Overview of Census Evaluation
through Demographic Analysis
Pres. 3
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Uses of Demographic Methods of Evaluation
 To complement results of matching methods of
evaluation to provide further information on likelihood of
errors in census data
 To assess the quality of census data where no matching
methods have been implemented
 Data can be from a single or multiple censuses or in
combination with other sources, e.g., surveys
 Suitability of demographic methods depends on
availability of information and on absence or presence of
abrupt changes in population
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Selected Demographic Methods
Presentation briefly covers five categories of methods
 Analyses of Age and Sex Distributions
 Stable Population Analysis of Age Distributions
 Comparison of Successive Censuses using Actual Data on
Components of Population Change
 Comparison of Successive Censuses using Estimates of
Components of Population Change
 Analysis of Cohort Survival Rates
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions
 Reasonableness of the age-sex distribution of enumerated
population provides information on quality of the census
 Age-sex distribution for a given level of fertility, mortality
and international migration follows a predictable pattern
 Unexplained departures from expected distributions signify
existence of errors in census enumeration
 Limitation of age-sex analysis is difficulty to derive direct
estimates of coverage and content error rates and often
require use of other methods, e.g., PES to verify findings
 It is also difficult to explain source of observed discrepancy
between constructed and census enumeration distributions
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Selected Methods:
 Ratios and indices providing numeric departures of recorded
age-sex distributions from expected distributions
 Graphic presentation (population pyramid; cohort analysis)
 Age ratios
 Sex ratios
 Summary indices
 Whipples and Myers’ indices (digit preference/age heaping)
 Age-sex accuracy index
 Stable population theory (stable age distribution)
 Quasi-stable population methods due to declining mortality
 Internal consistency (e.g., age by marital status)
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Population pyramid:
Example 1:
Example 2:
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Distortions in age pyramid could be due to:
 Under/over enumeration
 Age misreporting (including digit preference)
 Changes over time in fertility, mortality, migration
Therefore, additional investigation required……
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Population Pyramid by Single Years of Age
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Cohort Analysis:
 Single census display
 Multi-census display
 Size of each cohort should decline in successive censuses due to
mortality
 Lines for successive censuses should follow same pattern and
not cross (in absence of migration and errors in the censuses)
 Line for earlier census should be on top of that for later census
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Cohort analysis:
Example 1:
Example 2:
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Cohort analysis:
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Cohort Analysis (Contd.):
 Departure(s) from expected trend suggestive of age
misreporting either under-reporting or systematic transfer to
adjacent ages (most common at youngest and oldest ages)
 Departures may also reflect historical events and not just
misreporting (e.g., war resulting in small birth cohorts)
 Do not “smooth” the data
Therefore, additional investigation required……
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Age and Sex Ratios:
 Computations of quantitative assessment of “reasonableness”
of census age-sex distributions through age and sex ratios
 Ratios follow expected predictable patterns in human
populations
 Unexplained departures from predictable pattern indicative of
census error
 However, distinguishing effect on age and sex ratios of age
and/or sex-selective migration (internal and international)
from census error is difficult
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Age Ratios:
 Provide measure of “smoothness” of age distribution
 In absence of sharp swings in fertility, mortality and
migration, enumerated size of cohort equals average of two
immediately preceding and subsequent cohorts (i.e., ratio of
census count for a cohort to the average of the adjacent
cohorts ≈ 1
Sex Ratios:
 Number of males to females in an age group
 Sex ratio at birth between 102 and 107 but declines with age
due to higher male than female mortality
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Age Ratio (contd.):
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Sex Ratio:
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Sex Ratio (Contd.):
 Sex ratios from current census can be compared to
“expected” sex ratios based on previous census(es)
 In absence of sex-selective mortality or international
migration, sex ratios of total population and age
groups/cohorts in successive censuses should be relatively
stable from census to census
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Sex Ratio (Contd.):
 Unexplained fluctuations in sex ratios by age are indicative of
variations in coverage or accuracy of age reporting on a sex
selective basis from census to census
 In absence of census errors or other distorting factors,
changes in sex ratios of birth cohorts from census to census
should be consistent with sex mortality differentials under
current mortality conditions
 Where male mortality exceeds that of females, cohort sex
ratios would decline from census to census and vice versa if
female mortality exceeds that of males
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analyses of Age and Sex Distributions (Contd.)
Sex Ratio (Contd.):
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Summary Indices of Error in Age-Sex Data
Indices:
United Nations Age-Sex Accuracy Index
Whipple’s Index
Myers’ Blended Index
UN recommended index to measure relative importance
of age overstatement and understatement in
accounting for age heaping
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Summary Indices of Error in Age-Sex Data (Contd.)
Since they are summary measures of error in census
age and sex data:
 Are not substitutes of detailed inspection of data as for
the methods previously presented
 Do not provide insight into patterns of error in data as is
the case with methods just presented
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Stable Population Analysis of Age Distributions
 Recorded age distribution, by sex, compared to
appropriately chosen stable population
 Stable age distribution based on assumption of longterm constant levels of fertility and mortality, with no
international migration
c(x) = b l(x) exp (-rx)
Where:
c(x) = the infinitesimal proportion of the stable population at age x
b
= the constant birth rate
r
= the constant rate of natural increase
l(x) = the probability of survival from birth to age x
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Stable Population Analysis of Age Distributions
(Contd.)
 Required data for stable population analysis

