Basic measurements in Demography

Outline: Ratio Proportion Rate

1. Ratio Ratio is the relationship between two numbers ( one is divided by the other). Those included in the numerator may or may not be included in the denominator Examples: Sex Ratio: number or males/ number of females Risk Ratio: Risk of disease in one group(exposed) Risk of disease in another group ( unexposed)

If "a" is one number and "b" is another; a ratio between the two is: a/b or a:b means "so many "a" per unit of b".

Example 1: In a class of 50 students, 30 students were from Riyadh and 20 students were from out Riyadh. Find ratio of students from Riyadh to students from out Riyadh R= 30 : 20 or 30/20 = 1.50

Interpretation: for every 150 students from Riyadh there are 100 students from outside Riyadh.

Example 2: Sex ratio: is simply the ratio of males to females. This ratio is usually expressed as the number of males per 100 females. written as: males : females

Suppose we have: males = 1000; females = 900; then: sex ratio = 1000 : 900 or can also be written as: (10/9) = 1.11 Or can be written as: 111 : 100 There are 111 males for every 100 females

Year Males Females Sex ratio 2324 2134 1.00 2313 1.08 2271 0.99 2341 1991 2324 2134 1.00 1992 2313 2130 1.08 1993 2271 2276 0.99 1994 2341 2013 1.16 1995 2169 2096 1.03 1996 2063 2061 1997 2198 2018 1.09 1998 2339 2294 1.02 1999 2252 2122 1.06 2000 2092 2131 0.98

Characteristics of a Ratio: 1- Numerator is not part of denominator except in special Ratios ( rates, proportion) 2- Data should be collected over the same time period

2. Proportion A special ratio where a number if individuals within a defined group with the outcome of interest (numerator) is divided by the number of individuals enumerated in the population ( denominator) The numerator is a subset of the denominator a/a+b

Example In a class of 50 students, 30 students were from Riyadh and 20 students were from outside Riyadh.

50 20 30 Total Outside Riyadh Riyadh students Number Find: 1- proportion of students from Riyadh. Total Outside Riyadh Riyadh students 50 20 30 Number 2- proportion of students from out Riyadh

Proportion of students from Riyadh = Note that: All students in the class = 50 students from Riyadh + students from out Riyadh 30 + 20 (Number of students from Riyadh) (All students in the class)

30 = 0.6 50 20 = 0.4 50 (Number of students from out Riyadh) Proportion of students from Riyadh = 30 = 0.6 50 Proportion of students from out Riyadh = (Number of students from out Riyadh) (All students in the class) 20 = 0.4 50

Note that: Sum of all proportions should equal 1 (0.6 + 0.4) = 1 Example In a Medical Center we have: 1- 50 physicians 2- 150 nurses 3- 100 technicians

a- Find proportion of nurses in the medical center

2- Find proportion of physicians

proportion of technicians

Note that: Sum of all proportions should equal 1 ( ) = 1

Characteristics of proportion: 1- Numerator is part of denominator. 2- The value of the proportion will always be some decimal number between 0 and 1 0 ≤ P ≤ 1 3- Difficult to interpret

Percentage = proportion x 100 To make the proportion easy to interpret; we change it to percentage by multiplying by 100 Percentage = proportion x 100 Range of values for percentage is from 0 to 100. 0 ≤ Percentage ≤ 100

1- Percentage of nurses = ( ) x = % 2- percentage of physicians: Example: 1- Percentage of nurses = ( ) x = % 2- percentage of physicians: ( ) x 100 = % 3- percentage of technicians:

3. Rate Special ratio where a number if individuals within a defined group with the outcome if interest ( numerator) is divided by the number if individuals enumerated in the population (denominator) per unit length of time I.e. Rate is the number of persons (diseased or death) per unit of population per unit of time The numerator is a subset of the denominator = a/a+b

To calculate a rate the following are needed: defined period of time (year) defined population (country, city) number of events occurring during a period (number of deaths in a country during a year).

The formula for calculating a rate is given by: Rate = (a/ (a + b)) x k Where: a = frequency with which an event has occurred during some specified period of time, usually a year.

a + b = number of persons exposed to the risk of event during the same period of time. k = some number such as 10, 1000, 10,000. The nominator is a component part of a denominator. The purpose of multiplying by k is to avoid results involving very small numbers.

Rates are useful for: Comparing disease occurrence: in different locations whose populations differ in size. during different periods of time. For example: 19.5 cases of chickenpox/ 100,000 in 2001 135.8 cases per 100,000 in 1991.

Example: Suppose in a certain area, total number of population is 4,000,000. Suppose in a certain year 10,000 died. If we would like to compute death rate:

Death rate = x k = (10,000) / (40,000) x k = 0.0025 (Deaths in a year) We can select k to be 10,000. We expect population to be reduced by 25 for every 10,000. (Deaths in a year) x k (Total population)

In order to calculate rate and ratios, data are required on both: 1- The number of events occurring within the given time interval, and 2- The population exposed to the risk of experiencing those events. There are three main sources: 1- Population censuses 2- vital registration 3- Surveys

Exercises If the percentage of smokers among university students is 20%, then the proportion of smokers is ________

Blood type frequency proportion percentage O 13 A 5 B 3 AB 4 Total 25 (13/ 25) = 0.52 0.52 x 100 = 52% A 5 B 3 AB 4 Total 25

Gestational diabetes is a form of diabetes that occurs in some pregnant women during pregnancy. In a sample of 500 pregnant women in Riyadh selected from primary health care centers with no previous history of diabetes, 100 were found to have a gestational diabetes.

no gestational diabetes with gestational diabetes Women sample

a- Proportion of women who were found to have gestational diabetes is: ____________ b- Percentage of women who were found to have gestational diabetes is: ____________ c- Ratio of women with gestational diabetes to women with no gestational diabetes is___________

In a study on smoking status at King Saud University (KSU), a sample of 1000 students were selected. Each student was asked whether he smokes or not. It was found that among the students who were selected, 100 students smoke, based on this information we can say:

The proportion of smokers is: The percentage of smokers is: The ratio of smokers to non-smokers is: