DEMOGRAPHIC INDICES Rates,Ratios and Proportions Demographic data is used to develop rates, ratios and proportions, which make the data more useful. Rates,ratios and proportions are simple and easy to to calculate,however caution is needed in their interpratation. They form the basis for more advanced demographic analysis 1) Ratios Ratios are used to describe the degree of balance between two elements of the population, e.g., Males vs. females, children versus women of reproductive age i.e any numerator-denominator relationship The ratio is normalized to refer to a standard unit of people. Standard unit of people may be 100, 1000 or 100, 000 persons. In the calculation of a ratio, it is necessary to specify carefully what type of event or population is the reference. Examples of ratios frequently used in demographic work i) Sex ratio The sex ratio is the ratio of males to females in the population (normalized to 100). We calculate two sex-ratios: At birth, and in the total population. It is expressed as the number of males for every 100 females in a population. a) Sex ratio at birth It relates male births to female births in a given population in an area. It is computed as: SRB = No. of male births in population (i) * 100 No. of female births in population (i) Statistics on births are obtained from vital registration system. The sex ratio at birth is fairly standard, around 105 and varies between 102-107 male births per 100 female births. Due to higher mortality among males, the sex ratio in the total population switches to 95-97. For populations with high levels of sex-selective outmigration (such as male soldiers leaving a country for war), particularly in certain age groups (e.g. aged 15-29), the sex ratio may be even smaller. Ranges for sex ratios: Sex ratio at birth: 105 except for African populations, where it is 102-103 Sex ratio for total population: 101.5 Sex ratio for population 15-49, with heavy male outmigration: 99.9 Uses of sex ratio at birth Separation of births by sex. Evaluation of the quality of registration. Example 1 If the total no of births in a given population is 32,503, we may want to know how many boys and girls form the total number. If we assume the sex ratio at birth to be 103 males births per 100 female births in the population, then the number of male and female births in the total population is given as No. of male births = 103 * 32,503 203(m+f) = 16,492 males births No. of female births = 100 * 32,503 203 = 16,011 female births. Note: when separating the total population into males and females, the denominator is equal to the sex ratio at birth for males plus the sex ratio at birth for females. In most human population the sex ratio at birth varies between the narrow ranges of 102-107 male births per female births. For analytical purposes this can be used as a simple demographic model Any wide variations from this could be an indication of defective registration or enumeration. Example 2 Suppose the sex ratio at birth in a given population was found to be 113:100, then assuming a sex ratio at birth of 105 male births (worldwide average figure) to 100 female births; we have 105 = 113 100 x x105 = 11300 Therefore x = (11300) / (105) = 107.617 = 108 Where x is the number of female births per 113 male births, then the sex ratio at birth is assumed to be 105:100. Our calculation suggests that there is relative under-registration of about 8 percent of females in the registration system. This is on the assumption that males are completely registered. Example 3 The birth registers for a district show 2456 male births and 2102 female births. Calculate the sex ratio at birth. Sex ratio at birth: (2456 / 2102 ) * 100 = 117. 117 Males : 100 Females at birth Example 4 In France in 2001 there were 770,945 births. Of these, 394,297 were male and 376,648 were female. Calculate the sex ratio at birth (SRAB) SRAB = 394297 X 100 = 1.047 376648 =1.047 X 100 = 104.7 = 105 So for every 100 girls born, there were 105 boys born. ii) Dependency ratios This is the ratio that quantifies the number of persons in a population who are not economically active for every 100 economically active persons in that population. Economically inactive populations are 0 – 14, 65 years and above. Economically active population is 15 – 64 years. Dependency ratio can be calculated by dividing the population 0-14 years and 65 years and older by the population that is in the 15-64 year age group. Example: A community has 41,650 children under age 14 and 6,800 persons age 65 and over. The total population is 85,000. Calculate the dependency ratio. The dependency ratio is: (48450/(85000- 48450)) * 100 = 133. You can also use the percentages from age distributions. Example: (57%/43%) * 100 = 133. You can calculate separate dependency ratios: a) Child dependency ratio (Pop 0-14 / Pop 15-64) b) Old age dependency ratio (Pop 65+/Pop 15-64). iii) Child-woman ratio This is