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　　1. Audit sampling
　　ISA530 Audit Sampling and Other Means of Testing defines audit sampling as:
　　The application of audit procedures to less than 100% of the items within an class of transactions or account balance such that all sampling units have chance of selection. This will enable the auditor to obtain and evaluate audit evidence about some characteristic of the items selected in order to form or assist in forming conclusion concerning the population.
　　In exceptional cases, sampling may not be appropriate:
　　（1）Cases where the auditor is ‘on enquiry’
　　（2）Populations are too small to justify sampling approach
　　（3）All transactions in particular are are of great monetary significance
　　（4）‘Sensitive’ items, such as directors’ emoluments
　　（5）Population is non-homogeneous
　　But normally audit sampling is inevitable for the reasons given below.
　　Full substantive testing is impossible in large assignments.
　　Even if theoretically possible, full substantive testing is time-consuming and expensive
　　Full substantive testing may not verify that transactions are ALL recorded （i.e. it may not demonstrate completeness）
　　For sampling to be acceptable:
　　（1）Population must be sufficiently large
　　（2）Anticipated error rates must be low
　　（3）Each unit in the population must be identifiable
　　（4）Population must be representative of transaction types under review, and of time period under review
　　（5）Population must be homogeneous
　　（6）Each item in the population must stand an equal chance of selection
　　Sampling risk is the risk that the conclusion drawn by the auditor, based on sample, will be different from that which he would have drawn had he examined the entire population.
　　2. Constructing samples
　　 Steps in sampling
　　（1）Sample design
　　（2）Selection of the sample
　　（3）Evaluation of sample
　　ISA530: when designing （the size and structure of） an audit sample, the auditor should consider the specific audit objectives, the population from which the auditor wishes to sample, and the sample size.
　　The population is the entire set of dat from which the auditor wishes to sample in order to reach conclusion.
　　The essential feature of population is that it must be homogeneous, i.e, composed of similar or uniform parts.
　　Often the auditor will analyze population into strata.
　　ISA530: when determining the sample size, the auditor should consider sampling risk, the tolerable error and the expected error.
　　Sampling risk applies both to tests of control and to substantive procedures.
　　Tolerable error is the maximum error in the population that the auditors are willing to accept and still conclude that the audit objective has been achieved.
　　ISA530: the auditor should select sample items in such way that the sample can be expected to be representative of the population.
　　Methods of selection include:
　　（1）Simple random selection
　　（2）Value weighted selection
　　（3）Systematic selection
　　（4）Block sampling
　　（5）Haphazard selection （or judgment sampling）
　　Test results are evaluated by
　　（1）First, define what constitutes an error by reference to the audit objectives
　　（2）Errors, identified in the sample are then projected across the population as whole.
　　 3. Statistical and non-statistical sampling procedures compared
　　 Statistically based sampling involves the use of techniques from which mathematically constructed conclusions about the population can be drawn.
　　Any sampling procedures which do not meet this definition are referred to as non-statistical or judgment sampling.
　　Areas where statistical sampling and judgment sampling procedures are similar
　　（1）Determining objectives
　　（2）Defining the population
　　（3）Defining what constitutes an error or exception
　　（4）Testing the selected items
　　Areas where statistical sampling and judgment sampling procedures differ
　　（1）Determining the sample size
　　（2）Selecting the sample items
　　（3）Evaluating results
　　（4）Projecting results over the whole population
　　（5）Assessing the risk of an incorrect conclusion
　　The advantages and disadvantages of using statistical sampling rather than judgment sampling are summarized in the table below:
　　Advantages Disadvantages
　　Conclusions can be drawn in quantitative terms　It may be difficult to extract samples, especially if documents are not sequentially numbered
　　Sample selected will be unbiased　Initiative may be stifled and staff become de-motivated
　　Its use forces clarification of audit objectives in that confidence and precision levels must be predetermined　Results may be misunderstood if staff are not properly trained in the use of the technique
　　Time and money may be saved by the avoidance of excessive checking　It is not suitable for all applications
　　Acceptance of the known risk involved in statistical sampling is preferable to the unknown risks when large numbers of items are selected judgmentally　Although judgment is reduced at the more detailed selection and testing level, the importance of judgment when deciding the confidence level, precision and meaning of error is greatly increased.
　　More precise information can be given to the client in the letter of weakness
　　4. Further aspects of statistical sampling
　　4.1 Attribute sampling aims to detect what proportion of population has, or lacks, defined characteristic or attribute. It is therefore useful in tests of control.
　　‘Failure’ in control procedure is given equal weight, regardless of their monetary value.
　　The title of this subsection is therefore correct as far as the origin of this technique is concerned. However, in response to demands from audit firms for statistical method which could measure monetary deviations, an attribute sampling technique was developed by statisticians which could express conclusion in monetary terms – monetary unit sampling （MUS）.
　　Sample size is calculated as:
　　Reliability factor ÷ precision required
　　The reliability factor is taken from statistical tables.
　　The precision required is the auditor’s assessment of the acceptable error rate. It is expressed as proportion of the population （i.e. if the auditor is prepared to accept two incorrect items in every 100, the precision required is +/- 0.02; if the precision required is three errors per 100 items, the figure is +/- 0.03）.
　　This implies, as one would expect, that the lower the level of precision the auditor is prepared to accept, the smaller the sample size he will have to test.
　　4.2 Variables sampling aims to detect the monetary value of an overstatement or understatement.
　　In its pure form, it is complicated procedure, mainly because it requires estimation of both the number of units in population and the standard deviation of the population. The latter in particular is difficult to determine.
　　To avoid these difficulties, many audit firms instead use monetary unit sampling （MUS）.
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