CIA Part 2: Section 7

Example of confidence level and interval

Based on sample, sales department authorized a sale after checking the credit score of the customer 88% of the time. If the confidence interval is 6%, auditor can be confident that between 82% and 94% of all company's sales were authorized after checking credit scores. (+/- 6% of the 88%) Confidence level is auditor's desired reliability of the sample. If specified confidence level is 95% and precision is 6%, auditor can be 95% confident that percentage of all company's sales that were authorized after checking credit is between 82% and 94%.

In a normal distribution, mean, median and mode are

the same and tails are identical

Variables Sampling

- used for continuous variables, such as weights or monetary amounts - provides info about whether stated amount is materially misstated - both upper and lower limits are relevant (an AR balance can be under- or overstated)

Difference Estimation Characteristics

- used when sampling for monetary values - individual carrying amounts must be known - sufficient misstatements must exist to be reliable - reliable and efficient when small errors predominate

Cost-Benefit Analysis

- Analysis using expected value provides more objective basis for setting control limits - Limits of controls should be set so cost of investigation is less than or equal to the benefits derived - Expected costs include investigation cost and cost of corrective action (Prob being out of control x cost of corrective action) + (Prob being in control x investigation cost) = Total expected cost

Confidence level

- area under the curve - percentage of times that a sample is expected to be representative of the population i.e. a confidence level of 95% should result in representative samples 95% of the time

Monetary-Unit Sampling Characteristics

- less accurate when many errors are expected - estimates monetary amounts of errors when expected error frequency is low - because sampling unit is monetary, method increases likelihood of selecting large items - measure of variability not needed

Unstratified MPU Characteristics

- less efficient than ratio when high error rate expected - bad if many small balance account errors exist

Stratified MPU Characteristics

- less efficient than ratio when high error rate expected - bad if many small balance account errors exist - greater emphasis on larger items - increases audit efficiency with subpopulations - variability within stratum reduced

Ratio Estimation Characteristics

- more efficient than MPU when high error rate expect. - reliable and efficient when small errors predominate - audit amounts should be proportional to carrying amounts - appropriate for proportional differences - minimum number of differences must be present

Attribute Sampling Characteristics

- not used to estimate monetary amount - used for applications involving binary (yes/no) propositions

Distance in standard deviations (Confidence coefficient) corresponding to percentage of data points covered (Confidence Level/area under the curve)

1 - 68% 2 - 95.5% 3 - 99.7%

Advantages of judgmental sampling

1. Can be less expensive and less time consuming 2. No special knowledge of statistics or software 3. Auditor has greater discretion to use his or her judgment and expertise to avoid wasting time testing immaterial items

Sample size for variables test depends on four factors:

1. Confidence level - greater desired confidence level, greater sample size should be 2. Population size - larger the population, larger the sample but above certain population size, sample size does not increase 3. Tolerable misstatement (precision) - interval around the sample statistic that is expected to include the true balance of the population at the specific confidence level, narrower the precision, larger the sample 4. Standard deviation (variability)- measure of variability of amounts in the population, increase in estimated standard deviation increases sample size

Basic steps in statistical plan

1. Determine the objectives of the plan 2. Define the population 3. Determine acceptable levels of sampling risk 4. Calculate the sample size 5. Select the sampling approach 6. Take the sample 7. Evaluate the sample results 8. Document the sampling procedures

Disadvantages of judgmental

1. Does not provide quantitative measure of sampling risk 2. Does not provide quantitative expression of sample results 3. If auditor not proficient, sample may not be effective

Advantage of chart

1. Identifies when process is out of control if X's fall outside regular limits 2. makes trends and cycles visible

Disadvantages of statistical sampling

1. More expensive and time consuming 2. Requires special statistical knowledge and training 3. Requires statistical software

Other chart types

1. P charts- show % of defects in a sample based on attribute (acceptable/not acceptable) 2. C charts- show defects per item, also attribute control chart 3. R chart- shows range of dispersion of a variable, such as size or weight 4. X-bar chart- shows sample mean for a variable

