47,7 4,6 7,9 0,63 6,7 9,1 15,6 49,0 1,05 46,9 51,1 4,2
Males 18,9 0,90 17,1 20,7 9,3 44,1 1,12 41,9 46,3 5,0 7,7 0,64 6,4 9,0 16,3 47,1 1,12 44,9 49,3 4,7
Females 22,2 0,93 20,4 24,0 8,2 47,1 1,08 45,0 49,2 4,5 8,1 0,68 6,8 9,4 16,5 50,8 1,08 48,7 52,9 4,2
Cyprus
Total 15,3 0,68 14,0 16,6 8,7 9,6 0,60 8,4 10,8 12,3 4,4 0,38 3,7 5,1 16,9 22,9 0,82 21,3 24,5 7,0
Males 13,8 0,74 12,3 15,3 10,5 9,8 0,68 8,5 11,1 13,6 4,0 0,48 3,1 4,9 23,5 21,5 0,90 19,7 23,3 8,2
Females 16,8 0,73 15,4 18,2 8,5 9,5 0,61 8,3 10,7 12,6 4,8 0,42 4,0 5,6 17,2 24,4 0,88 22,7 26,1 7,1
Czech
Republi c
Total 9,0 0,44 8,1 9,9 9,6 6,2 0,42 5,4 7,0 13,3 6,4 0,40 5,6 7,2 12,3 14,4 0,53 13,4 15,4 7,2
Males 8,0 0,50 7,0 9,0 12,3 5,8 0,46 4,9 6,7 15,5 5,2 0,42 4,4 6,0 15,8 12,7 0,58 11,6 13,8 9,0
Females 10,0 0,47 9,1 10,9 9,2 6,5 0,43 5,7 7,3 13,0 7,6 0,47 6,7 8,5 12,1 16,0 0,57 14,9 17,1 7,0
Germa ny
Total 15,6 0,38 14,9 16,3 4,8 4,5 0,23 4,0 5,0 10,0 11,1 0,36 10,4 11,8 6,4 19,7 0,41 18,9 20,5 4,1
Males 14,9 0,43 14,1 15,7 5,7 4,4 0,27 3,9 4,9 12,0 10,7 0,43 9,9 11,5 7,9 18,6 0,47 17,7 19,5 5,0
Females 16,4 0,43 15,6 17,2 5,1 4,7 0,26 4,2 5,2 10,8 11,6 0,43 10,8 12,4 7,3 20,9 0,46 20,0 21,8 4,3
Denmar k
Total 13,3 0,68 12,0 14,6 10,0 2,7 0,33 2,1 3,3 24,0 10,3 0,68 9,0 11,6 12,9 18,3 0,72 16,9 19,7 7,7
Males 13,1 0,83 11,5 14,7 12,4 2,8 0,43 2,0 3,6 30,1 9,4 0,83 7,8 11,0 17,3 17,7 0,88 16,0 19,4 9,7
Females 13,4 0,82 11,8 15,0 12,0 2,5 0,38 1,8 3,2 29,8 11,1 0,84 9,5 12,7 14,8 19,0 0,88 17,3 20,7 9,1
Estoni a
Total 15,8 0,61 14,6 17,0 7,6 9,0 0,53 8,0 10,0 11,5 8,9 0,55 7,8 10,0 12,1 21,7 0,71 20,3 23,1 6,4
Males 15,4 0,71 14,0 16,8 9,0 9,3 0,64 8,0 10,6 13,5 9,6 0,67 8,3 10,9 13,7 21,5 0,84 19,9 23,1 7,7
Females 16,2 0,69 14,8 17,6 8,3 8,7 0,55 7,6 9,8 12,4 8,2 0,62 7,0 9,4 14,8 22,0 0,78 20,5 23,5 6,9
Greece
Total 20,1 0,92 18,3 21,9 9,0 11,6 0,73 10,2 13,0 12,3 7,5 0,58 6,4 8,6 15,2 27,7 1,02 25,7 29,7 7,2
Males 19,3 0,97 17,4 21,2 9,9 10,9 0,80 9,3 12,5 14,4 6,4 0,58 5,3 7,5 17,8 26,0 1,07 23,9 28,1 8,1
Females 20,9 0,99 19,0 22,8 9,3 12,2 0,77 10,7 13,7 12,4 8,5 0,72 7,1 9,9 16,6 29,3 1,11 27,1 31,5 7,4
