# Selection of the Sample

Sample should be selected in such a manner that it is representative of the population from which the sample is being selected. It will necessitate that each item in the population has an equal chance of being included in the sample. Some of the important methods of selecting the sample are discussed below –

1. Random Sampling : Random selection ensures that all items in the population or within each stratum have a known chance of selection. It may involve use of random number tables. Random sampling includes two very popular methods which are discussed below:–

•  Simple random sampling : Under this method each unit of the whole population e.g. purchase or sales invoice has an equal chance of being selected. The mechanics of selection of items may be by choosing numbers from table of random numbers by computers or picking up numbers randomly from a drum. It is considered that random number tables are simple and easy to use
and also provide assurance that the bias does not affect the selection. This method is considered appropriate provided the population to be sampled consists of reasonably similar units and fall within a reasonable range. For example the population can be considered homogeneous, if say, debtors balances fall within the range of Rs. 5,000 to Rs. 25,000 and not in the range between
Rs. 25 to Rs. 2,50,000.
• Stratified Sampling : This method involves dividing the whole population to be tested in a few separate groups called strata and taking a sample from each of them. Each stratum is treated as if it were a separate population and if proportionate of items are selected from each of these stratum. The number of groups into which the whole population has to be divided is determined
on the basis of auditor judgment. For example in the above case, debtors balances may be divided into four groups as follows:-
1.  balances in excess of Rs. 1,00,000;
2.  balances in the range of Rs. 75,000 to Rs. 1,00,000;
3.  balances in the range of Rs. 25,000 to Rs. 75,000; and
4.  balances below Rs. 25,000.

From these above groups the auditor may pick up different percentage of items from each of the group. From the top group i.e. balances in excess of Rs. 1,00,000, the auditor may examine all the items; from the second group 25 per cent of the items; from the third group 10 per cent of the items; and from the lowest group 2 per cent of the items may be selected.
The reasoning behind the stratified sampling is that for a highly diversified population, weights should be allocated to reflect these differences. This is achieved by selecting different proportions from each strata. It can be seen that the stratified sampling is simply an extension of simple random sampling.

2. Interval sampling or systematic sampling : It involves selecting items using a constant interval between selections, the first interval having a random start. The interval might be based on a certain number of items (for example every 20th voucher) or a monetary totals (for example every Rs. 1,000 in the cumulative value of the population). When using systematic selection, the auditor should determine that the population is not structured in such a manner that the sampling interval corresponds with a particular pattern in the population. For example, if in a population of branch sales, a particular branch sales occur only as every 100th item and the sampling interval selected is 100. The result would be that either the auditor would have selected all or none of the sales of that particular branch. To minimise the effect of the possible known buyers through a pattern in the population, more than one starting point
may be taken. The multiple random starting point is taken because it minimises the risk of interval sampling pattern with that of the population being sampled.

•  Block Sampling : This method involves the selection of a defined block of consecutive items. For example take the first 200 sales invoices from the sales day book in the month of September, alternatively take any four blocks of 50 sales invoices. Therefore, once the first item in the block is selected, the rest of the block follows an items to the completion. There is a close similarity
between this method and judgmental sampling. Consequently it has similar characteristics, namely, simplicity and economy. On the other hand there is a risk of bias and of establishing a pattern of selection which may be noted by the auditees.
•  Cluster sampling : This method involves dividing the population into groups of items known as clusters. A number of clusters are randomly selected from all the clusters rather than individual items of the population. Cluster sampling can be used together with both unrestricted random and stratified sampling, for example 500 to 540, 2015 to 2055 etc. The first item i.e. 500, 2015 is
randomly selected from random number tables. The items of selected cluster can either be checked completely or a randomly selected proportion of them can be examined. The cluster is less effective for a given sample size than unrestricted random and stratified samples as items are not individually selected. However, the time saved can be utilised to have a larger sample to
make the sample results more reliable. As per AAS 15, when determining the sample size, the auditor should consider sampling risk, the tolerable error, and the expected error. Sampling risk arises from the possibility that the auditor’s conclusion, based on a sample, may be different from the conclusion that would be reached if the entire population were subjected to the same audit procedure.
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