1 of 39

CHAPTER 9: TRANSFORMING DATA INTO�EVIDENCE �(PART 2)

2 of 39

Learning Objectives

Explain the application of descriptive statistics in forensic accounting engagements
Identify and describe various methods for displaying data
Explain the purpose and application of data mining in forensic accounting engagements
Identify examples of data analysis software, and explain the advantages and disadvantages of each
Explain Benford’s Law and describe specific digital analysis tests

3 of 39

Explain the Application of Descriptive Statistics in Forensic Accounting Engagements

Learning Objective 1

4 of 39

Descriptive Statistics

Purpose is to describe data using various numerical measures and graphical depictions
forensic accountants must first develop familiarity with the data

Facilitate ease and efficiency of analytic process
Determine whether a specific method can be applied
Expert testimony must be

Based on sufficient relevant data
Stated within reasonable degree of professional certainty
Describe samples of data
the purpose of statistics is to “summarize data, analyze them, and draw meaningful inferences that lead to improved decisions

Before applying quantitative methods, forensic accountants must first develop a familiarity with the data. This basic understanding not only facilitates the ease and efficiency of the analytic process, but may also determine whether a specific method can be applied (or how the data must be modified to accommodate the method).
In most cases, a data set cannot be evaluated in its entirety (that is, observations cannot be individually considered).
Thus, it is helpful to create a summary description of the data, which can be accomplished using the tools of descriptive statistics.
In a general sense, the purpose of statistics is to “summarize data, analyze them, and draw meaningful inferences that lead to improved decisions.”
Expert testimony must be based on sufficient relevant data and stated within a reasonable degree of professional certainty. Importantly, neither of these concepts requires absolute precision.
Even in statistical analysis, there is some degree of imprecision.
In fact, a key function of statistics is defining this imprecision, which is represented by terms such as the error rate, significance level, or confidence level.
The purpose of descriptive statistics is to describe data using various numerical measures and graphical depictions.
A population is the entire group of observations in which we are interested, whereas a sample is a subset of observations selected from the population.

A measure that describes a population is called a parameter, and a measure that describes a sample is called a statistic.
Thus, descriptive statistics are simply measures that describe samples of data.

5 of 39

Descriptive Statistics

The purpose of descriptive statistics is to describe data using various numerical measures and graphical depictions
A population is the entire group of observations in which we are interested, whereas a sample is a subset of observations selected from the population
A measure that describes a population is called a parameter, and a measure that describes a sample is called a statistic
Thus, descriptive statistics are simply measures that describe samples of data.

6 of 39

Inferential Statistics

Descriptive statistics can be contrasted with inferential statistics, the purpose of which is to draw conclusions (or inferences) about a population based on information obtained from a sample Less likely be used by forensic accountants
in forensic accounting engagements applications are much more limited
The most basic feature is the number of observations. This feature is important because it determines the scope of the analysis

Descriptive statistics can be contrasted with inferential statistics, the purpose of which is to draw conclusions (or inferences) about a population based on information obtained from a sample.
Although inference, in general, is often used in forensic accounting engagements, applications of statistical inference are much more limited. This is because statistical inference requires that a sample be drawn randomly from a population.
Although it is sometimes possible to obtain a random sample, a forensic accountant’s data set is usually created based on some specific criteria (such as observations for a specific time period or with a magnitude above or below some threshold) or limited by availability.
Unlike inferential statistics, descriptive statistics can be used in any engagement that involves analysis of a numerical data set.
The larger the data set, the more valuable these summary measures.
The most basic feature is the number of observations. This feature is important because it determines the scope of the analysis.

7 of 39

Identify and Describe Various Methods for Displaying Data

Learning Objective 2

8 of 39

Common Descriptive Measures

Numerous measures are used to describe a data set
Calculation of these measures is a necessary starting point for analyzing any large data set in a forensic accounting engagement
The various descriptive measures can be categories:

The key measures of central tendency

Mean: The average value calculated by adding all the observations and dividing by the number of observations
Median :The center point of the data set
Mode: The most frequently occurring value
Of these three measures, the mean is the most commonly recognized

Numerous measures are used to describe a data set. Calculation of these measures is a necessary starting point for analyzing any large data set in a forensic accounting engagement.
The purpose is to provide a broad overview or “feel” of the data distribution, which serves as a basis for preliminary evaluation.
The various descriptive measures can be divided into two categories:

Measures of central tendency

Central tendency is the tendency for quantitative data to cluster around certain values. This clustering often (but not always) occurs near the center of the data distribution.
The key measures of central tendency are:

Mean: The average value calculated by adding all the observations and dividing by the number of observations.
Median: The center point of the data set, when the observations are ordered by magnitude. This can be a single observation or a point between two observations.
Mode: The most frequently occurring value.