Spain
Total 20,7 0,51 19,7 21,7 4,8 4,0 0,25 3,5 4,5 12,3 9,8 0,38 9,1 10,5 7,6 25,5 0,54 24,4 26,6 4,2
Males 20,1 0,53 19,1 21,1 5,2 3,8 0,25 3,3 4,3 12,9 9,5 0,41 8,7 10,3 8,5 24,9 0,57 23,8 26,0 4,5
Females 21,3 0,54 20,2 22,4 5,0 4,1 0,28 3,6 4,6 13,4 10,1 0,43 9,3 10,9 8,3 26,1 0,58 25,0 27,2 4,4
Annexes 8
37Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-ri sk-of -pove rty r ate (POV ) Severe mate rial de priva tion ra te (DEP) % of in dividu als ag ed less t han 60 li ving in ho use-
holds w ith ver y low work inten sity (LW I) At-risk- of-povert y or social exclus ion (ARO PE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Finland
Total 13,1 0,42 12,3 13,9 6,3 2,8 0,21 2,4 3,2 14,7 9,1 0,40 8,3 9,9 8,6 16,9 0,47 16,0 17,8 5,5
Males 12,4 0,48 11,5 13,3 7,6 2,6 0,25 2,1 3,1 18,8 9,4 0,46 8,5 10,3 9,6 16,0 0,53 15,0 17,0 6,5
Females 13,8 0,51 12,8 14,8 7,2 3,1 0,27 2,6 3,6 17,1 8,8 0,49 7,8 9,8 10,9 17,7 0,56 16,6 18,8 6,2
France
Total 13,3 0,56 12,2 14,4 8,3 5,8 0,40 5,0 6,6 13,5 9,8 0,43 9,0 10,6 8,6 19,2 0,58 18,1 20,3 5,9
Males 12,6 0,62 11,4 13,8 9,6 5,7 0,39 4,9 6,5 13,4 9,2 0,46 8,3 10,1 9,8 18,3 0,67 17,0 19,6 7,2
Females 13,9 0,57 12,8 15,0 8,0 5,8 0,50 4,8 6,8 16,9 10,5 0,50 9,5 11,5 9,3 20,0 0,59 18,8 21,2 5,8
Hungar y
Total 12,3 0,64 11,0 13,6 10,2 21,6 0,75 20,1 23,1 6,8 11,8 0,57 10,7 12,9 9,5 29,9 0,80 28,3 31,5 5,2
Males 12,6 0,70 11,2 14,0 10,9 21,5 0,79 20,0 23,0 7,2 11,2 0,62 10,0 12,4 10,9 29,4 0,85 27,7 31,1 5,7
Females 12,0 0,64 10,7 13,3 10,5 21,6 0,77 20,1 23,1 7,0 12,5 0,59 11,3 13,7 9,3 30,3 0,82 28,7 31,9 5,3
Irelan d
Total 16,1 0,98 14,2 18,0 11,9 7,5 0,67 6,2 8,8 17,5 22,9 1,20 20,5 25,3 10,3 29,9 1,17 27,6 32,2 7,7
Males 15,9 1,03 13,9 17,9 12,7 7,1 0,68 5,8 8,4 18,8 21,5 1,29 19,0 24,0 11,8 29,3 1,27 26,8 31,8 8,5
Females 16,2 1,14 14,0 18,4 13,8 8,0 0,81 6,4 9,6 19,8 24,4 1,38 21,7 27,1 11,1 30,5 1,33 27,9 33,1 8,5
Icelan d
Total 9,8 0,61 8,6 11,0 12,2 1,8 0,28 1,3 2,3 30,5 5,6 0,51 4,6 6,6 17,9 13,7 0,69 12,3 15,1 9,9
Males 9,8 0,68 8,5 11,1 13,6 1,6 0,29 1,0 2,2 35,5 5,5 0,59 4,3 6,7 21,0 13,4 0,78 11,9 14,9 11,4
Females 9,8 0,72 8,4 11,2 14,4 2,0 0,38 1,3 2,7 37,2 5,7 0,63 4,5 6,9 21,7 14,0 0,83 12,4 15,6 11,6
Italy
Total 18,2 0,70 16,8 19,6 7,5 6,9 0,54 5,8 8,0 15,3 10,2 0,40 9,4 11,0 7,7 24,5 0,81 22,9 26,1 6,5
Males 16,8 0,74 15,3 18,3 8,6 6,7 0,55 5,6 7,8 16,1 8,8 0,42 8,0 9,6 9,4 22,6 0,85 20,9 24,3 7,4
Females 19,5 0,71 18,1 20,9 7,1 7,1 0,56 6,0 8,2 15,5 11,6 0,46 10,7 12,5 7,8 26,3 0,82 24,7 27,9 6,1
Lithua nia
Total 20,2 1,03 18,2 22,2 10,0 19,5 1,07 17,4 21,6 10,8 9,2 0,66 7,9 10,5 14,1 33,4 1,21 31,0 35,8 7,1
Males 20,7 1,21 18,3 23,1 11,5 19,5 1,30 17,0 22,0 13,1 9,6 0,77 8,1 11,1 15,7 32,9 1,42 30,1 35,7 8,5
Females 19,8 1,07 17,7 21,9 10,6 19,5 1,04 17,5 21,5 10,5 8,7 0,84 7,1 10,3 18,9 33,8 1,24 31,4 36,2 7,2
Luxembo urg
Total 14,5 0,83 12,9 16,1 11,2 0,5 0,13 0,2 0,8 51,0 5,5 0,42 4,7 6,3 15,0 17,1 0,86 15,4 18,8 9,9
Males 14,6 0,90 12,8 16,4 12,1 0,4 0,13 0,1 0,7 63,7 4,8 0,46 3,9 5,7 18,8 16,5 0,92 14,7 18,3 10,9
Females 14,4 0,91 12,6 16,2 12,4 0,7 0,19 0,3 1,1 53,2 6,3 0,51 5,3 7,3 15,9 17,7 0,94 15,9 19,5 10,4
Latvi a
Total 21,3 0,82 19,7 22,9 7,5 27,4 0,89 25,7 29,1 6,4 12,2 0,73 10,8 13,6 11,7 38,1 0,96 36,2 40,0 4,9
Males 21,7 0,96 19,8 23,6 8,7 26,8 1,02 24,8 28,8 7,5 13,4 0,87 11,7 15,1 12,7 37,6 1,11 35,4 39,8 5,8
Females 21,0 0,79 19,5 22,5 7,4 27,9 0,89 26,2 29,6 6,3 11,0 0,69 9,6 12,4 12,3 38,5 0,95 36,6 40,4 4,8
Malta
Total 15,0 0,72 13,6 16,4 9,4 5,7 0,47 4,8 6,6 16,2 8,3 0,51 7,3 9,3 12,0 20,3 0,79 18,8 21,8 7,6
Males 14,5 0,77 13,0 16,0 10,4 5,6 0,52 4,6 6,6 18,2 6,6 0,52 5,6 7,6 15,4 19,4 0,85 17,7 21,1 8,6
Females 15,5 0,77 14,0 17,0 9,7 5,8 0,51 4,8 6,8 17,2 10,0 0,65 8,7 11,3 12,7 21,2 0,85 19,5 22,9 7,9
8Annexes
38 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-ri sk-of -pove rty r ate (POV ) Severe mate rial de priva tion ra te (DEP) % of in dividu als ag ed less t han 60 li ving in ho use-
holds w ith ver y low work inten sity (LW I) At-risk- of-povert y or social exclus ion (ARO PE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Nether lands
Total 10,3 0,67 9,0 11,6 12,7 2,2 0,47 1,3 3,1 41,9 8,2 0,73 6,8 9,6 17,4 15,1 0,88 13,4 16,8 11,4
