# Statistically Oriented Techniques and VISION:Excel

**Document ID :**KB000028110

**Last Modified Date :**14/02/2018

Generally speaking, Internal and External auditors use sampling techniques to reduce their efforts and therefore conclude their audits within a reasonable time frame. Sampling always introduces a small amount of inaccuracy between what is true about the sample versus what is true about the population as a whole. Statistically Oriented Sampling Techniques help to quantify that inaccuracy.

For Statistically Oriented Sampling Techniques, VISION:Excel will calculate the statistically correct sample size, automate the selection of the sample, and provide guidelines, as dictated by the particular sampling technique, for evaluating the sample.

When you use a Statistically Oriented Sampling technique you are tied to very specific goals as defined by that technique. You are attempting to derive an estimate from a sample that should be somewhat close to the truth regarding the population as a whole. Here again, we divide these sampling techniques into two groups:

Attribute Oriented Sampling:

- Attribute Estimation Sampling
- Discovery Sampling
- Acceptance Sampling

Value Oriented Sampling:

- Dollar Unit Sampling
- Estimation Sampling of Values
- Proportional Sampling
- Stratified Mean Estimation Sampling

**Attribute Oriented Sampling**

In Attribute Oriented Sampling, every item in the population must have or not have a particular characteristic as defined by you. It is a binary situation; either an item has the characteristic or it doesn't. For instance, the balance amount in a record, when compared to the balance amount in the original handwritten statement, is correctly entered or it is not correctly entered.

With Attribute Estimated Sampling, you want to discover how many items in a population have a given characteristic by taking a random sample and counting the number of items in the sample with that characteristic. You then extrapolate to get an estimate of the answer you seek. For example in a file of 10,000 records, you find in your sample of 200 records, 10 records (5% of 200) whose balance amount has been incorrectly entered. You would estimate that there are 500 (5% of 10,000) records in the file with a balance amount that has been incorrectly entered. Attribute Estimation Sampling will also give you the upper and lower bounds of that estimate, i.e. 500 + or - 5.

If you want to select a sample that has at least one item with the given characteristic, you would use the Discovery Sampling technique. You want to find and examine an item that has the given characteristic.

Acceptance Sampling works well when you need a statistically valid method for accepting or rejecting a group of items. A sample is selected from a group, and if the sample contains more that a pre-designated number of characteristic (error) items, the whole group is rejected.

**Value Oriented Sampling**

Value Oriented Sampling presumes that a value is associated with each item in the population. The value could be any measure, i.e. money, tons, inches, etc. and can be designated in fractional amounts, i.e. $10.25, 6.782 kilometers.

The purpose of Dollar Unit Sampling is to determine, within statistical bounds, the dollar amount of errors in an accounting population. Dollar Unit Sampling is a statistical sampling technique that gives every dollar in an accounting population an equal opportunity to be included in the sample. Given the recorded total value of a population, how much of that total value is actually erroneous due to any number of reasons including careless entry? That's the question which Dollar Unit Sampling will determine within statistical bounds.

Estimation Sampling of Values will answer the question, "what is the true value of my population within statistical bounds?" For instance, to determine the actual value of a company's accounts receivables, you would take the total of the balances on the accounts receivables file. An auditor must then be mindful of questions, such as "were all of the balances entered correctly and could there be fraudulent activities hidden in the numbers?" Estimation Sampling of Values can help by determining the actual value, within statistical limits, of the population without the effort of manually going through every single handwritten statement.

The Proportional Sampling technique was designed to discover both compliance and substantive errors in a population. Compliance errors refer to errors committed in violation of internal procedure, such as missing mandatory signatures on documents that were subsequently electronically recorded as part of the internal procedure. Substantive errors refer to differences in the actual values versus the recorded values. The Proportional Sampling technique will quantify the number of compliance errors and the total value of the substantive errors.

The Stratified Mean Estimation Sampling technique divides the population into sub-populations each defined by a lower and upper valued limit. Then the Estimation Sampling of Values technique is applied to each of the sub-populations. Why stratify first? In both of these sampling techniques, the statistically correct sample size is determined from information you provide about the population or sub-populations. For populations that have widely disparate values, stratifying first into more homogeneously valued sub-populations will cause the aggregate sample size to be smaller than the sample size determined from the population as a whole. Of course, a smaller sample size means less effort to examine the sample items and evaluate the sample, while maintaining the same degree of accuracy.