## How to Perform Error Assurance with ADA

Introduction

Error Assurance is intended to assist attribute sampling planning for performance audits. However, it can be used in any attribute sampling situation where the user would like to see the likelihood of getting MORE than a critical number of errors rather than LESS than a critical number of errors in the sample. In some cases, an auditor conducting a performance audit sampling plan will want to ensure they find errors. Using the Error Assurance module, the user can enter a conservative (low) estimate of the population error occurrence rate and set a desired minimum number of errors for the sample they consider to be material to then in turn calculate the required sample size and/or calculate the likelihood of achieving that minimal error number or no errors at all. A sample can then be extracted using the ADA Random Sampling module since uniform random sampling should be employed to draw an unbiased, statistically valid sample. The Error Assurance algorithm is also employed in Classical Variable Sampling to help ensure the user gets enough errors to yield statistically tractable results. While traditional attribute sampling is conducted with the hypergeometric cumulative distribution function (CDF), error assurance employs the hypergeometric complementary CDF, which is also called the survival function.

Attribute Sampling Plan and Extract can be used solely for the calculation of the appropriate sample size and it can also be used to then extract that sized sample from a population file if provided. If no data file is open in ADA when the Plan and Extract module is executed, the Population Size value starts with the value zero, which must be changed. If the Extract button is subsequently selected after planning a sample size, then the user will be prompted to choose the appropriate population file. It will need to have the same number of records as the entered Population Size entry to proceed. If a data file is already open in the ADA Project Viewer when the Plan and Extract module is executed, then the number of records from that file will be used as the Population Size entry. You can change the Population Size entry, but keep in mind that Extract will not proceed unless the number of records from the file matches the Population Size entry. The program will offer the opportunity to replan the sample size after resetting the Population Size entry based on the file chosen if the user chooses to do so. If you plan to extract a sample, the best practice is to open the population file first in ADA and then run Attribute > Plan and Extract. Then, after entering the desired Sample Size Planning inputs, click Plan to get the calculated sample size. Once satisfied with the resulting sample size (if not, change the inputs and click Plan again), enter the output filename and click Extract to obtain the sample.

Note: If, after clicking Plan, the user changes the Sample Size Planning inputs and then clicks Extract without clicking Plan first, then the program will replan the sample size based on the new inputs and immediately extract the sample. Thus, it is a best practice to click Plan after changing the Sample Size Planning inputs. That way there are no surprises.

Formats Supported by Attribute Sampling Error Assurance

ADA’s Attribute Sampling Error Assurance utility does not work on any data, just user inputs.

Using the Dialog

The dialog box consists of three sections: General Inputs, Sample Size Calculations and Likelihood of Observing Minimal Errors. The General Inputs entries affect both the Sample Size Calculations and Likelihood of Observing Minimal Errors. In addition to these, a confidence level entry is required to calculate the sample size. Likewise, a sample size input is required to calculate the likelihood observing the minimum number of errors specified in the General Inputs section.

**General Inputs**. This section requires Population Size, the Minimal Population Error and the Minimal Material Sample Error., the Confidence Level and the Random Seed Number. Once provided, the user can employ the sections for calculating sample size and likelihoods.

**Population Size**. The number of items or records in the population data file. This is automatically filled in if an ADA data file is already open when the Error Assurance module is executed.

**Minimal Population Error**. The user’s best guess, estimate or anticipated error for the population. Unlike with traditional attribute sampling, this does not reflect a materiality goal for the auditor as it is merely descriptive of the amount of error in the population. The hypergeometric calculator will calculate probabilities assuming there is this much error in the population. As such, since the user will likely be unsure of the true population error rate and may consider a range of error rates to be a good possibility, then the lowest rate in that range of error rates will yield more conservative sample sizes and likelihoods.

**Population Error Rate**. The user can enter the error rate as a percentage of the total population size.

**Population Number of Errors**. The user can enter the total number of errors in the population.

For a population of size 10,000, a population error rate of 10% corresponds to 1,000 errors in the population. Either entry will yield the same answer.

**Minimal Material Sample Error**. The user sets the material amount of error they expect to achieve with the sample. In performance audits a certain number of errors may be considered material in terms of affecting users’ judgment of the goodness of a sample. A sample with more errors can lead to greater impact in terms of depth and breadth of findings. As more errors are found, then one or both of the following occur: 1) additional errors of the same type will yield a greater understanding of the extent of a problem and/or 2) more areas of improvement are identified as different types of errors are found. The material minimal number of errors in the sample represents a lower bound for the amount of error required.

**Minimal Number of Errors**. The user can enter the minimum number of errors in the sample regardless of the sample size.

**Minimal Sample Error Rate**. The user can enter the error rate as a percentage of the unknown or entered sample size.

**Sample Size Calculations**. This section calculates the minimum sample size to achieve the minimal material sample error at the desired level of confidence.

**Confidence Level for Achieving Minimum Errors**. Defines the desired likelihood of getting the minimal number of errors or more.

**Likelihood of Observing Minimal Errors**. This section calculates the probability of observing no errors as well as the minimal number of errors in a sample based on the General Inputs and Sample Size entries.

**Sample Size**. Sets the size of the sample one plans to use.

Questions

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