Transcript Basic summaries for demographic studies

Basic summaries for
demographic studies
(Session 03)
SADC Course in Statistics
Learning Objectives
At the end of this session, you will be able to
• interpret and use demographers’ shorthand
notation
• correctly distinguish & use absolute &
relative numbers, and ratios & rates
• explain the definitions, and thinking
behind, different death rates
• recognise the detailed accuracy needed in
demographic studies
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Demographic “shorthand”
Standard symbols are very common in
demography to represent common ideas/
data summaries too long-winded to write
out in full each time ~ they are not 100%
predictable so take care in interpretation.
Example ~ P usually represents a total
population size; P0 and Pt may be size of
population at times 0 and t; but elsewhere
Px could represent the population aged x
[between xth and (x+1)th birthdays]
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Absolute & relative numbers
An actual count is referred to as “absolute”;
a relative number could be a count
expressed per 100, or per 1000 i.e.
compared to (relative to) another number.
Example ~ 59 children left a school last term
(absolute number). 590 children were
registered at the start of term, so 59/590
= 0.1 or = 10% left (relative number).
Fractions can confuse laymen so we express
them as “one in ten” or “ten per hundred”.
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When to use absolute and relative
When you need to express the actual size of
something, use absolute numbers, but for
comparing things of different sizes usually
“correct for” differences by using relative
numbers.
Example ~ 12 cases of stochastic fever
occurred in Mauritius in 2003 as opposed
to 20 in Mozambique in same year. Per
million population these figures equate to
roughly 10.7 and 1.06, accounting for
different population sizes.
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Ratio
Of course a ratio is just one number divided
by another.
Example ~ in the school’s entry year, grade
1, there were 50 girls and 47 boys: the
Male/Female ratio is 47/50 [ or 0.94]
In the school’s final year, grade 12, there
were 10 girls and 17 boys: the
Male/Female ratio is 17/10 [or 1.70]
Demographers call these “age-specific” or
“grade-specific” sex ratios. M/F is
standard definition of sex ratio [not F/M]
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Proportion
A proportion is a number representing part,
divided by a number representing the
whole of the same thing. All proportions
are ratios, not all ratios are proportions.
Example ~ the proportion of girls in grade
1(as above) is 50/(50 + 47) = 50/97 [or
0.5155]. The proportion of boys in grade
12 is 17/27 [or 0.6296]. The proportion
of boys, in each case, is 1 – proportion of
girls.
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Rates – the time dimension
Ratios and proportions are point-in-time still
snapshots. Where events occur through
time - and where they are concerned with
the speed (flow) - demographers use rates.
Example ~ death rate. In one calendar year
50,000 population members died. The
mid-year population was 10,000,000. The
“death rate per thousand (all ages)” was:[50,000 / 10,000,000] x 1000 =
5 deaths per 1000 per year
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Ratio or rate?
Demography requires very precise language.
The term “ratio” is only used for a static,
point-in-time measure with no associated
concept of “speed”.
Even though it involves dividing one number
by another, the term “rate” is specifically
used for a quantity which involves a sense
of “speed” and can be expressed as being
“per unit of time”.
Misusing these terms is a naïve amateur
error!
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Some basic death rates: 1
• Crude death rate is number of deaths in
the defined population in a one-year period
(D) divided by the mid-year size of the
population (P): m = [D/P]
• Age-specific death rate is no. of deaths of
those aged x, in year (Dx)/ size of mid-year
population aged x (Px) : mx = [Dx/Px]
• Figures sometimes x1000 and expressed
“per 1000 per year” since rates are
fractions much less than 1.
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Some basic death rates: 2
Note there is an age-specific death rate for
every age.
• Sometimes an age-specific rate over a
range of ages from exact age (birthday) x
up to but not including exact age (x + n) :No. of deaths of those aged x up to but not
including (x + n), in year (nDx) divided by
size of mid-year population aged x up to but
not including (x + n) , (nPx)
nmx
= [nDx/nPx]
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Data for death rates: 1
Usually the number of deaths (D, Dx or nDx)
comes from death registration, if that is
available and reasonably reliable. It may
have to be estimated by other means e.g.
scaled up from a survey, if not.
Usually the mid-year population estimate
(P, Px or nPx respectively) comes from a
census population (reported by age)
projected forward from the last census
date.
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Data for death rates: 2
The 2 quite distinct sources/data-collection
processes can each have their own sorts of
inaccuracy, e.g. coverage errors, so
typically such rates are affected by the
combined set of errors ~ take care!
Professional demographers look carefully at
patterns e.g. of age-specific death rates in
several countries in several years and have
mathematical methods to “smooth” values
that are out of line e.g. if m23 is much
bigger than m21 , m22 and m24 , m25
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Mortality rates: 1
A key theoretical, rather than practical, idea
is that of one “birth cohort”, envisaged as a
set of people all born at the same time.
From a cohort, certain numbers will die at
each age. The number who die between
exact ages x and (x+1) divided by the total
number who lived to age x, is denoted qx. It
is the estimated probability of dying aged x.
In demographic jargon this is called the
age-specific mortality rate.
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Mortality rates: 2
• The probability of surviving from exact age x
to exact age (x+1) is denoted px.
Of course
px + qx = 1.
• Death rate figures (e.g. mx) derived from
real population figures broadly represent
chances of dying, but are not probabilities.
• A standard approximation links mx and qx.
If mid-yr popn aged x is Px, & deaths in year
are Dx then start-of-year popn that suffered
those deaths was about [Px + ½ Dx]
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Mortality rate algebra
So mx = [Dx/Px], while approximately
qx = Dx / [Px + ½ Dx]
= (Dx/Px) / [1 + ½ (Dx/Px)]
on dividing top and bottom by Px.
qx = mx / [1 + ½ mx]
= 2mx / [2 + mx]
So data-derived death rate (mx) feeds into
the last formula to give estimated
probability of dying (or mortality rate), qx.
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Mortality rate arithmetic
In a population of 30-year-old males, the
mid-year popn size was estimated at
112,250. In the course of the year 1500
deaths occurred to this population, so
mx = [Dx/Px] = 1500/112,250 = 0.01336
qx = 2mx / [2 + mx] = 0.01327
so where mx is quite small, there is not
much difference between the two rates.
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Other demographic rates: 1
There are hundreds of other rates in regular
use. Age-sex specific rates are derived for
one sex only as on previous slide. Rates
are “crude” if they are not specific: usually
a whole range of ages lumped together.
Comparing separate populations that have
different age-structures uses either full
sets of age-specific rates or compromise
summaries, “standardised rates”. See
later module I4.
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Other demographic rates: 2
This 1 session is about demographic thinking.
It is not a demographic methods course!
Other very important indices relating to births
include birth rate, (age-specific) fertility
rates, total fertility rate and there are many
others for different phenomena e.g.
nuptiality rates, in- and out-migration rates.
Mortality is conceptually easier in occurring
to one individual. Other rates more directly
involve >1 person.
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Practical work follows to
ensure learning objectives
are achieved…
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