Males 9,7 0,65 8,4 11,0 13,1 2,3 0,52 1,3 3,3 44,3 7,3 0,76 5,8 8,8 20,4 14,1 0,90 12,3 15,9 12,5
Females 10,8 0,78 9,3 12,3 14,2 2,2 0,47 1,3 3,1 41,9 9,1 0,88 7,4 10,8 19,0 16,0 0,99 14,1 17,9 12,1
Norway
Total 11,2 0,52 10,2 12,2 9,1 2,0 0,25 1,5 2,5 24,5 7,3 0,45 6,4 8,2 12,1 14,9 0,57 13,8 16,0 7,5
Males 10,1 0,58 9,0 11,2 11,3 2,2 0,30 1,6 2,8 26,7 7,2 0,53 6,2 8,2 14,4 13,8 0,64 12,5 15,1 9,1
Females 12,2 0,66 10,9 13,5 10,6 1,9 0,29 1,3 2,5 29,9 7,3 0,57 6,2 8,4 15,3 15,9 0,72 14,5 17,3 8,9
Poland
Total 17,6 0,47 16,7 18,5 5,2 14,2 0,45 13,3 15,1 6,2 7,3 0,29 6,7 7,9 7,8 27,8 0,53 26,8 28,8 3,7
Males 17,4 0,53 16,4 18,4 6,0 14,1 0,49 13,1 15,1 6,8 6,7 0,34 6,0 7,4 9,9 27,0 0,59 25,8 28,2 4,3
Females 17,7 0,48 16,8 18,6 5,3 14,4 0,48 13,5 15,3 6,5 8,0 0,30 7,4 8,6 7,4 28,5 0,55 27,4 29,6 3,8
Portug al
Total 17,9 0,94 16,1 19,7 10,3 9,0 0,69 7,6 10,4 15,0 8,6 0,66 7,3 9,9 15,0 25,3 1,00 23,3 27,3 7,7
Males 17,3 0,99 15,4 19,2 11,2 9,2 0,77 7,7 10,7 16,4 8,4 0,75 6,9 9,9 17,5 24,8 1,09 22,7 26,9 8,6
Females 18,4 0,96 16,5 20,3 10,2 8,8 0,68 7,5 10,1 15,1 8,8 0,69 7,4 10,2 15,4 25,8 1,03 23,8 27,8 7,8
Romania
Total 21,0 1,08 18,9 23,1 10,1 30,9 1,25 28,5 33,4 7,9 6,8 0,53 5,8 7,8 15,3 41,4 1,28 38,9 43,9 6,1
Males 20,7 1,12 18,5 22,9 10,6 30,6 1,28 28,1 33,1 8,2 6,0 0,54 4,9 7,1 17,6 40,7 1,32 38,1 43,3 6,4
Females 21,4 1,10 19,2 23,6 10,1 31,2 1,30 28,7 33,7 8,2 7,7 0,57 6,6 8,8 14,5 42,0 1,32 39,4 44,6 6,2
Sweden
Total 12,9 0,44 12,0 13,8 6,7 1,3 0,14 1,0 1,6 21,1 5,9 0,36 5,2 6,6 12,0 15,0 0,46 14,1 15,9 6,0
Males 11,4 0,49 10,4 12,4 8,4 1,2 0,16 0,9 1,5 26,1 5,7 0,42 4,9 6,5 14,4 13,4 0,52 12,4 14,4 7,6
Females 14,3 0,55 13,2 15,4 7,5 1,4 0,18 1,0 1,8 25,2 6,1 0,43 5,3 6,9 13,8 16,6 0,58 15,5 17,7 6,8
Slovenia
Total 12,7 0,43 11,9 13,5 6,6 5,9 0,30 5,3 6,5 10,0 6,9 0,34 6,2 7,6 9,7 18,3 0,48 17,4 19,2 5,1
Males 11,3 0,49 10,3 12,3 8,5 5,6 0,34 4,9 6,3 11,9 6,0 0,41 5,2 6,8 13,4 16,5 0,56 15,4 17,6 6,7
Females 14,1 0,49 13,1 15,1 6,8 6,3 0,36 5,6 7,0 11,2 8,0 0,42 7,2 8,8 10,3 20,1 0,55 19,0 21,2 5,4
Slovakia
