An Evaluation of the Age and Sex Data from the Census Population of Canada,

Provinces and Territories, 1971 to 2001

BYShirley Loh, Ravi Verma and Margaret Michalowski

Prepared for presentation at the Canadian Population Society Annual Meetings, Winnipeg, Manitoba, June 2004. This paper reports the results of research and analysis undertaken by Demography Division, Statistics Canada staff. It reflects the opinions of the authors and, not necessarily, those of Statistics Canada and is released to inform and to encourage discussion.

Outline of Presentation

• Objectives & Review of literature

• Methodology:

Pyramid, Digit Preference Index,

Age-Sex Accuracy index

• Source of Data

• Results

• Conclusion and Discussion

Objectives and Review of literature

Objectives:• To investigate if age heaping is present in single

year age data on population

• To examine the overall accuracy of population data by age and sex

• To compare the level of accuracy of age-sex population with some countries

Review of Literature:• Norland, Litven and Cottrell (1977)

• Bourbeau and Lebel (2000)

• Poston and associates (2003)

Methodology

• Graphical presentation of population by age and sex

• Computing Myers’ indices for detecting digit preference in single year age reporting

• Computing age-sex accuracy index (U.N. Method) based on 5 year age group

Myers’ Index(unadjusted)

Calculation of Myers' Index for the Census Population for Canada, 1971 (Age range: 20-69)

Population with terminal digit a Weights for Blended Population Deviation of percentfrom 10.00

Terminal digit, a Starting at Starting at Column 1 Column 2 Number Percent (signs disregarded)age 20+a age 30+a (1)x(3)+(2)x(4)= distribution (6)-10.00=

(1) (2) (3) (4) (5) (6) (7)

0 ……………………….. 1,312,688 931,643 1 9 9,697,475 9.41 0.591 ……………………….. 1,279,233 907,788 2 8 9,820,770 9.53 0.472 ……………………….. 1,239,109 868,791 3 7 9,798,864 9.51 0.493 ……………………….. 1,231,712 855,511 4 6 10,059,914 9.76 0.244 ……………………….. 1,224,163 833,769 5 5 10,289,660 9.99 0.015 ……………………….. 1,164,711 834,905 6 4 10,327,886 10.02 0.026 ……………………….. 1,153,462 830,377 7 3 10,565,365 10.25 0.257 ……………………….. 1,139,818 816,490 8 2 10,751,524 10.43 0.438 ……………………….. 1,115,520 803,429 9 1 10,843,109 10.52 0.529 ……………………….. 1,088,204 792,392 10 0 10,882,040 10.56 0.56Total (X) (X) (X) (X) 103,036,607 100.00 3.59

Summary Index of age preference = Total / 2 (X) (X) (X) (X) (X) (X) 1.80

U.N. Method for Age-Sex Accuracy(Unadjusted, Canada, 1971)

Criteria of the U.N. INDEXUnder 20 → Accurate20 to 40 → InaccurateOver 40 → Highly Inaccurate

Population Analysis of sex ratios Analysis of age ratios Male Female

Age Male Female Ratio Successive Deviation Deviation differences Ratio1 from 100 Ratio1 from 100

[(1)/(2)]*100= (5)-100= (7)-100=(1) (2) (3) (4) (5) (6) (7) (8)

Under 5 years ………………. 929,604 886,551 104.86 (X) (X) (X) (X) (X)5 to 9 years ………………….. 1,152,427 1,101,578 104.62 0.24 109.18 9.18 109.29 9.2910 to 14 years ………………. 1,181,450 1,129,288 104.62 0.00 106.11 6.11 105.47 5.4715 to 19 years ………………. 1,074,431 1,039,915 103.32 1.30 101.21 1.21 100.14 0.1420 to 24 years ………………. 941,775 947,628 99.38 3.94 100.45 0.45 103.95 3.9525 to 29 years ………………. 800,712 783,410 102.21 -2.83 99.92 -0.08 98.41 -1.5930 to 34 years ………………. 660,873 644,550 102.53 -0.32 91.42 -8.58 91.93 -8.0735 to 39 years ………………. 645,048 618,822 104.24 -1.71 99.11 -0.89 97.74 -2.2640 to 44 years ………………. 640,769 621,759 103.06 1.18 101.83 1.83 99.93 -0.0745 to 49 years ………………. 613,413 625,627 98.05 5.01 105.79 5.79 108.30 8.3050 to 54 years ………………. 518,899 533,639 97.24 0.81 95.58 -4.42 96.33 -3.6755 to 59 years ………………. 472,413 482,312 97.95 -0.71 104.91 4.91 103.84 3.8460 to 64 years ………………. 381,692 395,321 96.55 1.40 99.34 -0.66 98.07 -1.9365 to 69 years ………………. 296,049 323,909 91.40 5.15 100.82 0.82 100.11 0.1170 to 74 years ………………. 205,578 251,802 81.64 9.76 94.29 -5.71 98.86 -1.1475 to 79 years ………………. 139,995 185,515 75.46 6.18 96.13 -3.87 100.20 0.2080 to 84 years ………………. 85,680 118,491 72.31 3.15 94.87 -5.13 96.77 -3.2385 to 89 years ………………. 40,623 59,386 68.41 3.90 (X) (X) (X) (X)

Total (irrespective of sign) …. (X) (X) (X) 47.59 (X) 59.63 (X) 53.26Mean (X) (X) (X) 2.80 (X) 3.73 (X) 3.33Index = 3 times mean difference in sex ratios plus mean deviations of male and female age ratios. = 3 x 2.80 + 3.73 + 3.33 = 15.46

