Statistical Sampling in Audit

1 Statistical Sampling in Audit 1. Introduction: Our knowledge our attitudes and our actions are based to a very large extent on observations of few samples. This is equally true in everyday life, in scientific research and also in Audit . A person s opinion of an institution that conducts thousands of transactions every day is often determined by the one or two encounters which he or she has had with the institution in the course of several years. In science and human affairs alike we lack the resources to study more than a fragment of the phenomena that might advance our knowledge. Sampling consists of selecting some part of a population to observe so that one may estimate something about the whole population.

2 For example to estimate the amount of recoverable oil in a region, a few (highly expensive) sample holes are drilled .The situation is similar in a national opinion survey, in which only a sample of the people in the population is contacted, and the opinions in the sample population is used to estimate the proportions with the various opinions in the whole population. To estimate the prevalence of a rare disease, the sample might consist of a number of medical institutions, each of which has records of patients treated. Sampling is the science that guides quantitative studies of content, behavior, performance, materials and causes of differences Some obvious questions for such studies are how best to obtain the sample and make the observations and, once the sample data are in hand, how best to use them to estimate the characteristic of the whole population.

3 Obtaining the observations involves the question of sample size, how to select the sample, what observational methods to use, and what measurements to record. These are the issues, which are scientifically addressed, in Statistical Sampling . In the basic Statistical Sampling setup, the population consists of a known, finite number of N units - such as transactions, households, people etc. With each unit a value of variable of interest is associated, may be referred to as x-value of the unit .The x-value of the unit in the population is viewed as fixed, unknown quantity. The units in the population are identifiable and may be labeled with numbers 1,2,..,N. Only a sample of the units in the population are selected and observed.

4 The data collected consist of the x-value for each unit in the sample, together with the unit s label. The procedure by which the sample of units is selected from the population is called Sampling design. The usual inference problem in Sampling is to estimate some summary characteristics of interest of the population, such as the mean or the total of the x-values after observing only the sample. The basic Statistical Sampling view assumes that the variable of interest is measured on every unit in the sample is without error, so that the errors in the estimates occur only because just part of the population is included in the sample. Such errors are referred to as Sampling errors.

5 But in real survey situation non- Sampling errors may arise also. It may be due to non-response, measurement error, fatigue, detectability problems etc. 2. Sampling in Audit . In the early stages of the development of independent Audit , it was not an uncommon practice for an auditor to perform a 100% examination of the entries and records of the entities audited. However, as the economy grew, it quickly became apparent that a 100 % examination of the tremendous volume of entries was unwarranted and uneconomical. This developed into the test or test check approach, which is both widely accepted and widely used in Audit .It is quite obvious that such a method, involving examination of a portion of a large quantity of entries in order to draw conclusions about the larger group, is a Sampling operation, even though the word sample is not generally used in connection with a test.

6 When Sampling became a widely accepted tool in Audit then another concept called Risk Assessment came almost simultaneously, which allowed auditor to focus on risky areas through an objective analysis of available information about the auditable unit. This is somewhat similar to auditor s judgment based on auditor s experience and skill. The main idea of risk analysis is to identify risky areas in an objective way so that the auditor can focus on more risky area and optimally use available resources to meet overall Audit objectives. Obviously Sampling based only on risk assessment is non- Statistical Sampling . These non- Statistical samplings have been called by different names in literature as 1) Judgmental Sampling , 2) Convenient Sampling , 3) Purposive Sampling or, 4) Haphazard Sampling .

7 Auditors may choose a non- Statistical Sampling plan that is, they may want to rely on judgment or specific knowledge about the population in selecting units for Audit . Auditors cannot use the results from the judgmental (non- Statistical ) sample to draw conclusions about the population in general. Alternatively, the specific knowledge (or judgment) about the population units may be used to develop a statistically valid Sampling plan based on which one can draw conclusion about the population. One method could be to use this knowledge to divide the population into several homogeneous sub-groups called strata, and from each stratum some units may be sampled using some Statistical procedure for Audit .

8 Such Sampling plan will improve the Audit procedure. The users of the Audit report expect fairness in the selection procedure and more transparent reporting. The auditors on the other hand are interested in commenting about the nature of problems in the population from the Audit findings in the sample. The Statistical Sampling , which provides estimates including the reliability of the estimates of character of interest, is the scientific solution to these problems. The Audit reports based on this scientific approach are defensible. This enhances the acceptability and effectiveness of Audit report. 3. Definition & advantages of Statistical Sampling . The essential features of Statistical Sampling are: (i) The sample items should have a known probability of selection- for example, by random selection.

9 (ii) The sample results should be evaluated mathematically that is, in accordance with probability theory. Just because one of these requirement is met does not mean that the application is Statistical . For example, practitioners and others will sometimes state that they are using Statistical Sampling solely because a random number method is employed to select the sample. However this is not Statistical Sampling as no attempt has been made to evaluate mathematically sample findings (condition no. 2). Statistical Sampling allows auditors to calculate sample reliability and risk of reliance on sample. It permits auditors to optimize the sample size given the mathematically measured risk they are willing to accept.

10 In this both - over auditing and under auditing can be avoided. It enables auditors to make objective statements about the sample population on the basis of sample observations. In other words, the sample finding can be projected to the population. 4. Various Statistical Sampling methods . The simplest form of random/ Statistical Sampling consists in selecting the sample unit-by-unit (or, item-by-item), ensuring equal probability of selection to every unit at each draw. This technique of selection is termed as Simple Random Sampling (SRS). SRS are of two types: In Simple Random Sampling With Replacement (SRSWR) a unit is selected from the Sampling frame (list of units in the population); the unit is replaced back and the next unit is selected; the process is repeated till a sample of the desired size is selected.