Total 12,0 0,57 10,9 13,1 9,3 11,4 0,55 10,3 12,5 9,5 7,9 0,52 6,9 8,9 12,9 20,6 0,67 19,3 21,9 6,4
Males 11,7 0,65 10,4 13,0 10,9 11,1 0,61 9,9 12,3 10,8 7,4 0,57 6,3 8,5 15,1 19,6 0,76 18,1 21,1 7,6
Females 12,2 0,58 11,1 13,3 9,3 11,8 0,56 10,7 12,9 9,3 8,4 0,55 7,3 9,5 12,8 21,6 0,69 20,2 23,0 6,3
United
Kingdo m
Total 17,1 0,59 15,9 18,3 6,8 4,8 0,36 4,1 5,5 14,7 13,1 0,63 11,9 14,3 9,4 23,1 0,67 21,8 24,4 5,7
Males 16,4 0,68 15,1 17,7 8,1 4,8 0,40 4,0 5,6 16,3 12,4 0,70 11,0 13,8 11,1 22,1 0,77 20,6 23,6 6,8
Females 17,8 0,61 16,6 19,0 6,7 4,9 0,40 4,1 5,7 16,0 13,9 0,70 12,5 15,3 9,9 24,2 0,71 22,8 25,6 5,8
Source: authors’ c alculations based on the anony mised EU-SILC mic ro- data les provided by Eu rostat for statistical/re search purposes only (Vers ion 01-03-13)
Annexes 8
39Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
Table 1d: Standard error estimates for the at-risk-of-poverty or social exclusion indicator (AROPE) and its three sub-indicators, 2011
At-ri sk-of -pove rty r ate (POV ) Severe ma teria l depr ivati on rate (D EP) % of indiv idual s aged le ss than 6 0 living in house -
holds w ith ver y low work inten sity (LW I) At-risk- of-povert y or social exclus ion (ARO PE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Austri a
Total 12,6 0,58 11,5 13,7 9,0 3,9 0,35 3,2 4,6 17,6 8,0 0,51 7,0 9,0 12,5 16,9 0,63 15,7 18,1 7,3
Males 11,7 0,68 10,4 13,0 11,4 3,5 0,38 2,8 4,2 21,3 7,0 0,56 5,9 8,1 15,7 15,2 0,73 13,8 16,6 9,4
Females 13,5 0,62 12,3 14,7 9,0 4,3 0,40 3,5 5,1 18,2 9,1 0,61 7,9 10,3 13,1 18,5 0,68 17,2 19,8 7,2
Belgiu m
Total 15,3 0,86 13,6 17,0 11,0 5,7 0,53 4,7 6,7 18,2 13,7 0,87 12,0 15,4 12,4 21,0 0,98 19,1 22,9 9,1
Males 14,6 0,93 12,8 16,4 12,5 5,9 0,63 4,7 7,1 20,9 13,2 0,93 11,4 15,0 13,8 20,4 1,07 18,3 22,5 10,3
Females 16,0 0,89 14,3 17,7 10,9 5,4 0,51 4,4 6,4 18,5 14,3 0,96 12,4 16,2 13,2 21,5 1,00 19,5 23,5 9,1
Bulgar ia
Total 22,2 0,97 20,3 24,1 8,6 43,5 1,07 41,4 45,6 4,8 11,0 0,75 9,5 12,5 13,4 49,0 1,07 46,9 51,1 4,3
Males 20,8 1,00 18,8 22,8 9,4 42,4 1,13 40,2 44,6 5,2 11,1 0,78 9,6 12,6 13,8 47,6 1,14 45,4 49,8 4,7