Of these three measures, the mean is the most commonly recognized.
Its advantage is that it considers the magnitude of all the observations, representing the point where their mass (or weight) is concentrated.
In contrast, the median does not consider the magnitude of each observation, only whether it is located in the upper or lower half of the distribution. For this reason, the median is not affected by extreme observations (outliers).

Measures of variability

Measures of variability describe how the observations are dispersed around the mean. Low variability indicates that the observations are tightly clustered around the mean. High variability indicates that the observations are located farther from the mean. Two data sets can have the same number of observations and the same mean, median, and mode but have different variability.
Three common measures of variability include:

Range: The difference between the values of the largest and smallest observations.
Variance: The average of the squared deviations of the observations from the mean.
Standard deviation: The square root of the variance.

Like the mean, the variance and standard deviation have the advantage of considering all the observations in the data set.
Compared to the variance, the standard deviation is more easily interpreted because it is stated in terms of basic units (rather than squared units).

9 of 39

Measures of Variability

Measures of variability
Three common measures of variability include:

Range:the difference between the values of the largest and smallest observations
Variance:The average of the squared deviations of the observations from the mean
Standard deviation: The square root of the variance

Of these three measures, the mean is the most commonly recognized.
Its advantage is that it considers the magnitude of all the observations, representing the point where their mass (or weight) is concentrated.
In contrast, the median does not consider the magnitude of each observation, only whether it is located in the upper or lower half of the distribution. For this reason, the median is not affected by extreme observations (outliers).

Measures of variability

Measures of variability describe how the observations are dispersed around the mean. Low variability indicates that the observations are tightly clustered around the mean. High variability indicates that the observations are located farther from the mean. Two data sets can have the same number of observations and the same mean, median, and mode but have different variability.
Three common measures of variability include:

Range: The difference between the values of the largest and smallest observations.
Variance: The average of the squared deviations of the observations from the mean.
Standard deviation: The square root of the variance.

Like the mean, the variance and standard deviation have the advantage of considering all the observations in the data set.
Compared to the variance, the standard deviation is more easily interpreted because it is stated in terms of basic units (rather than squared units).

10 of 39

Histogram

Histogram is a bar chart in which each bar represents a single interval

Height of the bar indicates number (or frequency) of observations in the interval
The histogram is an important data analysis tool because it illustrates the shape of the data distribution, which is a key determinant of the analytic methods that can be applied
First step—defining intervals
Matter of judgment for analyst
Inverse relationship between size of intervals and number of intervals for a given data set; the smaller the intervals, the larger the number of intervals
Every observation should be included in only one interval
Not appropriate to create equal intervals in forensic accounting engagement

A histogram is a bar chart, in which each bar represents a single interval and the height of the bar indicates the number (or frequency) of observations in the interval.
The histogram is an important data analysis tool because it illustrates the shape of the data distribution, which is a key determinant of the analytic methods that can be applied.
The first step in creating a histogram is defining the intervals, which is a matter of judgment for the analyst.

There is an inverse relationship between the size of the intervals and the number of intervals for a given data set; the smaller the intervals, the larger the number of intervals.
Using a larger number of intervals provides a more detailed picture of the data distribution, but it may be misleading if the observations are heavily weighted in only a few intervals.
In most cases, between seven and twelve intervals is sufficient.
The choice within this range depends on the number of observations in the data set (more intervals for larger data sets).
Although there is no prescription for the proper number of intervals, it is necessary that the intervals contain all observations in the data set and do not overlap. In other words, every observation should be included in only one interval.

Although it is common practice to create intervals of equal size, this is usually not appropriate in a forensic accounting engagement.
Because financial data sets often contain much larger quantities of small numbers than large numbers, using equal intervals results in a histogram that has many observations in the first few intervals and very few observations in the remaining intervals.
Like many aspects of a forensic accounting engagement, defining the intervals for a histogram is an iterative process, where the analyst considers various alternatives before selecting one that is most appropriate for the specific purpose of the analysis.
Repeated trials in creating a histogram, which allow the analyst to view and consider several different variations of the shape, are actually helpful.

