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)

*with 95% confidence?*

**of the true proportion****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.

Useful links:

http://www.tbrieder.org/publications/books_english/lemeshow_samplesize.pdf

http://apps.who.int/iris/bitstream/10665/41607/1/0471925179_eng.pdf?ua=1

The examples described in this post have been adapted from ‘Sample Size Determination in Health Studies- A Practical Manual’, by Lwanga and Lemeshow (first link).