Calculating sample size for a monetary unit sample

Before sampling a set of data, you must calculate the statistically appropriate sample size, and other values required by the subsequent sample and evaluate operations.

The Calculate Sample Size feature in Analytics calculates the required values for you based on input values you provide.

The importance of calculating a sample size

Calculating an appropriate sample size is critical to the validity of the subsequent sample. If the sample is not valid, or representative, you cannot reliably project the results of audit procedures you perform on the sample to the entire population.

Do not skip calculating a sample size, or guess at a sample size.

Most of the input values you use to calculate sample size are based on your professional judgment. Ensure that you fully understand the implications of the values before relying on the results of sampling in a production environment. Consult audit sampling resources, or an audit sampling specialist, if you are in doubt.

How input values affect sample size

Input values affect the sample size calculated by Analytics. You can use the Calculate button in the Size dialog box to experiment with how the different input values affect the sample size.

The table below summarizes the effect of input values on sample size.

Increasing this input value:	Decreases sample size	Increases sample size
Confidence
Population
Materiality
Expected Total Errors

Steps

1. Select Sampling > Record/Monetary Unit Sampling > Calculate Size.

   Note

   The menu option is disabled if a table is not open.

2. On the Main tab, select Monetary.
3. Enter the input values to use for calculating the sample size:
   • Confidence
   • Population
   • Materiality
   • Expected Total Errors

   Note

   The input values are explained in detail below.

4. (Optional) Click Calculate to see a preview of the output results.

   Tip

   Clicking Calculate instead of OK allows you to experiment with different input values before outputting the results.

   Note

   The output results are explained in detail below.

5. On the Output tab:
   1. In the To panel, select one of the following:
      • Screen displays the results in the Analytics display area

        Tip

        You can click any linked result value in the display area to drill down to the associated record or records in the source table.

      • File saves or appends the results to a text file

        The file is saved outside Analytics.

   2. If you selected File as the output type, do one of the following:
      • Enter a file name in the Name text box.
      • Click Name and enter the file name, or select an existing file in the Save or Save File As dialog box to overwrite or append to the file.

        If Analytics prefills a file name, you can accept the prefilled name, or change it.

        You can also specify an absolute or relative file path, or navigate to a different folder, to save or append the file in a location other than the project location. For example: C:\Results\Output.txt or Results\Output.txt.

      Note

      ASCII Text File or Unicode Text file (depending on which edition of Analytics you are using) is the only option for File Type.

6. Click OK.
7. If the overwrite prompt appears, select the appropriate option.

Size dialog box inputs and results

The tables below provide detailed information about the input values and output results in the Size dialog box.

Main tab – input values

Input values – Size dialog box	Description
Confidence	Your desired confidence level that the resulting sample is representative of the entire population. For example, entering 95 means that you want to be confident that 95% of the time the sample will in fact be representative. Confidence is the complement of “sampling risk”. A 95% confidence level is the same as a 5% sampling risk.
Population	The absolute value of the numeric sample field. Note To get the absolute value, profile or generate statistics on the sample field.
Materiality	The maximum total amount of misstatement that can occur in the sample field without being considered a material misstatement. For example, entering 29000 means that the total amount of misstatement must be greater than $29,000 to be considered a material misstatement.
Expected Total Errors	The total amount of misstatement that you expect the sample field to contain. For example, entering 5800 means that you expect the total amount of misstatement to be $5,800. Note The Expected Total Errors you specify must be less than Materiality. If the difference between them is too small, the error message Error rate too high for calculation appears. In audit sampling terms, the degree of sampling precision represented by the difference is too small to be calculated for the confidence level you specified.

Main tab – output results

Output results – Size dialog box	Description
Sample Size	The required sample size.
Interval	The interval value – required for the fixed interval and the cell selection methods.
Maximum Tolerable Taintings (%)	The maximum accumulated tainting percentages that can occur in misstated amounts in the resulting sample without exceeding the Materiality. Note The Maximum Tolerable Taintings (%) value reported by Analytics can be greater than 100%. For more information, see Maximum Tolerable Taintings (%).

An example of inputs and results

Maximum Tolerable Taintings (%)

Maximum Tolerable Taintings (%) provides one way of evaluating misstatement in a population.

If you use this method, you know in advance the threshold value reported by Analytics, before you begin audit procedures on the sampled data. If cumulative errors you observe in the course of performing the procedures exceed the threshold value, you know at that point that the sample field is materially misstated.

After performing your substantive procedures on sampled data you can sum all the individual tainting percentages from any misstated amounts. If the sum of the tainting percentages is less than or equal to the Maximum Tolerable Taintings (%) reported by Analytics, you can consider that the amounts in the sample field as a whole are not materially misstated, for your specified confidence level.

Statistical validity of sample sizes generated by Analytics

Analytics generates statistically valid sample sizes for most analyses. Exceptions may apply in the following situations:

• You are sampling data sets of less than 1000 records.
• Your organization has in-house sampling experts who can define sample sizes precisely tailored to your needs.
• Your organization has mandated the use of another sampling tool or methodology.

Poisson distribution versus binomial distribution

Two commonly used methods of generating sample sizes are the Poisson and the binomial distributions. Analytics generates sample sizes using the Poisson distribution.

For typical data sets of a thousand or more records, the Poisson and the binomial distributions generate nearly identical sample sizes. For populations of under a thousand records, sample sizes determined with the Poisson distribution tend to be slightly larger and therefore more conservative than sizes determined with the binomial distribution. The binomial distribution adjusts the sample size downward for small populations but the Poisson distribution does not. With very small populations, the sample size generated by the Poisson distribution can actually exceed the population size.

When calculating sample sizes in Analytics, recognize that for record sampling of small data sets, the sample size may be larger than you need. This larger sample size does not present an obstacle to analysis because it is common practice to manually oversample small populations.