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Conducting the engagement: Sampling (Statistical concepts (Measures of…
Conducting the engagement: Sampling
Statistical concepts
Populations and samples
Sampling
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
Less expensive and less time consuming
If auditor is experienced no time is wasted on testing immaterial items.
Disadvantages
Does not provide a quantitative measure of sampling risk
Does not provide a quantitative expression of sample results
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
Provides a quantitative measure of sampling risk, confidence level and precision
Provides a quantitative expression of sample results
Helps auditor to design an efficient sample
Disadvantages
More expensive and time consuming than nonstatistical sampling
Requires special statistical knowledge and training
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
Determine the objectives of the plan
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
Determine acceptable levels of sampling risk
Calculate the sample size
Using tables or sample size formulas
Stratification
Select the sampling approach
Take the sample
Evaluate the sample results
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