Which of the following most likely would be an advantage in using classical variables sampling rather than monetary unit sampling?

Classical variables sampling is a statistical sampling method for estimating:

• the total audited value of an account or class of transactions
• the total amount of monetary misstatement in an account or class of transactions

Classical variables sampling works best with financial data that has the following characteristics:

Note

In addition to financial data, you can use classical variables sampling with any numeric data that has a variable characteristic – for example, quantity, units of time, or other units of measurement.

How it works

Classical variables sampling allows you to select and analyze a small subset of the records in an account, and based on the result estimate the total audited value of the account, and the total amount of monetary misstatement.

The estimates are computed as ranges:

• The point estimate is the midpoint of the range.
• The upper limit and the lower limit are the two end points of the range.

  You can also choose to compute a one-sided estimate or range, with a point estimate and only an upper limit, or only a lower limit.

You compare the estimated range to the book value of the account, or to the misstatement amount that you judge is material, and make a determination regarding the account.

Classical variables sampling supports making this sort of statement:

• There is a 95% probability that the true audited value of the account is between 45,577,123.95 and 46,929,384.17, a range that contains the account book value of 46,400,198.71. Therefore the amounts in the account are fairly stated.
• There is a 95% probability that the misstatement in the account balance is between – 813,074.76 and 539,185.46, which does not exceed the monetary precision of ±928,003.97. Therefore the amounts in the account are fairly stated.

Overview of the classical variables sampling process

Caution

Do not skip calculating a valid sample size.

If you go straight to drawing a sample of records, and guess at a sample size, there is a high likelihood that the projection of your analysis results will be invalid, and your final conclusion flawed.

The classical variables sampling process involves the following general steps:

1. Prepare (plan) the classical variables sample
2. Draw the sample of records
3. Perform your intended audit procedures on the sampled data.
4. Evaluate the following:
   • whether the audited value of the sampled data, when projected to the account as a whole, falls within an acceptable range of the recorded book value
   • whether the observed levels of monetary misstatement in the sampled data represent an acceptable or unacceptable amount of misstatement in the account as a whole

Numeric length limitation

Several internal calculations occur during the preparation stage of classical variables sampling. These calculations support numbers with a maximum length of 17 digits. If the result of any calculation exceeds 17 digits, the result is not included in the output, and you cannot continue with the sampling process.

Note that source data numbers of less than 17 digits can produce internal calculation results that exceed 17 digits.

Values are retained and prefilled between stages

When you use Analytics for classical variables sampling you enter information in three separate dialog boxes, and run the associated commands, in this order:

1. CVS Prepare dialog box
2. CVS Sample dialog box
3. CVS Evaluate dialog box

As you move through this process, information from one dialog box is prefilled into the next dialog box. Prefilling saves considerable labor, and removes the risk of accidentally entering incorrect values and invalidating the sample.

Important considerations

• Changing prefilled values normally you should not change any of the prefilled values. Changing prefilled values can negate the statistical validity of the sampling process.

  Caution

  Update prefilled values only if you have the statistical knowledge to understand the effect of the change.

• Temporary storage of values values that automatically prefill the CVS Sample and the CVS Evaluate dialog boxes are only stored temporarily, and are deleted when you close the Analytics project.

Guidelines

Follow these guidelines to make the end-to-end CVS process as smooth as possible:

• Do not close the Analytics project between the CVS Prepare and CVS Sample stages.

  Tip

  If you do close the project, you can restore the temporary CVS values by re-entering the required information in the CVS Prepare dialog box, or by re-running the CVSPREPARE command from the log.

• Optional. After running CVS Prepare and CVS Sample, save the commands to a script. You can copy the commands from the output display or from the log.

  You can also copy the preliminary version of the CVSEVALUATE command that is included in the output of CVS Sample.

  If required, you can re-run one or more of the CVS commands from the script. Type COMMENT before any command you do not want to run. You will probably need to update the preliminary version of the CVSEVALUATE command. For more information, see Performing classical variables sampling.

Stratification

Classical variables sampling gives you the option of numerically stratifying the records in a population before drawing a sample.

The benefit of stratification is that it often dramatically reduces the required sample size while still maintaining statistical validity. A reduced sample size means less data analysis work is required to reach your goal.

How it works

Stratification works by dividing a population into a number of subgroups, or levels, called strata. Ideally, the values in each stratum are relatively homogenous.