The census count of population (which is to be evaluated) by
single years of age or 5-year age groups by sex

Estimates of 2 of the following parameters – (a) the growth
rate r in the population; (b) the birth rate b; and (c) the
probability of surviving from birth to age x (lx function)
[Note that an estimate of the expectation of life at birth e, may be
used to select a model life table to represent mortality conditions
in the population under review]
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Stable Population Analysis of Age Distributions
(Contd.)
 Few, if any, populations are genuinely stable
 For many countries, there are no developed systems
of vital and migration statistics
 Therefore, parameters b, r, and l(x) used to derive
stable age distribution for census evaluation are, for
many countries, indirect estimates which are subject
to error
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Stable Population Analysis of Age Distributions
(Contd.)
Computational Procedure:
Step 1 – calculation of proportional age distribution of the
census population
C(x) = 5Nx / N *100
Where:
5Nx is the number of enumerated persons aged x to x+4
N is the total population enumerated
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Stable Population Analysis of Age Distributions
(Contd.)
Computational Procedure (Contd.):
Step 2 – Selection of a model life table
 Model stable population chosen based on two of the
parameters – r, b, or l(x) in the population
 Model stable age distribution calculated by interpolating
between print values in model life tables that correspond
to two of the parameters – r, b, or l(x) in the population
Step 3 – Comparison of the recorded and stable age
distribution, i.e., enumerated population by age/sex
divided by stable population by age/sex
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Stable Population Analysis of Age Distributions
(Contd.)
Computational Procedure (Contd.):
 Differences between the recorded and “expected” age
distributions could be due to:
 Changes in fertility/mortality in the population under
study resulting in violation of notion of “stable population”
 Age misreporting (overstatement, understatement)
 Under-coverage of specific age group (e.g. children)
 International migration of specific age segments (young
adult males)
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Comparison of Successive Censuses using Actual Data
“Expected population” derived using population
enumerated at previous census plus information on
intercensal births, deaths and net international migration

