Evaluation and Analysis of Age and Sex StructureWhat to look for at the evaluation Possible data errors in the age-sex structure, including o Age misreporting (age heaping and/or age

Regional workshop on the Production of Population Estimates and Demographic IndicatorsAddis Ababa, 5-9 October

Evaluation and Analysis

of Age and Sex Structure

François Pelletier & Thomas Spoorenberg

Population Estimates and Projections Section

Evaluation method of age and sex distribution data

� Basic graphical toolso Graphical analysis

• Population pyramids

• Graphical cohort analysis

o Age and sex ratios

o Summary indices of error in age-sex data

• Whipple’s index

• Myers’ Blended Method

Regional Workshop on the Production of Population Estimates and Demographic Indicators

Addis Ababa, 5-9 October 2015

Importance of age-sex structure

� Planning purposes – health services, education

programs, transportation, labour supply

� Social science, economist, gender studies

� Studying population dynamics – fertility, mortality,

migration

� Insight on quality of census enumeration

� Having strong effect on other characteristics of a

population

o Determined by fertility, mortality and migration, and follows

fairly recognizable patterns



What to look for at the evaluation

� Possible data errors in the age-sex structure, including o Age misreporting (age heaping and/or age exaggeration)

o Coverage errors – net underenumeration (by age or sex)

� Significant discrepancies in age-sex structure due to extraordinary events o High migration, war, famine, HIV/AIDS epidemic etc.



Approaches to collecting age and its impact on quality

� Age - the interval of time between the date of birth and the date of

the census, expressed in completed solar years

� Two approaches

o The date of birth (year, month and day) - more precise information and is preferred

o Completed age (age at the individual’s last birthday) – less accurate

• Misunderstanding: the last, the next or the nearest birthday?

• Rounding to nearest age ending in 0 or 5 (age heaping)

• Children under 1 may be reported as 1 year of age



Basic graphical methods – Population Pyramid

� Basic procedure for assessing the quality of census data on age and

sex

� Displays the size of population enumerated in each age group (or

cohort) by sex

� The base of the pyramid is mainly determined by the level of fertility

in the population, while how fast it converges to peak is determined

by previous levels of mortality and fertility

� The levels of migration by age and sex also affect the shape of the

pyramid



Population pyramid – France, 1954 (Source: Pison 2014)









Population pyramid – High population growth



50,000 25,000 0 25,000 50,000

05

1015202530354045505560657075808590

95+

Population

Age Central African Republic, 1988 Census

MALE FEMALE

Wide base, triangle-shaped

pyramid indicates high fertility

Source: United Nations Statistics Division, Demographic Yearbook Statistical Database

Population pyramid – Low population growth



500,000 300,000 100,000 100,000 300,000 500,000

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95+

Population

Age Italy, 2011 Census

MALE FEMALE

“baby boom”

1940-45 Birth deficit

due to WWII

Flattening and narrowing base

Indicates long-term low fertility

Population pyramid – Detecting errors

� Age misreporting errors (heaping) among adults

� Under enumeration of young children (< age 2)

� High fertility level

� Smaller population in 20-24 age group

>> extraordinary events in 1950-55?

� Less men relative to women in 20-44 age group

>> labor out-migration?



320,000 220,000 120,000 20,000 80,000 180,000 280,000

05

101520253035404550556065707580

85+

Population

Age YEMEN, 1975 Census

MALE FEMALE


1,500,000 750,000 0 750,000 1,500,000

0-45-9

10-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980-84

85+

Population

Age YEMEN, 1975 Census

MALE FEMALE




100,00075,000 50,000 25,000 0 25,000 50,000 75,000100,000

05

101520253035404550556065707580859095

100+

Population

Age TUNISIA, 1966 Census

MALE FEMALE

Age heaping

120,00090,000 60,000 30,000 0 30,000 60,000 90,000120,000

05

101520253035404550556065707580859095

100+

Population

Age TUNISIA, 1994 Census

MALE FEMALE

Declining fertility





30,000 20,000 10,000 0 10,000 20,000 30,000

05

101520253035404550556065707580

85+

Population

Age Bahrain, 2010 Census

MALE FEMALE

500,000 300,000 100,000 100,000 300,000 500,000

0-4

10-14

20-24

30-34

40-44

50-54

60-64

70-74

80-84

Population

Age U.A.E., 2005 Census

MALE FEMALE

!!! Effect of Labor migration !!!