Females 23,5 0,99 21,6 25,4 8,3 44,6 1,10 42,4 46,8 4,8 10,9 0,79 9,4 12,4 14,2 50,4 1,10 48,2 52,6 4,3
Switz erland
Total 15,0 0,57 13,9 16,1 7,4 1,0 0,26 0,5 1,5 51,0 4,7 0,41 3,9 5,5 17,1 17,2 0,61 16,0 18,4 7,0
Males 13,7 0,63 12,5 14,9 9,0 1,1 0,40 0,3 1,9 71,3 4,1 0,44 3,2 5,0 21,0 15,6 0,72 14,2 17,0 9,0
Females 16,3 0,60 15,1 17,5 7,2 0,9 0,18 0,5 1,3 39,2 5,2 0,47 4,3 6,1 17,7 18,7 0,63 17,5 19,9 6,6
Cyprus
Total 14,5 0,66 13,2 15,8 8,9 10,7 0,70 9,3 12,1 12,8 4,5 0,36 3,8 5,2 15,7 23,5 0,85 21,8 25,2 7,1
Males 12,6 0,71 11,2 14,0 11,0 10,6 0,77 9,1 12,1 14,2 4,0 0,43 3,2 4,8 21,1 21,5 0,92 19,7 23,3 8,4
Females 16,3 0,72 14,9 17,7 8,7 10,7 0,74 9,2 12,2 13,6 5,0 0,40 4,2 5,8 15,7 25,4 0,92 23,6 27,2 7,1
Czech
Republi c
Total 9,8 0,49 8,8 10,8 9,8 6,1 0,41 5,3 6,9 13,2 6,6 0,43 5,8 7,4 12,8 15,3 0,57 14,2 16,4 7,3
Males 8,9 0,55 7,8 10,0 12,1 5,6 0,42 4,8 6,4 14,7 5,8 0,48 4,9 6,7 16,2 13,7 0,62 12,5 14,9 8,9
Females 10,6 0,52 9,6 11,6 9,6 6,7 0,45 5,8 7,6 13,2 7,4 0,47 6,5 8,3 12,4 16,9 0,60 15,7 18,1 7,0
Germa ny
Total 15,8 0,38 15,1 16,5 4,7 5,3 0,23 4,8 5,8 8,5 11,1 0,38 10,4 11,8 6,7 19,9 0,41 19,1 20,7 4,0
Males 14,9 0,43 14,1 15,7 5,7 5,0 0,26 4,5 5,5 10,2 10,4 0,43 9,6 11,2 8,1 18,5 0,46 17,6 19,4 4,9
Females 16,8 0,44 15,9 17,7 5,1 5,7 0,27 5,2 6,2 9,3 11,8 0,45 10,9 12,7 7,5 21,3 0,47 20,4 22,2 4,3
Denmar k
Total 13,0 0,71 11,6 14,4 10,7 2,6 0,35 1,9 3,3 26,4 11,4 0,76 9,9 12,9 13,1 18,9 0,77 17,4 20,4 8,0
Males 13,0 0,88 11,3 14,7 13,3 2,0 0,35 1,3 2,7 34,3 10,7 0,90 8,9 12,5 16,5 18,2 0,94 16,4 20,0 10,1
Females 13,0 0,86 11,3 14,7 13,0 3,3 0,49 2,3 4,3 29,1 12,0 0,93 10,2 13,8 15,2 19,5 0,95 17,6 21,4 9,5
Estoni a
Total 17,5 0,65 16,2 18,8 7,3 8,7 0,48 7,8 9,6 10,8 9,9 0,57 8,8 11,0 11,3 23,1 0,73 21,7 24,5 6,2
Males 17,6 0,77 16,1 19,1 8,6 8,8 0,55 7,7 9,9 12,3 10,8 0,69 9,4 12,2 12,5 23,2 0,86 21,5 24,9 7,3
Females 17,4 0,72 16,0 18,8 8,1 8,6 0,53 7,6 9,6 12,1 9,1 0,65 7,8 10,4 14,0 22,9 0,80 21,3 24,5 6,8
Greece
Total 21,4 0,78 19,9 22,9 7,1 15,2 0,77 13,7 16,7 9,9 11,8 0,69 10,4 13,2 11,5 31,0 0,94 29,2 32,8 5,9