Source of Data

• Census population by age and sex, adjusted for net census undercount, 1971-2001

Results: Myers' Index of Age Heaping by Sex, Unadjusted Census Population, Canada

(Age Interval 20-69)

0

0.5

1

1.5

2

2.5

1961 1966 1971 1976 1981 1986 1991 1996 2001

male

female

Results (cont’d): Myers’ Index of Age Heaping, Canada, Provinces and Territories

  1971 1976 1981 1986 1991 1996 2001

Age Interval: 20-69

Canada 1.7 1.2 1.4 1.6 1.6 1.5 1.5

Newfoundland 1.3 1.3 1.2 1.4 1.3 1.2 1.2

Prince Edward Island 1.8 2.3 1.4 2.3 1.5 1.7 1.2

Nova Scotia 1.6 1.7 1.5 2.0 1.8 1.5 1.7

New Brunswick 1.6 1.7 1.4 1.7 1.7 1.4 1.6

Quebec 1.7 1.0 1.4 1.3 1.6 1.3 1.6

Ontario 1.9 1.2 1.4 1.6 1.7 1.6 1.5

Manitoba 2.0 1.5 1.9 1.7 2.0 1.6 1.7

Saskatchewan 1.8 1.6 1.9 1.8 2.1 1.5 1.8

Alberta 1.6 1.2 1.3 1.5 1.2 1.4 1.2

British Columbia 1.9 1.4 1.5 1.9 1.6 1.9 1.3

Yukon 2.2 1.2 1.6 1.0 1.5 1.1 1.1

Northwest Territories 1.8 1.3 1.1 1.0 0.9 1.2 0.8

Results (cont’d): United Nations Age-sex Accuracy

Index, Canada, Provinces and Territories   1971 1976 1981 1986 1991 1996 2001

Canada 16 18 21 21 20 19 19N.L. 19 19 22 23 22 20 21P. E. I. 25 26 27 22 23 25 26N. S. 20 19 22 21 22 20 22N. B. 19 21 22 23 22 21 21Que. 17 19 21 23 21 21 23

Ont. 20 21 24 23 23 21 21

Man. 17 18 19 20 20 19 20

Sask. 16 16 17 18 19 20 21

Alta. 19 16 21 20 19 19 18

B. C. 20 21 23 22 21 20 20

Yukon 132 86 61 58 50 51 50

N. W. T. 53 50 39 43 38 55 57

: Accurate : Inaccurate : Highly Inaccurate

Limitations of the UN Age-sex Accuracy Index (Siegel and Swanson, 2004)

• Central age group not included in the calculation of the age ratio

• Expected decline in sex ratio with increasing age not considered

• Considerable weight is given to the sex ratio component in the formula

Results (cont’d): Revised Age-Sex Accuracy Index, Canada, Provinces and Territories

  1971 1976 1981 1986 1991 1996 2001

Canada 14 15 18 18 17 16 16

N.L. 16 16 19 20 19 18 18

P. E. I. 21 22 23 19 20 22 22

N. S. 17 16 19 18 19 17 19

N. B. 16 17 19 20 19 18 18

Que. 14 16 18 19 18 18 19

Ont. 17 18 20 20 19 18 18

Man. 14 15 16 17 17 16 17

Sask. 13 13 14 15 16 17 18

Alta. 16 13 17 17 16 16 16

B. C. 17 18 20 19 18 17 17

Yukon 122 80 56 52 45 46 44

N. W. T. 47 45 35 39 34 49 52

: Accurate : Inaccurate : Highly Inaccurate

Results (cont’d): Age-Sex Accuracy Index for Canada in 2001 and for 42 Countries of

the World in 2000Country ASAI Country ASAI

Highly inaccurate AccurateUnited Arab Emirates 110.4 Canada (2001)* 19.7Bahrain 64.8 Finland 19.4Saudi Arabia 62.7 Jordan 19.1Kuwait 58.1 Gaza Strip 18.8Macau S.A.R. 46.5 Sweden 18.3Russia 40.9 Vietnam 17.2

France 16.6Inaccurate Italy 16.5Hong Kong S.A.R. 34.6 Uganda 15.9North Korea 29.6 Spain 15.4Somalia 29.0 Japan 15.0South Korea (1970) 27.8 United Kingdom 14.6South Korea (1995) 26.2 Ireland 14.1China 23.9 West Bank 14.1Singapore 23.5 Israel 14.0Taiwan 22.2 Indonesia 13.9Germany 22.1 Iran 13.8Yemen 21.7 United States 12.8Yugoslavia 21.4 Kenya 11.5Bangladesh 21.3 Thailand 10.9Iraq 21.3 South Africa 10.7Zambia 20.3 Syria 10.4Liberia 20.1 Sri Lanka 10.3

* based on unadjusted population

Conclusion

Myers’ Indices: Single Year Age Data

• No preference or avoidance of any year of birth

Age-sex Accuracy Indices: Five Year Age Group Data

• Accurate age-sex population data for Canada and all provinces except Prince Edward Island, Yukon and Northwest Territories

• The quality of Canadian age-sex population data is highly comparable to Sweden and Finland

Unadjusted Census Population – Myers’ indices and age-sex accuracy indices slightly higher than those based on adjusted census population

Discussion

• No explanation provided by the United Nations for the classification of the three categories

• Did the introduction of question on date of birth in 1971 improve the quality of age-heaping?