Audit Sampling Flashcards
Risk
Auditing is all about risk
Risk is unavoidable because auditor’s do not examine 100% of the evidence
Statistical Sampling
Allows an auditor to quantify risk
Measures in mathematical terms the amount of risk that an auditor is taking
Types of Sampling
Attribute Sampling - tests of controls (compliance)
Test population for a certain characteristic (i.e. attribute). Used as a test of internal controls (compliance)
Ex. How many accounts receivable have never filed a credit application?
Variable samping - substantive tests
Trying to estimate the dollar value of a population. Used as a substantive test of details
Ex. How much does the value vary from stated amount in financials?
Sampling Plan: Step 1
# Define the population Almost infinite amount of potential populations are in a typical set of financial statements
Must use auditor judgment to define in precise terms the population to be sampled
Sampling: Concept 1
Concept 1: Must assume that the defined population has the properties of a Normal Curve
Central Limit Theorem: The arithmetic mean of all the samples drawn from the population would form a perfect normal curve
Sampling: Concept 2
In order for the sample to be mathematically valid, it must be an unrestricted, random sample
Randomness - every item in the population must have an equal chance of being selected
One place where auditor judgement (bias) may not exist
Random Sample: use a random number generator; audit the transactions/balances indicated by the random numbers; come to a conclusion about each
Systematic Sampling
Weak form of randomness:
Randomly select a first item
Select every 10th item after that
A weak form of randomness
If the population has any order, misleading results
Strongest form of randomness is the use random number generator and audit the transaction until the end.
Sampling: Concept 3
Variability
Variability causes uncertainty; the more variability, the larger the sample size
Standard Deviation - the standard measure of variability
Mean per unit projection/estimation
Audited Sample Size divided by sample size = Sample arithmetic mean
Multiply that by population size = estimated popluation value (point estimate)
1 Standard Deviation / Precision at 68%
Will encompass 68% of the curve
Number of standard deviations (1) x standard error of the mean x population size = precision
68% confident that the value is the point estimate plus or minus the precision
1.96 Standard Deviation
Will encompass 95% of the curve
Number of standard deviations (1.96) x standard error of the mean x population size = precision
95% confident that the value is the point estimate plus or minus the precision
Tolerable Misstatement
What the auditor is willing to accept
Relates to auditor’s judgement of materiality
Smaller tolerable misstatement, larger sample size (inverse relationship)
Ratio Estimation
Audited Sample value divided by book sample value = ratio
Ratio multiplied by book population value = point estimate
Difference Estimation
Audited sample value minus book sample value = sample value difference
Divded by number of sample items = difference per item
Difference multiplied by number of population = population value difference
Add book population value = point estimate
Stratified Sampling
Split population into several smaller populations
Reduce variability for smaller sample sizes
Sampling Risk
Sample could be wrong
No guarantee that a random sample is representative of a population
Alpha Risk in Variable Sampling
Financial statement correct (they are fairly stated)
Sample says material error (sample is wrong)
Modify opinion unnecessarily
Risk of incorrect rejection
Beta Risk in Variable Sampling
Financial statements incorrect
Sample says correct (sample is wrong)
Fail to modify opinion
Risk of incorrect acceptance
Attribute Sampling: Looking for?
Error rate (point estimate)
Tolerable Error Rate
Error rate auditor is willing to tolerate
Alpha Risk in Attribute Sampling
Internal Control is effective
Sample says material weakness (sample is wrong)
Assess control risk too high (risk of under-reliance on controls)
Result: Too much substantive testing
Beta Risk in Attribute Sampling
Internal Control is ineffective
Sample says no material weakness (sample is wrong)
Assess control risk too low (risk of over-reliance on controls)
Result: Too little substantive testing
Expected Error Rate and relationship to sample size
Direct relationship:
High error rate: Large Sample
Low error rate: Small sample
Tolerable Error Rate and relationship to sample size
inverse relationship:
High error rate: Small Sample
Low error rate: Large sample
Discovery Sampling
Type of attribute sampling
A predetermined probability of discovering one item
use with critical items
expect error rate to be very low
PPS Sampling (dollar unit sampling)
Probability proporationate to size
Uses attribute sampling table to assist in sampling variables
From table obtain reliability factor
Tolerable misstaement divided by reliability factor = sampling interval
Population value / sampling interval = sample size
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PPS Sampling Advantages
Sample size not affected by variability
Start picking sample before the entire population is available
Population automatically stratified… larger value items have a higher change to be selected in the sample.
Calculating Allowance for Sampling Risk
Equals the difference between the upper precision limit and the sample deviation risk (errors/sample size)