Males 20,9 0,84 19,3 22,5 7,9 14,9 0,81 13,3 16,5 10,7 10,9 0,75 9,4 12,4 13,5 29,6 1,00 27,6 31,6 6,6
Females 21,9 0,82 20,3 23,5 7,3 15,4 0,81 13,8 17,0 10,3 12,8 0,76 11,3 14,3 11,6 32,3 0,99 30,4 34,2 6,0
Spain
Total 21,8 0,55 20,7 22,9 4,9 3,9 0,27 3,4 4,4 13,6 12,2 0,45 11,3 13,1 7,2 27,0 0,58 25,9 28,1 4,2
Males 21,1 0,57 20,0 22,2 5,3 3,7 0,26 3,2 4,2 13,8 11,8 0,49 10,8 12,8 8,1 26,6 0,63 25,4 27,8 4,6
Females 22,4 0,58 21,3 23,5 5,1 4,0 0,31 3,4 4,6 15,2 12,6 0,52 11,6 13,6 8,1 27,3 0,61 26,1 28,5 4,4
8Annexes
40 Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-ri sk-of -pove rty r ate (POV ) Severe ma teria l depr ivati on rate (D EP) % of indiv idual s aged le ss than 6 0 living in house -
holds w ith ver y low work inten sity (LW I) At-risk- of-povert y or social exclus ion (ARO PE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Finland
Total 13,7 0,45 12,8 14,6 6,4 3,2 0,24 2,7 3,7 14,7 9,8 0,45 8,9 10,7 9,0 17,9 0,50 16,9 18,9 5,5
Males 13,2 0,52 12,2 14,2 7,7 3,2 0,29 2,6 3,8 17,8 10,2 0,53 9,2 11,2 10,2 17,3 0,58 16,2 18,4 6,6
Females 14,2 0,53 13,2 15,2 7,3 3,2 0,28 2,7 3,7 17,2 9,3 0,52 8,3 10,3 11,0 18,5 0,59 17,3 19,7 6,3
France
Total 14,0 0,49 13,0 15,0 6,9 5,2 0,32 4,6 5,8 12,1 9,3 0,41 8,5 10,1 8,6 19,3 0,54 18,2 20,4 5,5
Males 13,5 0,53 12,5 14,5 7,7 5,1 0,34 4,4 5,8 13,1 9,0 0,46 8,1 9,9 10,0 18,6 0,61 17,4 19,8 6,4
Females 14,5 0,51 13,5 15,5 6,9 5,4 0,35 4,7 6,1 12,7 9,7 0,45 8,8 10,6 9,1 19,9 0,57 18,8 21,0 5,6
Hungar y
Total 13,8 0,61 12,6 15,0 8,7 23,1 0,75 21,6 24,6 6,4 12,1 0,58 11,0 13,2 9,4 31,0 0,79 29,5 32,5 5,0
Males 14,1 0,67 12,8 15,4 9,3 22,7 0,80 21,1 24,3 6,9 11,8 0,63 10,6 13,0 10,5 30,5 0,85 28,8 32,2 5,5
Females 13,6 0,61 12,4 14,8 8,8 23,5 0,75 22,0 25,0 6,3 12,4 0,59 11,2 13,6 9,3 31,4 0,78 29,9 32,9 4,9
Icelan d
Total 9,2 0,60 8,0 10,4 12,8 2,1 0,27 1,6 2,6 25,2 6,2 0,56 5,1 7,3 17,7 13,7 0,70 12,3 15,1 10,0
Males 9,0 0,65 7,7 10,3 14,2 2,0 0,30 1,4 2,6 29,4 6,0 0,61 4,8 7,2 19,9 13,3 0,77 11,8 14,8 11,3
Females 9,4 0,75 7,9 10,9 15,6 2,1 0,35 1,4 2,8 32,7 6,4 0,70 5,0 7,8 21,4 14,1 0,87 12,4 15,8 12,1
Italy