A statistical algorithm (the Neyman method) sets the boundaries between the strata. The algorithm positions the boundaries to minimize the dispersion of values within each stratum, which decreases the effect of population variance. Reducing the variance, or 'spread', reduces the required sample size. By design, the range of each stratum is not uniform.

The required number of samples is then calculated on a per-stratum basis, and totaled, rather than on the basis of the entire, unstratified population. For the same set of data, the stratified approach typically results in a much smaller sample size than the unstratified approach.

Pre-stratification using cells

As part of the stratification process, you specify the number of cells to use to pre-stratify the population. Cells are uniform numeric divisions, and narrower than strata.

A statistical algorithm uses the count of the records in each cell as part of the calculation that assigns optimal strata boundaries. Cells are not retained in the final stratified output.

At a minimum, the number of specified cells must be twice the number of specified strata.

Note

Pre-stratification cells and the cells used in the cell method of sample selection are not the same thing.

Too much of a good thing

Stratification is a powerful tool for managing sample size, but you should exercise care when specifying the number of strata and the number of cells.

As a starting point, try:

• 4 to 5 strata
• 50 cells

After a certain point, increasing the number of strata, or the number of cells, has little or no effect on sample size. However, these increases can adversely affect the design of the sample, or the performance of Analytics when stratifying large data sets.

Regarding sample design, when you reach the evaluation stage you need to have a minimum number of misstatements in each stratum in order to reliably project misstatements to the entire population. If you have too many strata in relation to the number of misstatements, problems can occur with the projection.

The certainty stratum

Defining a certainty stratum is another available stratification option.

Using a certainty stratum has two benefits:

• Individually significant items, or high value items, are automatically included in the sample, and not at risk of being excluded by the random selection method.
• Certainty stratum items are removed from the sample size calculation. Because of their nature, high value items can significantly increase population variance, and the required sample size, if they are included in the calculation.

Defining a certainty stratum

To define a certainty stratum, you specify a numeric cutoff value. All key-field book values greater than or equal to the cutoff value are automatically selected and included in the sample. The remainder of the population is sampled using the random selection method.

Note

The lower you set the certainty stratum cutoff value, the more you increase the overall sample size.

You should avoid setting the cutoff value unnecessarily low. Consult a sampling specialist if you are unsure where to set the value.

Top and bottom certainty strata

The certainty stratum option in Analytics defines a top certainty stratum only. Numbers greater than or equal to the cutoff value are included in the certainty stratum.

You may also want a bottom certainty stratum, to automatically include large negative values in the sample, and to reduce variance.

To create a bottom certainty stratum, you can use either of the following methods:

• Before beginning the classical variables sampling process, use a filter and extract all values from the population that are less than or equal to a bottom cutoff value.

  You can keep these records in a separate table, or you can append them to the output table containing the samples from the rest of the population.

  For more information, see Extracting and appending data.

• During the CVS Prepare and CVS Sample stages, use an If condition to filter out bottom certainty stratum items.

  Caution

  This method is riskier, and less recommended, because you have to remember to consistently apply the If condition at both stages, and during any subsequent repetition of the stages.

How classical variables sampling selects records

Classical variables sampling uses the following process for selecting sample records from an Analytics table:

• You specify a numeric field as the basis for the sampling. The sampling unit is an individual record in the table.
• Using the random selection method, Analytics selects samples from among the records in the table.
• If you are using stratification, a roughly equal number of records are randomly selected from each stratum.
• If you are not using stratification, records are randomly selected from the entire population.
• The selected records are included in the sampling output table.

Example

In a table with 300 records, divided into 3 strata, Analytics could select the following record numbers:

In an unstratified table with 300 records Analytics could select the record numbers displayed below. You can see that the selected record numbers are less evenly distributed.

Note

The record numbers below are grouped in three columns for ease of comparison, but the columns do not represent strata.

Unbiased sample selection

Classical variables sampling is unbiased and it is not based on the amounts contained in a record. Each record has an equal chance of being selected for inclusion in the sample. A record containing a $1000 amount, a record containing a $250 amount, and a record containing a $1 amount all have the same chance of being selected.

In other words, the probability that any given record will be selected has no relation to the size of the amount it contains.

What is an advantage in using classical variables sampling?

Which of the following would most likely be an advantage in using classical variables sampling rather than?

What is classical variable sampling?

Which of the following is an improper technique when using monetary unit statistical sampling in an audit of accounts receivable?