How to use the direct age-standardized rate calculator
- Enter one line for each age group: the group name, the number of cases, the population and the standard population.
- Choose whether rates are shown per 1,000, 10,000 or 100,000 people, and the width of the interval.
- Read the standardized rate, the crude rate, the standard error and the interval.
- Use the table to see how each age group contributes, then download the CSV.
Formula
Group rate = cases / population
Weight = standard population of the group / total standard population
Standardized rate = sum of (weight x group rate)
Variance = sum of (weight^2 x cases / population^2)
Interval = rate +/- z x square root of the variance
The crude rate is all cases divided by the whole population. The two agree only when the population has the same age mix as the standard.
Three age groups
Suppose the groups 0-39, 40-64 and 65 and over have 20, 100 and 250 cases in populations of 40,000, 35,000 and 25,000, and the standard population has the same sizes. The group rates are 50, 285.71 and 1,000 per 100,000.
The weights are 40%, 35% and 25%, so the standardized rate is 370.00 per 100,000, the same as the crude rate because the population matches the standard. The standard error is 19.24 and the 95% interval is 332.30 to 407.70.
Why standardize
Age has a strong effect on many rates, such as illness or death. A town with many older residents will have a higher crude rate than a young town even if the risk at every age is the same. Direct standardization removes that difference by applying the age-specific rates of each population to one common age structure, the standard population. Two standardized rates can then be compared directly.
The result depends on the standard. A different standard population gives a different number, so the weights must be stated whenever you quote a standardized rate and must be the same for all populations you compare.
About the interval
The interval treats each count of cases as a Poisson count and uses a normal approximation for the sum. It works well when each age group has a reasonable number of cases. With only a few cases in a group the interval is too narrow or can reach below zero, which is why it is cut off at 0. Public health agencies often use exact or gamma-based intervals for small counts.
This page works with the weights you type and is for calculation and learning. It does not choose a standard population for you and it is not a substitute for guidance from a public health agency.
Assumptions and limits
- Cases are whole numbers and cannot exceed the population of the group.
- The standard population is whatever you enter, in any unit, because only the shares matter.
- The normal interval is approximate for small counts.
- The figures are examples, not data from any real place. Nothing is uploaded.
Frequently asked questions
What is the difference between direct and indirect standardization?
Direct standardization applies your group rates to a standard population. Indirect standardization applies standard rates to your population and gives a ratio. This page does the direct kind.
Which standard population should I use?
Use the one that your field or agency uses so that your results can be compared with published ones. Enter its age group counts as the standard.
Why is the standardized rate equal to the crude rate in the example?
The example population has the same age mix as the standard, so the weights match the population shares and the two rates agree.
How many age groups can I use?
From 2 to 40 lines.