# Selecting the Audit Sample using Systematic Sampling

Systematic sampling is a statistical sampling method where every n^{th} item is selected from the population to form the audit sample. The sampling frame (or population) must be ordered in some manner to use systematic sampling. The steps to produce a systematic audit sample are:

- Calculate the sampling interval – n = no of items in population / required sample size
- Select a random starting point within the first interval
- Extract every n
^{th}item

This may be easier to explain with an example. Lets say we have a population containing 360 items, and we need to sample 30 items. This gives a sampling interval of 12. Therefore we would pick a random start point between 1 and 12 (e.g. 7) and then extract every 12^{th} item.

In this example, we would extract the following items… 7, 19, 31, 43, 55, 67… … 331, 343, 355.

From a practical perspective, it is relatively easy to construct formulas in Excel to extract a systematic sample – you can use the following formula

=IF(MOD(ROW()-[start point],[interval])=0,1,0)

=IF(MOD(ROW()-7,12)=0,1,0) using the above example

This formula works by looking at the row number, subtracting the starting point, and then checking to see if it is visible by the sampling interval. If it is divisible (without leaving a remainder) then it returns a 1, and if it is not divisible it returns a 0. You can then apply filters to only show those records with a 1, and this is your audit sample.

Alternatively you can use software such as TopCAATs for you, which will extract the audit sample to a new worksheet.

When using systematic sampling, you have to be careful to ensure that there is not bias in the population, or that your sampling interval does not introduce bias in the audit sample. For example, imagine you were selecting a sample of stock locations, and the warehouse was laid out so that all the even locations were on one side of the aisle and all the odd locations on the other. If you selected every 50^{th} item and started at item 20, you would never pick an odd location, and therefore there is no chance of ever selecting items on one side of the aisles. In this scenario, a random sampling approach would be more suitable.

Therefore systematic sampling is most appropriate when looking over a period of time, as it ensures an even spread of items being selected in the audit sample over the period under review.