# Auditing – Probability Proportional to Size

**Objective of using probability proportional to size sampling (PPS) to test account balances**

-PPS tests the reasonableness of a recorded account balance or class of transactions.

-Probability Proportional to Size (PPS) is used to determine the accuracy of financial accounts i.e. to test for overstatements.

**How specifically Probability Proportional to Size has been used to test this company’s accounts balances**

The process of using PPS in testing this company’s accounts balances involves the following steps:

- Determine the objective of the test- Probability Proportional to Size tests the reasonableness of a recorded account balance. In this situation we are going to use PPS in testing account balances and transactions of overstatements (Brewer & Hanif, 2013).
- Define the population. The population is the account balance of the company being tested.

- Define the sampling unit. The sampling unit in PPS are the individual dollars in the population.
- Consider the completeness of the population- As with other sampling plans, the auditor must assure him/herself if that the physical representation of the population being tested includes the entire population (Lin, 2011).
- Identify individually significant items-PPS automatically includes in the sample any unit that is individually significant.

- Select an audit sampling technique- Here we have selected PPS.
- Determine a sample size- A PPS sample divides the population into sampling intervals and select a logical unit from each sampling interval.

- Using the formula, sample size=(Book value of population * Reliability Factor)/(Tolerable error-(Anticipated Error*Expansion factor)) =approx. 169.
- Sampling interval= Book value of the population/Sample size.

=3460000/169

=20473

- Determine the method of selecting the sample- Probability Proportional to Size samples are generally selected using systematic sampling with a random start. All logical units (e.g. accounts) with dollar amounts greater than or equal to the sampling interval are certain to be selected.
- Perform the audit procedures- The auditor must apply appropriate audit procedures to determine an audit value for each logical unit included in the sample.
- Evaluate the results and arriving at a conclusion about the population- misstatements found should be projected to the population and an allowance for sampling risk should be calculated. When the sampling contains misstatements, the upper limit on misstatements is the total of projected misstatement and the allowance for sampling risk (with its two subcomponents) (Stage & Intermountain Forest and Range Experiment Station, 2010).

Upper limit On = Projected misstatements + Allowance for sampling risk.

Misstatements (Basic precision) & (incremental allowance forProjected misstatements)

Since the logical unit is greater than the sampling interval, therefore the actual amount of misstatement is considered to be the projected misstatement.

I.e. projected misstatement=$ 63400

And allowance for sample risk= Basic precision + incremental allowance for projected misstatements

But basic precision=Reliability factor*sampling interval

=3*20473.

=61419

And incremental allowance for project misstatement is determined by ranking the misstatement for logical units that are less than the sampling intervals from highest to lowest and considering the incremental changes in reliability factors for the actual numbers of misstatements found(Whittington, & Delaney, 2008). One must subtract 1.00 from each incremental change to isolate the incremental allowance for projected misstatements.i.e 3-1=2.

Hence upper limit on misstatement= 63400+61419+2

=$124821.

- Decision rule: Comparing the upper limit on misstatement to tolerable misstatement, since the upper limit on misstatement is greater than the tolerable misstatement, the sum results do not support the conclusion that the population is not misstated by more than the tolerable misstatement. This may be due to the fact that : either
- The population is misstated,
- The auditor’s expectation of misstatement was low and resulted in too small of a sample, or

- The sample is not a representative of the population.

**The purpose of the sample size and the sampling interval **

– A good sample size enables us to make precise inferences/conclusion about a population characteristic from a sample characteristics (Whittington, & Delaney, 2008).

– Sampling interval separates a population into relatively homogenous groups to reduce the sample size by minimizing the effect of variation of items (i.e standard deviation) in the population.