Population balancing method
 P1 = P0 + B – D + M (Population balancing equation)
P1 = Population enumerated in
P0 = Population enumerated in
B, D = Intercensual number of
M = Intercensal number of net
census being evaluated
previous census
births and deaths
international migrants
Requires accurate vital statistics and information on
international migration
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Comparison of Successive Censuses using Actual Data
 For census evaluation purposes, need equation
P1 = P0 + B – D + M + e
Where e is the residual that’s needed to balance the equation
 However, values of e are affected by values of P0, B, D and M
 Need to evaluate accuracy of data for balancing equation and
to make adjustments as necessary before application to
evaluation
 However, adjustments for migration are problematic due
to lack of comprehensive information
 To obtain net coverage error in second census, need to adjust
first census for net coverage error as well
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Population Balancing Equation
Data required:
Population counts from census under evaluation, P1, and
from a previous census, P0
 If estimate of net coverage error is sought, previous
census to be adjusted accordingly. Otherwise, resulting
estimate represents relative coverage error of second to
first census
Number of intercensal births, deaths, and net
international migration, adjusted for underregistration
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Comparison of Successive Censuses using Estimates
Where vital registration data are unavailable of very
deficient
Indirect estimates of intercensal fertility and mortality
levels are available for a demographic survey or current
census can be used with previous census to derive an
“expected” population
Use of “cohort component” method to project population
enumerated at first census to reference date of second
census based upon intercensal estimated levels and age
schedules of fertility, mortality and migration
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Cohort Component Method
Data required:
Population enumerated in two successive censuses by
age (either single or five-year age groups) and sex
Life table survival rates by sex assumed representative
of intercensal period
Age-specific fertility rate schedule for women 15-49
years assumed to represent level and age structure of
fertility during intercensal period
Estimate of sex-ratio at birth
Estimates of intercensal level and age pattern of net
international migration
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Cohort Component Method (Contd.)
Computational Procedure:
 Step 1 – survival of population enumerated in first census
on a cohort-by-cohort basis to second census based on agespecific survival rates from life table assumed
representative of intercensal mortality conditions in
population under study
 Step 2 – Adjustment of “surviving” cohort populations to
take into account intercensal migration
 Step 3 – Estimation of intercensal number and timing of
births on basis of assumed schedule of fertility rates and
projected intercensal child-bearing age female population.
Births are survived to second census to yield estimate of
children under specified age at second census
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Cohort Component Method (Contd.)
Concerns:

Like population balancing equation, estimates of error for cohort
component method are “residual” estimates which are affected
by accuracy of information on components of change and of first
census.




Serious concern in countries with unreliable vital statistics where
indirect fertility/mortality estimates are used
Indirect estimates may be unreliable due to violation of
assumptions underlying techniques and errors in underlying data
(age reporting, fertility, mortality data)
Estimating net migration is particularly problematic
Like for population balancing equation, estimates of error are
estimates of relative or differential error between the two
censuses
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analysis of Cohort Survival Rates
 Based upon comparison of the size of birth cohorts
enumerated in successive censuses
 In population closed to migration, changes in cohort size
between censuses is attributed to mortality
 In absence of census errors, ratio of persons in birth cohort
enumerated in census to those enumerated in first census should
approximate survival rate based on prevailing mortality
conditions
 In closed populations, departures of observed from expected
cohort survival rates should indicate census error in one or
both censuses
 Where net migration is significant, “expected” population should
be modified accordingly
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analysis of Cohort Survival Rates (Contd.)
Data required:
Population enumerated in two successive censuses by
age and sex
Life table by sex assumed representative of intercensal
mortality conditions (based on estimate of level of
mortality in population)
Information on volume of intercensal net migration by
age and sex
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analysis Cohort Survival Rates (Contd.)
Computational Procedure:
 Step 1 – Adjustment of one of the censuses to minimize
distorting effects of migration on cohort survival rates (by
adding or subtracting number of net migrants to one of the
censuses)
 Step 2 – Calculation of census cohort survival rates
 Step 3 – Calculation of life-table survival rates
 Step 4 – Calculation of cohort survival ratios
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Analysis Cohort Survival Rates (Contd.)
Observations:
 Method requires only two census counts and an estimate of
level of mortality for selection of model life table

Knowledge of fertility not required as method does not assess
coverage of population born between the two censuses
 Where net migration is significant, estimate is required for
adjustments to minimize distorting effects
 Limitation of method is that when used on only two
censuses, it is difficult to separate:


Census errors from other “factual” distortions
Coverage errors from content errors
 Utility of method increases significantly when three or more
censuses are compared
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Thank You!
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census
Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010