11 of 39

Absolute Versus Relative Frequency

A Histogram is simply a graph of the frequencies of grouped data
Frequencies can be represented as absolute frequencies or relative frequencies
Absolute frequency: Count of observations within an interval
Relative frequency: Percentage of total number of observations that fall within an interval
Only difference is labeling of vertical axis
Advantage of relative frequency

Described relative to a standard quantity
Can be interpreted as probabilities

12 of 39

Skewness

Skewness is a measure of degree of asymmetry of a data distribution around its mean

Positively skewed: Distribution is more heavily weighted toward smaller numbers
Negatively skewed: when a distribution extends farther to the right than to the left
For a symmetric distribution, mean, median, and mode are all equal
An important fact to keep in mind is that, for a symmetric distribution (with no skewness), the mean, median, and mode are all equal
For a right-skewed distribution, the mean is greater than the median, which is greater than the mode. The opposite is true for a left-skewed distribution

13 of 39

Discrete Versus Continuous Distributions

Discrete distribution: Observations are countable, and there is a discrete jump between successive values

Example: Money
Because money is measured to the cent, it is considered a discrete variable

Continuous distribution: Values can be measured to an infinite small degree of accuracy

Example: Time, weight, and distance

Both can be graphed as histograms

Difference is that, with a continuous distribution, measurement scale can be refined

In a discrete distribution, the observations are countable, and there is a discrete “jump” between successive values.

Because money is measured to the cent, it is considered a discrete variable

In contrast, values in a continuous distribution can be measured to an infinitesimally small degree of accuracy. In other words, the values are continuous—there is no discrete jump.

Examples of continuous variables include time, weight, and distance.

Both discrete and continuous distributions can be graphed as histograms.
The difference is that, with a continuous distribution, the measurement scale can be refined (for example, from feet to inches to centimeters, and so on).
As the scale of measurement becomes more precise, the width of the intervals (bars) in the histogram decreases until the graph approaches a smooth curve.
As noted previously, a frequency distribution can be interpreted as a probability distribution. Thus, the continuous distribution can be interpreted as a probability curve, where probabilities are measured as areas under the curve.
As required of all relative frequency distributions (or probability distributions), the total area under the curve is 1.00, or 100%.

14 of 39

Normal Distribution

A variable is said to be normally distributed when:

It is affected by many independent causes
Effect of each cause is not substantially large compared to others

Important features of the normal distribution include the following:

Symmetric around its mean mean—that is, it has zero skewness
Mean, median, and mode are all equal
Described by its mean and standard deviation

Important in inferential statistics

If a variable is affected by many independent causes and the effect of each cause is not substantially large compared to the others, then the variable will be approximately normally distributed.

Examples include test scores, the amount of oil produced by a well, and the heights of individuals in a group.

Important features of the normal distribution include the following:

It is symmetric around its mean—that is, it has zero skewness.
Because it is symmetric, its mean, median, and mode are all equal.
It is completely described by its mean and standard deviation. In other words, graphing the distribution does not require knowledge of the individual data points, just the mean and standard deviation.
The curve is bell-shaped. For this reason, the normal distribution is often called the “bell curve.”

The concept of the normal distribution is particularly important in inferential statistics, where the choice of statistical method depends on whether the distribution is assumed to be normal.

15 of 39

Evaluating the Distribution of a Data Set

The forensic accountant’s next challenge is evaluating the distribution of the data in comparison to previously determined expectations

Such expectations are based on benchmarks such as past experience for the subject entity
Comparison between actual and expected values can range from very simple to very complex
Finally, it is possible that changes in external variables (such as economic factors, weather, and industry competition) may temporarily or permanently alter the expected distribution

After becoming familiar with the data through the application of descriptive statistics, the forensic accountant’s next challenge is evaluating the distribution of the data in comparison to previously determined expectations.
Such expectations are often based on benchmarks such as past experience for the subject entity or the experience of industry peers.
Depending on one’s knowledge of the process that generates the data, the comparison between actual and expected values can range from very simple to very complex.
When a precise definition of expected values is available, the accuracy of the evaluation process is greatly enhanced.
In addition to magnitude, timing is another important dimension for evaluating the distribution of a data set.

For example, the distribution of a company’s sales for a calendar year may not be comparable to distributions for shorter intervals, such as a quarter or a month.
In some industries, sales of higher-priced items may be more frequent at certain times of the year, which would skew the distribution over particular intervals. Similarly, if sales are slow in a particular month, there may not be a sufficient number of transactions to reflect the expected distribution.
Finally, it is possible that changes in external variables (such as economic factors, weather, and industry competition) may temporarily or permanently alter the expected distribution.
For example, the recent economic crisis has profoundly impacted sales patterns in many industries.