Advantages of statistical sampling

1. Provides quantitative measure of sampling risk, confidence level and precision 2. Provides quantitative expression of sample results 3. Helps auditor design efficient sample

Variations in process parameter could have several causes:

1. Random variations by chance, nothing you can do 2. Implementation deviations due to human or mechanical failure 3. Measurement variations from error in measurement of actual results 4. Model fluctuations caused by errors in formulation of a decision model 5. Prediction variances from errors in forecasting data used in a decision model

Primary Methods for variables sampling

1. Unstratified mean-per-unit 2. Stratified mean-per-unit 3. Difference estimation 4. Ratio estimation 5. Monetary unit sampling

Sample size for an attribute test depends on four factors:

1. the greater the desired confidence level, the larger the sample size should be 2. population size- sum of items to be considered for testing, bigger population means bigger sample 3. expected deviation rate- greater the population deviation, larger sample size should be 4. tolerable deviation rate (desired precision) is highest allowable percentage of population that can be in error and still allow auditor to rely on tested control lower tolerable deviation rate, larger sample should be

Acceptance Sampling

Determines the probability that the rate of defective items in a batch is less than a specified level.

Statistical Quality Control

Determines whether a shipment or production run of units lies within acceptable limits and whether production processes are out of control

Ratio estimation

Estimates the population misstatement by multiplying the recorded amount of the population by the ratio of the total audited amount of the sample items to the total recorded amount.

Statistical Control Charts

Graphic aids for monitoring the status of any process subject to acceptable or unacceptable variations during repeated operations Applications include: 1. Unit cost of production 2. Direct labor hours used 3. Ratio of actual expenses to budgeted expenses 4. Number of calls by sales personnel 5. Total AR

Stop-or-Go Sampling (Sequential Sampling)

In sampling, a method designed to avoid oversampling for attributes by allowing the auditor to stop an audit test before completing all steps, if the results have become clear.

Coefficient of variability

Measures the relative variability within the data and is calculated by dividing the standard deviation of the sample by the mean.

Block (cluster) sampling

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

Pareto Diagrams

a bar chart that assists managers in what is commonly called 80:20 analysis. 80% of all effects are the results of only 20% of all causes - managers optimize their time by focusing their effort on the sources of most problems

For variables sampling application, confidence level is complement of

allowable risk/acceptable risk of incorrect rejection

Discovery Sampling

appropriate when even a single deviation (noncompliance) is critical - sample size is calculated so it will include at least one instance of a deviation if deviations occur

Interval (Systematic) sampling

assumes that items are arranged randomly in the population. If they are not, random selection method should be used. Example is testing multiple months for SOX controls or selecting every 35th item in list

Discrete variables, such as yes/no decision whether to authorize payments of invoices are tested using

attribute sampling

Nonsampling risk

audit risk not related to sampling i.e. auditor fails to detect an error in a sample due to auditor inattention or fatigue

Mean-per-unit (MPU) estimation (Unstratified MPU)

averages audited amounts of the sample items, multiplies average by number of items in the population to estimate population amount. Achieved precision at desired level of confidence is then calculated

Achieved upper deviation limit (UDL)

based on the sample size and the number of deviations discovered- auditors use table to find intersection of sample size and # deviations

Case Study

data collection method that identified hypotheses that can be tested on a larger scale

Modeling

data collection that simulates an existing fact, occurrence of circumstance for further study

Allowance for sampling risk (achieved precision)

difference between achieved UDL determined from standard table and sample deviation rate

Histogram

displays a continuous frequency distribution of the independent variable

Stratification

divide the population into subpopulations or strata to help minimize variability and it helps the auditor to apply more audit effort to larger elements or more risky parts of the population

Disadvantage of chart

does not indicate the cause of the variation

Attribute Sampling

each item in the population has an attribute of interest to the auditor i.e. evidence of proper authorization appropriate for discrete variables

