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## STATISTICAL SAMPLING

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### STATISTICAL SAMPLING

Presented

By

Arindam Nath (AAO)

ISW & IT Audit

O/o the Pr. Accountant General (Audit), Assam

WHAT IS SAMPLING?

- Defn. (SAS No. 39)
- Audit sampling is the application of an audit procedure to less than 100 percent of the items within an account balance or class of transactions for the purpose of evaluating some characteristic of the balance or class
- Testing less than 100% of the items and then forming an opinion about the population

JUDGEMENTAL AND STATISTICAL SAMPLING

- Audit sampling can be judgmental or statistical
- Judgmental sampling means checking a pre-determined proportion of transactions on the basis of the auditor’s judgment without using statistical procedures
- Sample size in statistical sampling is derived using the underlying laws of probability

WHY STATISTICAL SAMPLING?

- OBJECTIVITY
- Statistical sampling provides a measurable relationship between the size of the sample and the degree of risk.
- The auditor can specify a definite degree of risk (assurance level) using statistical sampling
- Lower sample size needs to be checked to provide assurance

AUDIT SAMPLING.

- It enable the auditor to form certain conclusions about that class or balance as a whole.
- An auditor can apply sampling in carrying out both compliance procedures (to evaluate the effectiveness of the internal control system) and substantive procedures (to obtain evidence regarding the completeness, accuracy and validity of the data).

ELEMENTS OF STATISTICAL SAMPLING

- The theory of statistical sampling is used in a large number of situations where a characteristic of a large mass of data is to be evaluated.
- In auditing, the auditor has to form his opinion about a large mass of data. Therefore, it is possible to apply statistical sampling techniques in auditing

Elementary Concepts of Statistical Sampling

- Sample: A sample is the part of an aggregate selected with a view to drawing inferences about the aggregate.
- Population: The aggregate or the totality from which the sample is drawn is called the population or the universe.

Cont.

- Stratification: For sampling to be effective, population should be more or less homogenous. In auditing situations (as in many other cases), population can seldom be homogenous in all respects.
- To make sampling more efficient, the total population in such a situation is divided into several sub-populations (each sub-population is called 'stratum') each of which is, in itself, more homogenous in nature.

Cont.

- each of which is, in itself, more homogenous in nature, size, importance or other characteristics than the population as a whole.
- A sample is then selected out of each stratum.
- This process is called 'stratification'.

Cont.

- Random Sample: A random sample is one where the elements constituting the sample are so selected that all the items in the population have an equal chance of selection.

Basic hypotheses

- population is a homogeneous group
- There is no bias in the selection of items of the sample.
- All items of the population have equal chance of being selected in the sample.

Approach to Statistical Sampling

Estimating the Qualitative Characteristics of a Population

- Attribute Sampling

Cont.

Estimating the Quantitative Characteristics of a Population

- Monetary Unit Sampling
- Variables Sampling:

Sampling methods

There are different ways in which a statistical sample can be selected.

- A simple random sampling ensures that every member of the population has an equal chance of selection..
- In cases where the population is non-homogeneous, a stratified sampling would be a better option
- Each sampling method has its practical use and limitation.

Designing a sample

- The basic stages that are involved in attributes sampling are mentioned below:

(a) Determining the sample size

(b)Selecting the sample and performing substantive audit tests on the sample

(c) Projecting the results

Determining the sample size:

- · Define clearly the target population and the error/exception (attribute) that audit wishes to test.
- Understand and apply
- tolerable error
- precision level
- confidence level
- occurrence rate

Cont.

- The sample size would be larger, higher the confidence level and precision required. Also if the occurrence rate in the population becomes larger the size of the sample would increase.
- In case of variables sampling, where the estimate of a quantity is required, sample size becomes a function of the standard deviation in the population rather than the occurrence rate.

Selecting the sample and performing substantive audit tests on the sample

- There are a large number of methods of sample selection.
- The most frequently used method is random selection
- Other methods are
- systematic selection method
- cell sampling method
- Auditing software, IDEA is an efficient tool for sample selection.

Projecting the results

- Once the audit tests are performed on the sample, the test results need to be projected to the population.
- Following this, a conclusion has to be reached whether the auditor can place an assurance on the systems.

Cont.

- In a case when the computed tolerable error is less than the tolerable error, the auditor can place the desired assurance on the systems.
- When the computed tolerable error is higher than the tolerable error, the auditor cannot derive assurance from the systems.

Advantages Of SS

- a. The sample result is objective and defensible.
- b.Objective evaluation of a test result is possible.
- c.The method provides a means of advance estimation of sample size on an objective basis.
- d.The method provides an estimate of sampling error.
- e. It may give more accurate results than a 100% examination for large population size as failure to detect errors tend to increase if the population size is very large.

f . It saves time and money.

- g. It may be combined and evaluated even though accomplished by different auditors.
- h. It helps in bringing the observations in sharp-focus as these can be analyzed fir each type of auditee.

Possible areas of application

- Audit of vouchers in CAP/CASS sections
- During local audit
- In reviews.
- In revenue audit

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