16 of 39

Methods for Displaying Data

How to best display data is of paramount importance to forensic accountants when presenting their ultimate findings to an untrained audience like a jury
Visual exhibits are utilized for two reasons:

Images are more effective than words in conveying complex ideas
Information can be communicated more efficiently in visual form

Ease of interpretation can be enhanced by graphing summary data in charts
Basic charts

Pie charts and bar graphs are used to display categories of data that sum to a total

The challenge of how to best display data is of paramount importance to forensic accountants when presenting their ultimate findings to an untrained audience, like a jury.
As a result of technological advances in recent years, dynamic visual exhibits (such as PowerPoint presentations) are permitted (and even expected) in most courtrooms.
Such tools are utilized for two primary reasons.

First, images are more effective than words in conveying ideas, especially complex ideas. As the old saying goes, “a picture is worth a thousand words.”
Second, information can be communicated more efficiently in visual form—that is, in less time and with more precision.

Quantitative data can be displayed in various ways.
The most basic form of presentation is a listing of the value for each individual observation.
For large data sets, this strategy is not feasible and does not provide any meaningful information.
Thus, it is often useful to summarize the data in some way (such as by value intervals, time intervals, or categories) and present the summary measures in tabular format.
Ease of interpretation can be further enhanced by graphing summary data in charts.
Two basic charts that can be used for a variety of purposes are pie charts and bar graphs.
Pie charts are used to display categories of data that sum to a total.

The “slices” of the pie represent the percentage of the total contained within each category.
A person viewing a pie chart does not have to know the specific values but can tell from the sizes of the “slices” what the largest components are.
If the slices are labeled with percentages rather than values, it is not necessary to infer the proportions.
Depending on the size of the pie graph, both values and percentages may be displayed.

Like pie charts, bar graphs can also display categorical data.

Histogram, a type of bar graph, illustrates the distribution of a data set in terms of absolute or relative frequency.
With time series data, the categories are specified as intervals of time (such as a month, quarter, or year).
In addition to charting a single time series, a bar graph can be used to chart multiple times series.
Graphing more than one time series together provides information about the relationship between the two data sets.
The relationship may be positive (moving in the same direction) or negative (moving in the opposite direction), or there may be no identifiable relationship.

Another means for displaying time series data is a line graph. A line graph is similar to a bar graph, but the values on the vertical axis are graphed as points along a line rather than the heights of bars.

17 of 39

Biases in Graphs

Any exercise of discretion in creating
Failure to include scale
Manipulating the scale—most common way
Inclusion (or lack thereof) of labels

A graph should always have a title
Whether to include labels for individual data points depends on purpose of the graph and available space
The goal is to achieve a balance—providing enough information to ensure accurate interpretation but not so much that the intended meaning is obscured

Any exercise of discretion in creating a graph is an opportunity to introduce bias, whether intentional or unintentional.
Perhaps the most common way that graphs are biased is by manipulating the scale.
Although it is more common to use a scale that includes zero, this is not necessarily the “right” approach.
If the purpose of the graph is to highlight the magnitude of annual changes, then a compressed scale may be appropriate.
In either case, what is important is that the scale is included in the graph, because failure to do so implies intentional deception.
Another way in which graphs can be manipulated is the inclusion (or lack thereof) of labels, including the title of the graph, labels of the horizontal and vertical axes, and labels of individual data points.
A graph should always have a title, as this is the first and primary means by which the graph communicates information.
Descriptive labels for the two axes may or may not be used, depending on their contribution to the overall clarity of the graph.
However, as noted previously, the scale of each axis should always be included.
Finally, the choice of whether to include labels for individual data points depends on the purpose of the graph and the available space.
The goal is to achieve a balance—providing enough information to ensure accurate interpretation but not so much that the intended meaning is obscured.

18 of 39

Explain the Purpose and Application of Data Mining in Forensic Accounting Engagements

Learning Objective 3

19 of 39

Data Mining

The goal of data mining is to find individual items of value—in this context, information—in a vast group of items, such as a large data set
Used to reduce large number of observations to smaller number that can be examined more closely
Used to identify relationships among factors, known as patterns

If patterns in existing data reflect expected or normal experience, they can be used to create data profiles to compare new data

Data profiles

May reflect past behavior of the system being studied
May be extrapolated from other similar systems
May be product of complex models

The goal of data mining is to find individual items of value—in this context, information—in a vast group of items, such as a large data set.
This information is valuable because it can be used to identify relationships among factors, known as patterns.
If these patterns in existing data reflect expected or normal experience, they can be used to create data profiles against which new data can be compared.
The ultimate goal of this comparative analysis is prediction of the likelihood that a deviant observation is the result of some external influence, such as error or fraud, and not attributable to mere chance.
Data profiles may reflect the past behavior of the system being studied (for example, an individual’s history of charges with a particular credit card), may be extrapolated from other similar systems (such as credit card usage among similar demographic groups), or may be the product of complex models that consider multiple factors.
Data profiles are often defined in terms of trends over time, which are examined with time series models, and data distributions, which are examined with the methods of descriptive statistics.
Changes in expected trends or observations that fall outside the expected distribution suggest the need for closer investigation.