the ratio of children under 5 per 1000 women of reproductive age. It is usually calculated by dividing the number of children in the age group 0-4 (of both sexes) by the number of women of reproductive age (15-49 years), and then multiplying by 1000. Child-woman ratio = Number of children <5years Number of women (15-49yrs) x 1000 Example A district in Viet Nam has a total population of 32,500, with 4896 children under age 5 and 10,200 women aged 15-49. Calculate the CWR (4896/10200) * 1000 = 480. iv) Maternal mortality ratio – Similar to maternal mortality rate This is the number of maternal deaths per 100,000 live births. Terms used interchangeably. However, Maternal Mortality Ratio is preferred to maternal mortality rate because of the difficulty in obtaining accurate data to calculate the rate of this relatively infrequent event in a population which is subject to great underestimation, since all pregnancies, births and deaths tend to be underreported The numerator only includes deaths to women during their pregnancy or in the first 6 weeks after delivery. This ratio is often used instead of the maternal mortality rate (the number of maternal deaths per 100,000 women aged 15-49 per year). 2) Proportion Proportions show the size of a sub-group of the population relative to the total population. They are calculated by dividing the number within the sub-group of interest by the total population Proportion = Pi P where : Pi is the sub-group of interest and P is the total population. Proportions are a special type of ratio in which the denominator includes the numerator e.g. The proportion of male deaths that occurred in a population Proportion = deaths to males deaths to males + deaths to females A proportion will always be between 0 and 1. However, we can express it as a percentage by multiplying the value by 100, or per 1000 by multiplying by 1000 and so on. Note: The subscript i is used to denote a subgroup of the population. Example In 2010, the total population of Argentina was 40,412. Of these, 3386 were aged under 5, or 0-4 years. a) Calculate the proportion of the population aged 0-4 in 2010. Proportion aged 0 – 4 = 3386 40412 = 0.08 The proportion of the population aged 0-4 years is 0.08. b) Calculate the percentage of the population aged 0-4 0.08×100 = 8%. N/B: the numerator (all those aged 0-4) is included in the denominator (all those aged 0-4 +all those above the age of 4). 3) Rates A rate is a measure of change in a population over a specified time period, (usually a year). These are special case ratios. They give the likelihood of the occurrence of a phenomenon within a given population at a given time and place. They study the dynamics in population e.g. Rate of incidence = No. of events that occur within a given time interval No. of members of the population who were exposed to the risk of the event during the same time interval In demography, rates are most frequently calculated for periods of one year. This means that the total number of person-years of exposure to risk can usually be approximated by the population at mid-year. When calculating a rate, the numerator is the number of events of interest (births, deaths, marriages, disease diagnoses etc.) that occur during the specified period of time. The denominator is either the number of person-years of exposure to risk during the time period, or an estimate of this. In demography, the mid-year population is often used as this estimate and is equivalent to the mean population for the period specified. Examples of true demographic rates True demographic rates are those which use the population at risk as the denominator and they include the Crude Death Rate and the General Fertility Rate among others. The General Fertility Rate (GFR) is a true rate as the denominator only includes those who are at risk of the event (in this case giving birth) during the specified time period. The GFR is calculated as the number of births to women of reproductive age (taken as those aged 15-44, or 15-49) in a year divided by the mid-year population of women of reproductive age, and expressed per 1000 women. Examples of false demographic rates Some demographic rates are called rates but are in fact ratios or proportions, for example, the Infant Mortality Rate (IMR) which is calculated as the number of deaths to infants less than 1 year old in a single year, divided by the number of live births in the same year. This is really a ratio as the denominator is not strictly the population at risk. If we took 2010 as the year of interest, some of infants who die in 2010 may have actually been born in the 2009, and are therefore not included in the denominator. On the other hand, some of the infants who are born in 2010, and are included in the denominator, may die in 2011 and therefore will not be included in the numerator. For this reason three-year averages of births and deaths are often used to calculate IMRs.