Difference estimation

estimates the misstatement of an amount by calculating the difference between the observed and recorded amounts for the items in the sample. - determines diff between audited and recorded amounts of items in sample, adds differences, calculates mean diff, multiplies mean by items in population, calculates achieved precision

Random sample

every item in the population has an equal and nonzero change of being selected

If the sample deviation rate exceeds the expected population deviation rate, achieved UDL

exceeds tolerable rate at given risk of overreliance and sample does not support planned reliance on control

Confidence interval

for a given confidence level is the range around a sample value that is expected to contain the true population value

For test of controls, confidence level is complement of allowable risk of overreliance on the control, i.e.

if risk is 5%, confidence level is 95% (100-95 = 5%)

For a given confidence level, size of confidence interval depends on sample size. So for larger sample size vs. smaller

larger- confidence interval is smaller smaller- true population value is expected to be in narrower range around sample value

If the mean is less than the median (less than mode)

left tail is longer and distribution is negatively skewed

Stratified MPU

means of increasing audit efficiency by separating population into logical groups, usually by ranges of tested amounts. Variability within each sub population is reduced and allows for smaller overall sample size

Standard deviation

measure of the dispersion of a set of data from its mean

Sample deviation rate

number of deviations observed in a sample divided by the sample size - best estimate of population deviation rate

Statistical Sampling

provides objective method of determining sample size and selecting items to be examined AND provides means of quantitatively assessing precision (how closely sample represents population) and confidence level (% of time sample will adequately represent population)

Confidence coefficient serves same function as in attribute sampling, but in variables it corresponds to

range around calculated amount rather than estimate of maximum error rate

Evaluation Synthesis

systematic procedure that organizes observations and results from separate engagements and combines them into a single evaluation for all of the included engagements

Missed Question #1: The auditor wishes to sample the perpetual inventory records to develop an estimate of the monetary amount of misstatement, if any, in the account balance. The account balance is made up of a large number of small-value items and a small number of large-value items. The auditor has decided to audit all items over $50k plus a random selection of all others. This audit decision is made because the auditor expects to find a large amount of errors in the perpetual inventory records but is not sure that it will be enough to justify taking a complete physical inventory. The auditor expects the errors to vary directly with the value recorded in the perpetual records. The most efficient sampling procedure to accomplish the auditor's objectives is

ratio estimation - estimates the population misstatement by multiplying the recorded amount of the population by the ratio of the total audit amount of the sample to its total recorded amount. It is reliable and efficient when small errors predominate and are not skewed. Not sampling very large items and not skewed

If the mean is greater than the mode

right tail is longer and the distribution is positively skewed (mode, median and then mean on number line)

Sampling risk

risk that sample is not representative of the population and may result in incorrect conclusion

Sampling risk is inversely related to

sample size

Sampling

selecting representative units from a total population, examining, and drawing conclusion about population based on those

Population's variability is extent to which the values of items are spread about the mean and is measured by

standard deviation

Standard error of the mean

standard deviation of the distribution of sample means

Control chart consists of

three lines plotted on a horizontal time scale - center line represents overall average range for process being controlled - other two lines are upper control limit (UCL) and lower control limit (LCL) - processes measured periodically and values (X) plotted on the chart

Fishbone Diagram (Cause and effect diagram)

total quality management process improvement technique useful in studying causation - organizes the analysis of causation and helps to identify possible interactions among causes

Nonstatistical Judgmental sampling

uses auditor's subjective judgment to determine sample size and sample selection

Monetary-unit Sampling (MUS) aka probability-proportional-to-size (PPS) sampling

uses monetary unit as sampling unit and applies attribute sampling to reach conclusion about probability of overstating monetary amounts - appropriate for testing account balances for overstatement when some items far larger than others in population so population is stratified and larger balances have higher chance of being selected

Normal Distribution

values form a symmetrical, bell-shaped curve centered around the mean

Continuous variables, such as monetary amounts of AR, are tested using

variables sampling