Crude and standardised death rates, fertility rates and other rates

Last time

Before we start: last time, in Changing every value, standardised scores and scaling, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Fair comparisons of rates

A town full of retired people will have more deaths than a town full of students, even if both are equally healthy. Crude rates ignore this; standardised rates allow for it. This lesson covers crude and standardised death rates, fertility rates, and the same idea in other settings.

The crude death rate

The crude death rate is the number of deaths divided by the total population, times 1,000. A town of 10,000 people with 100 deaths in a year has a crude death rate of 10 per thousand. But it ignores the age structure: an older population has more deaths, even if its people are no less healthy.

Age-specific death rates

An age-specific death rate is the number of deaths in an age group divided by the population of that group, times 1,000. Ages 0 to 39: 12 deaths among 6,000 people, a rate of 2. Ages 40 to 69: 24 among 3,000, a rate of 8. Ages 70 and over: 64 deaths among 1,000 people, a rate of 64 per thousand.

The standard population

A standard population gives a fixed age structure, such as the whole country's, as percentages or numbers in each age group. Each town's age-specific rates are applied to the same standard population. So differences between standardised rates come from health, not from age structure.

The standardised death rate

Multiply each age-specific rate by the standard population of that group, add, and divide by the total standard population. With a standard of 50, 35 and 15 per cent: 50 times 2, plus 35 times 8, plus 15 times 64, is 1,340. Divided by 100, that is 13.4. The standardised rate, 13.4, is higher than the crude rate, 10, because the town has fewer old people than the standard.

The working, in a table

The whole standardised death rate calculation in one table.

Fertility rates

A fertility rate uses births instead of deaths, usually per 1,000 females, as the question defines it. Age-specific fertility rates are found for each age group of women, and standardised with a standard population of females. Always use the definition the question gives, as questions define the rate in different ways.

Rates in other settings

The same method compares accident rates, illness rates or scoring rates, where the groups differ in make-up. Find the rate in each category, then apply a common standard so the groups are compared fairly. Crude rates are fine for describing one population, but standardised rates are needed to compare.

Mistakes that lose marks

Mistake one: comparing crude rates of places with different age structures. Mistake two: forgetting to divide by the total standard population. Mistake three: using the town's own population, instead of the standard, as the weights. The fix: age-specific rates, standard weights, then divide.

The full-marks tip

The full-marks tip: set the working out in a table, one row per age group. When comparing, say which place is healthier using the standardised rates, and why the crude rates mislead.

On one card

So, on one card: crude and standardised rates. Keep it for revision.