>> Importance of knowledge of the context


Population pyramid – Line instead of bars




� Population Pyramid (bar chart)>> Not always easy to determine differences by sex

� Use of line chart

3,000,000 1,500,000 0 1,500,000 3,000,000

05

101520253035404550556065707580

85+

Population

Age Bangladesh, 2001 Census

MALE FEMALE

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80+

Po

pu

lati

on

Age

Bangladesh, 2001 Census

Male

Female

Population pyramid – Line instead of bars




0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80+

Po

pu

lati

on

Age


Male

Female

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

7,000,000

8,000,000

9,000,000

Po

pu

lati

on

Age group


Male

Female

Basic graphical methods – Graphical cohort analysis

� Tracking actual cohorts over multiple censuses

� The size of each cohort should decline over each census due to mortality (with no significant international migration)

� The age structure (the lines) for censuses should follow the same pattern in the absence of census errors

� An important advantage >> possible to evaluate the effects of extraordinary events and other distorting factors by following actual cohorts over time



Graphical cohort analysis – Example (1)



1997 Census 2007 CensusBirth Cohort

Male Female Male Female

0-4 1,353,206 1,388,350 2002-2007

5-9 1,112,321 1,113,675 1997-2001

10-14 947,236 878,429 1,222,668 1,183,939 1992-1997

15-19 774,327 854,078 925,729 991,323 1987-1992

20-24 637,113 827,614 774,413 986,526 1982-1997

25-29 509,109 654,465 707,603 841,416 1977-1982

30-34 410,148 477,562 583,689 667,865 1972-1977

35-39 373,813 428,395 481,396 556,191 1967-1972

40-44 270,046 303,147 366,518 389,087 1962-1967

45-49 257,070 282,098 321,236 328,660 1957-1962

50-54 178,902 212,060 231,232 283,288 1952-1957

55-59 162,122 174,234 194,011 208,657 1947-1952

60-64 114,335 125,096 140,146 159,557 1942-1947

65-69 100,425 109,288 113,840 127,794 1937-1942

70-74 47,407 50,607 72,288 81,329 1932-1937

75-79 41,529 42,858 55,448 61,012 1927-1932

80-84 15,305 17,326 22,417 28,278 1922-1927

85-89 16,576 19,448 1917-1922

90-94 4,803 5,883 1912-1917

� Data is organized by birth

cohort

� Exclude open-ended age

category

� People who were born in

the same years are

compared in the analysis

Source: United Nations Statistics Division,

Demographic Yearbook Statistical

Database

Mozambique, 1997 and 2007 Censuses





0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1992

-199

7

1987

-199

2

1982

-199

7

1977

-198

2

1972

-197

7

1967

-197

2

1962

-196

7

1957

-196

2

1952

-195

7

1947

-195

2

1942

-194

7

1937

-194

2

1932

-193

7

1927

-193

2

1922

-192

7

1917

-192

2

1912

-191

7

1907

-191

2

Po

pu

lati

on

Birth cohort

Male - 1997 Census

Male - 2007 Census

MALE

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1992

-199

7

1987

-199

2

1982

-199

7

1977

-198

2

1972

-197

7

1967

-197

2

1962

-196

7

1957

-196

2

1952

-195

7

1947

-195

2

1942

-194

7

1937

-194

2

1932

-193

7

1927

-193

2

1922

-192

7

1917

-192

2

1912

-191

7

1907

-191

2

Po

pu

lati

on

Birth cohort

Female - 1997 Census


FEMALE





0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

Po

pu

lati

on

Birth cohort

Male - 2000 Census

Male - 2010 Census

Republic of Korea, 2000 and 2010 Censuses, Men





Republic of Korea, 2000 and 2010 Censuses, Women

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

Po

pu

lati

on

Birth cohort




Age ratios (1)

� In the absence of sharp changes in fertility or mortality, significant

levels of migration or other distorting factors, the enumerated size

of a particular cohort should be approximately equal to the average

size of the immediately preceding and following cohorts

� The age ratio for a particular cohort to the average of the counts for

the adjacent cohorts should be approximately equal to 1 (or 100 if

multiplied by a constant of 100)

� Significant departures from this “expected” ratio indicate either the

presence of census error in the census enumeration or of other

factors



Age ratios (2)

Age ratio for the age category x to x+4

�� 2 ∗ ��

��

�� = The age ratio for the age group to � 4

5� = The enumerated population in the age category to � 4

�� = The enumerated population in the adjacent lower age category

�� = The enumerated population in the adjacent higher age category



Age ratios (3) – example



0

0.2

0.4

0.6

0.8

1

1.2

1.4

5-9

10-1

4

15-1

9

20-2

4

25-2

9

30-3

4

35-3

9

40-4

4

45-4

9

50-5

4

55-5

9

60-6

4

65-6

9

70-7

4

75-7

9

Ag

e ra

tio

Age group

Mozambique – 1997 Census

Male

Female

0

0.2

0.4

0.6

0.8

1

1.2

1.4

5-9

10-1

4

15-1

9

20-2

4

25-2

9

30-3

4

35-3

9

40-4

4

45-4

9

50-5

4

55-5

9

60-6

4

65-6

9

70-7

4

75-7

9

80-8

4

85-8

9

Ag

e ra

tio

Age group

Mozambique – 2007 Census

Male

Female


Sex ratios (1) - calculation

Sex ratio by age group

Sex Ratio = ��

�

��

�

or Sex Ratio = ��

�

��

�

∙ 100

Where

��

� = Male population enumerated in a specific age group

��

� = Female population enumerated in the same age group



Value of sex ratio Interpretation

1 Same number of men and women in a given age group

Above 1 More men than women in a given age group

Below 1 Less men than women in a given age group

Sex ratios – Example (Expected sex ratio by age)



Source: United Nations Population Division, The World Population Prospects: The 2015 Revision

0

10

20

30

40

50

60

70

80

90

100

110

Sex

rat

io (

Nu

mb

er o

f m

en p

er 1

00 w

om

en)

Age group

Sweden, selected years 1950-2015

1950

1975

2000

2015

Sex ratios – Example



0

20

40

60

80

100

120

140

Sex

rat

io (

nu

mb

er o

f m

en p

er 1

00 w

om

en)

Age group


1997 Census

2007 Census

Rather sex ratio:

> Under-enumeration

of boys?

> Higher male child

mortality?

No decline at adult and older ages:

> Higher female mortality?

> Higher female out-migration?

> Under-enumeration of adult and older women?

> …


Sex ratios – Cohort analysis

> Excess of men in

1975-1980 birth

cohort in 2000

census only

> Other age groups:

as expected



0

20

40

60

80

100

120

Sex

rat

io (

nu

mb

er o

f m

en p

er 1

00 w

om

en)

Birth cohort

Republic of Korea, 2000 and 2010 Censuses

2000 Census

2010 Census


Sex ratios – Cohort analysis

> Very different

patterns found in

each census

> Some consistencies

for birth cohorts

1947-1952 to 1927-

1932




0

20

40

60

80

100

120

Sex

rat

io (

Nu

mb

er o

f m

en p

er 1

00 w

om

en)

Birth cohort


1997 Census

2007 Census

Summary indices – Whipple’s Index

� Developed to reflect preference for or avoidance of a particular terminal digit (or of each terminal digit)

� If heaping on terminal digits “0” and “5” is measured:

� ��…��!�"#

�∙��$��…��!#��!�"

∙ 100

� W ranges between 100, representing no preference for “0” or “5” and 500, indicating that only digits “0” and “5” were reported

� W is usually computed on the age range 23 to 62 >> childhood and older ages are often excluded because they are more strongly affected by other types of errors of reporting than by preference for specific terminal digits

Source: Shryock and Siegel (1980)



Whipple’s Index (3)

The index can be summarized through the following categories:

>> these values must be interpreted keeping in mind the past and present context



Value of Whipple’s index (W) Interpretation

<= 105 Highly accurate data

105 – 109.9 Fairly accurate data

110 – 124.9 Approximate data

125 – 174.9 Rough data

>= 175 Very rough data

Whipple’s index around the world (most recent census, 1985-2003)

Source: UN Demographic Yearbook special issue on age heaping: http://unstats.un.org/unsd/demographic/products/dyb/dybcens.htm



Improvement in the accuracy of age reporting over time



Whipple’s Index, Turkey 1950-2000

Summary indices – Myers` Blended Index

� It is conceptually similar to Whipple’s index, except that the index

considers preference (or avoidance) of age ending in each of the

digits 0 to 9 in deriving overall age accuracy score

� The theoretical range of Myers’ Index is from 0 to 90, where 0

indicates no age heaping and 90 indicates the extreme case where

all recorded ages end in the same digit



Conclusion: Uses and limitations

� Assessment of the age and sex structure of a population

enumerated is typically the first step taken in evaluating a data

collection operation by means of demographic methods

� Demographic methods provide:

• A quick and inexpensive indication of the general quality of data

• Evidence on the specific segments of the population in which the presence of

error is likely

• “Historical” information which may be useful for interpreting the results of

evaluation studies based on other methods, and in determining how the

collected data should be adjusted for use in demographic analyses



Conclusion: Uses and limitations

� The major limitation of age and sex structure analysis is that it is

not possible to derive separate numerical estimates of the

magnitude of coverage and content error on the basis of such

analyses alone

� It is often possible to assess particular types of errors which are

likely to have affected the population counts for particular

segments of the population. Estimates of coverage error from other

sources often are required to verify these observations



References

Pison, G. (2014), “1914-2014 : A century of change in the French population pyramid”, Population & Societies

No. 509 (March 2014)

Shryock, H. S. and Siegel, J. S. (1980), The Methods and Materials of Demography, Washington, D.C.: U.S.

Government Printing Office.

Moultrie T.A., R.E. Dorrington, A.G. Hill, K. Hill, I.M. Timæus and B. Zaba (eds), (2013), Tools for Demographic

Estimation, Paris: International Union for the Scientific Study of Population, available online at:

http://demographicestimation.iussp.org/

U.S. Census Bureau (n.d.), Population Analysis System (PAS), Washington, D.C., U.S. Census Bureau,

available online at: http://www.census.gov/population/international/software/uscbtoolsdownload.html



Documents

Evaluation and Analysis of Age and Sex StructureWhat to look for at the evaluation Possible data errors in the age-sex structure, including o Age misreporting (age heaping and/or age