Total 19,6 0,73 18,2 21,0 7,3 11,2 0,59 10,0 12,4 10,3 10,4 0,51 9,4 11,4 9,6 28,2 0,89 26,5 29,9 6,2
Males 18,3 0,75 16,8 19,8 8,0 10,9 0,60 9,7 12,1 10,8 9,2 0,53 8,2 10,2 11,3 26,4 0,91 24,6 28,2 6,8
Females 20,8 0,75 19,3 22,3 7,1 11,5 0,61 10,3 12,7 10,4 11,6 0,55 10,5 12,7 9,3 29,9 0,91 28,1 31,7 6,0
Lithua nia
Total 20,0 1,07 17,9 22,1 10,5 18,5 0,93 16,7 20,3 9,9 12,3 0,93 10,5 14,1 14,8 33,4 1,22 31,0 35,8 7,2
Males 19,8 1,25 17,4 22,3 12,4 18,1 1,08 16,0 20,2 11,7 12,5 1,08 10,4 14,6 16,9 33,2 1,44 30,4 36,0 8,5
Females 20,1 1,11 17,9 22,3 10,8 18,8 0,98 16,9 20,7 10,2 12,2 1,05 10,1 14,3 16,9 33,6 1,23 31,2 36,0 7,2
Luxembo urg
Total 13,6 0,81 12,0 15,2 11,7 1,2 0,22 0,8 1,6 35,9 5,8 0,41 5,0 6,6 13,9 16,8 0,83 15,2 18,4 9,7
Males 12,7 0,78 11,2 14,2 12,0 1,3 0,25 0,8 1,8 37,7 5,1 0,47 4,2 6,0 18,1 15,6 0,83 14,0 17,2 10,4
Females 14,5 0,96 12,6 16,4 13,0 1,1 0,25 0,6 1,6 44,5 6,6 0,52 5,6 7,6 15,4 18,0 0,98 16,1 19,9 10,7
Latvi a
Total 19,3 0,71 17,9 20,7 7,2 30,9 0,89 29,2 32,6 5,6 12,2 0,58 11,1 13,3 9,3 40,1 0,91 38,3 41,9 4,4
Males 20,0 0,81 18,4 21,6 7,9 30,4 0,98 28,5 32,3 6,3 12,8 0,66 11,5 14,1 10,1 39,8 1,02 37,8 41,8 5,0
Females 18,7 0,71 17,3 20,1 7,4 31,4 0,91 29,6 33,2 5,7 11,5 0,63 10,3 12,7 10,7 40,4 0,93 38,6 42,2 4,5
Malta
Total 15,4 0,69 14,0 16,8 8,8 6,3 0,46 5,4 7,2 14,3 8,1 0,51 7,1 9,1 12,3 21,4 0,77 19,9 22,9 7,1
Males 15,0 0,76 13,5 16,5 9,9 6,2 0,54 5,1 7,3 17,1 6,6 0,56 5,5 7,7 16,6 20,6 0,86 18,9 22,3 8,2
Females 15,8 0,73 14,4 17,2 9,1 6,4 0,48 5,5 7,3 14,7 9,7 0,62 8,5 10,9 12,5 22,2 0,82 20,6 23,8 7,2
Annexes 8
41Standard error estimation for the EU-SILC indicators of pover ty and social exclusion
At-ri sk-of -pove rty r ate (POV ) Severe ma teria l depr ivati on rate (D EP) % of indiv idual s aged le ss than 6 0 living in house -
holds w ith ver y low work inten sity (LW I) At-risk- of-povert y or social exclus ion (ARO PE)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence
interval at
95%
- lower
bound
Condence
interval at
95%
- upper
bound
Relative
margin
of error
(%)
Indicator
value
(%)
Estimated
standard
error (%
points
Condence