Overview of basic statistics

Counts, rates and proportions

The most basic measure used in public health is the count. This may be a count of events such as deaths or admissions to hospital, or a count of people with a particular attribute such as people who smoke. This count itself is essential information for planning health services for prevention and treatment. It tells you the scale of the issue in different areas, for example.

However, to investigate properly the distribution of disease and risk factors, and to make comparisons between different populations, the denominator population or population-years at risk in which the count was observed must also be taken into consideration. The simplest way of doing this is to divide the numerator count by the denominator population to give a proportion, rate, or percentage.

It is important to distinguish between these terms.

Proportions

Proportions are statistics where the denominator is the count of a ‘closed’ population. A ‘closed’ population is where a population is evaluated at a specific time point for a certain characteristic. The numerator is a subset of the denominator, so it is impossible for the numerator to be more than the denominator. Common examples of proportions in public health include survey prevalence of smoking or obesity, day cases as a proportion of elective admissions, discharge to usual place of residence, or stillbirths as a proportion of all live births and stillbirths.

Rates

Other statistics can have an ‘open’ population. This is a population which is evaluated over a period of time. It is often an estimated number rather than a count of individuals. People may enter or leave the population during this period for various reasons such as ageing, migration, birth, death or loss to follow-up, each contributing different periods at risk. The denominator is the sum of the population-periods at risk experienced by the individuals (or an approximation to this, such as a mid-year population estimate). The numerator is usually a count of events that occurred in the population over the period. We refer to such statistics as ‘rates’. Examples include mortality rates and cancer incidence rates.

In some circumstances, the numerator can be greater than the denominator, when events occur at a very high rate. For example, a hospice may have 100 beds, so the population at any one time is at most 100, but there may be several hundred deaths each year because individuals in the population change frequently.

The term ‘rate’ can be loosely applied to describe many public health statistics, some of which would be better described as proportions. The distinction is not important to the calculation of the statistic itself but is necessary to best determine the confidence interval method.

Percentages

Both proportions and rates are frequently multiplied by a scaling factor for presentation purposes, such as per 100,000. When this factor is 100 the statistic is usually described as a percentage. Most commonly, proportions are expressed as percentages, but rates, ratios and changes over time can also be presented this way: a percentage is not a type of statistic, but a method of presenting a statistic.

Page last updated: August 2024