# Relative and Absolute Precision in Sample Size calculation

Recently, I was asked to clarify the difference between relative precision and absolute precision in sample size calculation. This post aims to shed some light on the two concepts.

Review of Terms

True Population value: The actual value of a population parameter (e.g. prevalence). This is what investigators wish to capture by conducting studies.

Confidence Interval: A range of values likely to contain the (true but unknown) value of the  population parameter of interest.

Now let us consider the two terms in turn using two examples:

Example 1 (Absolute Precision)

A local health department wishes to estimate the prevalence of tonsillitis
among children under five years of age in its locality. It is known that the true rate is unlikely to exceed 20%.

The department wants to estimate the prevalence to within 5 percentage points of the true value, with 95% confidence.

How many children should be included in the sample?

Solution:

(a) Anticipated population proportion                               20%
(b) Confidence level                                                               95%
(c) Absolute precision (15%-25%)                                      5 percentage points

For P = 0.20 and d = 0.05 a sample size of 246 would be needed.

Example 2 (Relative Precision)

An investigator working for a national programme of immunization seeks
to estimate the proportion of children in the country who are receiving Measles vaccinations.

The vaccination coverage is not expected to be below 50%.

How many children must be studied if the resulting estimate is to fall within 10% (not 10 percentage points) of the true proportion with 95% confidence?

Solution:
(a) Anticipated population proportion                                    50%
(conservative choice)
(b) Confidence level                                                                     95%
(c) Relative precision (E) (from 45% to 55%)                         10% (of 50%)

For P = 0.50 and E = 0.10 a sample size of 384 would be needed.

As can be seen from the examples above, the difference is subtle, but discernible:

The term Absolute precision is used when one wishes to estimate the population parameter to within defined percentage points of the true value. This is described as ‘Estimating P to within “d” percentage points’

On the other hand, the term Relative precision is used when one wishes to estimate the population parameter to within a defined percentage of the population parameter itself. This is described as ‘Estimating P to within “E” of P’.

Although using either approach will likely yield similar looking output, the difference lies in how the output was generated.