Conducting the engagement: Sampling

Statistical concepts

Populations and samples

Sampling

  1. Selecting representative items from a population 2. Examining those selected items 3. Drawing a conclusion about the population

Main issue in sampling is choosing a sample that is representative of the population.

Population distributions

Discrete variables- Attribute sampling

Continues variables- Variables sampling

Measures of central tendency

Mean

Arithmetic average of a set of numbers

Median

Middle value if data are arranged in numerical order

Mode

Most frequently occurring value. If all values are unique no mode exists.

Confidence level and Confidence interval

Confidence level

Percentage of times that a sample is expected to be representative of the population

Confidence interval

Range around a sample value that is expected to contain the true population value.

Pilot sampling and standard error

Standard deviation of a population can be estimated using a pilot sample

Standard error of the mean

Standard deviation of the distribution of sample means.

Used to compute precision (confidence interval)

Larger the standard error wider the interval

Coefficient of variability

Measures the relative variability within the data

Standard deviation of sample/Mean

Sampling concepts

Nonstatistical (Judgemental) sampling

Uses auditors subjective judgement to determine the sample size and sample selection.

Advantages

  1. Less expensive and less time consuming
  1. If auditor is experienced no time is wasted on testing immaterial items.

Disadvantages

  1. Does not provide a quantitative measure of sampling risk
  1. Does not provide a quantitative expression of sample results
  1. If the auditor is not proficient the sample may not be effective.

Statistical sampling

An objective method of determining sample size and selecting the items to be examined.

Provides a means of quantitatively assessing precision and confidence level

Advantages

  1. Provides a quantitative measure of sampling risk, confidence level and precision
  1. Provides a quantitative expression of sample results
  1. Helps auditor to design an efficient sample

Disadvantages

  1. More expensive and time consuming than nonstatistical sampling
  1. Requires special statistical knowledge and training
  1. Requires statistical software

Nonsampling Vs sampling risk

Nonsampling risk

Audit risk not related to sampling

Sampling risk

Risk that a sample is not representative of the population

Selecting the sampling approach

Random sample

Every item in the population has an equal and nonzero chance of being selected

Random number tables are often used

Interval (Systematic) sampling

Assumes that items are arranged randomly in the population

If not a random selection method should be used

Divides the population by the sample size and selects every nth item after a random start in the first interval

Block (cluster) sampling

Randomly selects groups of items as the sampling units rather than individual items.

Disadvantage is that variability of items within the clusters may not be representative of the variability within the population.

Basic steps in a statistical plan

  1. Determine the objectives of the plan
  1. Define the population

Includes defining the sampling unit and considering the completeness of the population

Tests of controls- period covered is defined

Tests of details- individually significant items may be defined

  1. Determine acceptable levels of sampling risk
  1. Calculate the sample size

Using tables or sample size formulas

Stratification

  1. Select the sampling approach
  1. Take the sample
  1. Evaluate the sample results
  1. Document the sampling procedures

Attribute sampling

Uses

Each item in the population has an attribute of interest to the auditor

Appropriate for discrete variables

Used for tests of controls

Sample size

Confidence level

Percentage of times that a sample is expected to be representative of the population

Greater the desired confidence level the larger the sample size should be

For test of controls

(100% - Allowable risk of overreliance %)

Population size

Sum of the items to be considered for testing

For a very large population the population size has a very small effect on sample size

Expected deviation rate

Expected rate of occurrence

Greater the population deviation the larger the sample size should be

Tolerable deviation rate

Highest allowable percentage of the population that can be in the error and still allow the auditor to rely on the tested control

Lower the tolerable deviation rate, larger the sample size should be

Evaluation of sample results

Calculating sample deviation rate and the achieved upper deviation limit

Sample deviation rate (Best estimate of the population deviation rate)

No of deviations observed/ sample size

Achieved upper deviation limit (UDL)

Is based on sample size and number of deviations discovered

Allowance for sampling risk

Is the difference between achieved UDL and the sample deviation rate

Sample deviation rate equals No. of errors discovered in a sample/ sample size

Sample deviation rate>expected population deviation rate -Achieved UDL > Tolerable rate at the given risk of overrelience

Sample does not support the planned reliance on the control

Sample deviation rate < expected population deviation rate - Achieved UDL < Tolerable rate at the given risk level

Sample supports the planned reliance on the control

Other attribute sampling methods

Discovery sampling

Appropriate when even a single deviation is critical

Stop or go sampling (sequential sampling)

Objective is to reduce the sample size when the auditor believes the deviation rate in the population is low