20 of 39

Data Mining Applications

Data mining can be used in various fields such as :
Marketing research: Predicting consumer demand and sales
Drug research: Predicting effectiveness of drugs and likelihood of side effects
Credit scoring: Predicting likelihood of default or bankruptcy
Operations management: Predicting input usage and productive efficiency
Investment analysis: Predicting future changes in asset prices

21 of 39

Sorting

A straightforward form of data mining is sorting
After compilation with various data fields, data can be sorted by any individual data fields
Can accomplish several useful tasks:

Identify duplicate entries
Identify transactions with round numbers
Identify gaps in data sequence (such as dates, check numbers, or invoice numbers
Identify matches in data fields (such as employees and vendors with the same name or contact information)

A straightforward form of data mining is sorting. Once the data have been compiled into a spreadsheet with various data fields, they can be sorted by any of the individual data fields.
For example, to identify patterns in transaction dates, data will be sorted by date.
Similarly, to identify patterns in transaction amounts, data will be sorted by amount. Although the concept of sorting is simple, it can become more complex if multiple levels are used for the sort.
A sort with two levels sorts first by one factor and then by another factor (such as sorting by date and then by amount).
Depending on the number of data fields, multiple sort levels can be used.
Sorting can accomplish several useful tasks, examples of which include the following:

Identify duplicate entries.
Identify transactions with round numbers.
Identify gaps in the data sequence (such as dates, check numbers, or invoice numbers).
Identify matches in data fields (such as employees and vendors with the same name or contact information).
Compute category totals (such as total payments made to a specific vendor or employee or total payments for a specific expense category).
Highlight blanks (or lack of data) in a particular data field (such as employees without a Social Security number or vendors without an address).
Identify inconsistencies among data fields (such as incompatible telephone numbers and addresses or back-dated checks).

22 of 39

Sorting

Compute category totals (such as total payments made to a specific vendor or employee or total payments for a specific expense category)
Identify matches in data fields (such as employees and vendors with the same name or contact information).
Highlight blanks in a field (or lack of data) in a particular data field (such as employees without a Social Security number or vendors without an address)
Identify inconsistencies among data fields (such as incompatible telephone numbers and addresses or back-dated checks)

23 of 39

Ratio Analysis

Another simple form of data mining is the calculation of ratios for key observations in a data set
Used to identify variation and outliers within a data distribution
Commonly employed ratios:

Ratio of largest value to smallest value A larger ratio indicates greater variation in the data set
Ratio of largest value to second-largest value the relative size factor (RSF)
Ratio of smallest value to second-smallest value
Ratio of largest (or smallest) value to the mean

Another simple form of data mining is the calculation of ratios for key observations in a data set.
For data that have been sorted by amount, the largest value, second-largest value, and smallest value are easily identified.
Ratios among these values can be used to identify variation and outliers within a data distribution.
Several commonly employed ratios include:

Ratio of the largest value to the smallest value. This is similar in concept to the range, discussed earlier in the descriptive statistics section of this chapter. A larger ratio indicates greater variation in the data set.
Ratio of the largest value to the second-largest value. This ratio is known as the relative size factor (RSF). A large RSF indicates an outlier in the data set. Although outliers can be identified by other methods (such as a histogram or sorting), such methods do not provide a means for assessing the magnitude of the deviation. The value of the RSF is that it provides a numeric measure that can be compared to a benchmark or tracked over time.
Ratio of the smallest value to the second-smallest value. Like the RSF, this identifies outliers, but on the opposite side of the distribution.
Ratio of the largest (or smallest) value to the mean. This is another means of identifying outliers, using a different reference point.

24 of 39

Limitations of Data Mining

The efficiency of data mining can be evaluated in terms of the true signals it identifies (such as an error or fraud occurrence)
False positives or noise: Type I error
Failure to identify a true signal: Type II error
Trade-off between Type I and Type II errors ,Decreasing the occurrence of one increases the occurrence of the other

Tendency for forensic accountants to focus on findings consistent with working hypothesis

May ignore other relevant findings

Forensic accountant must be mindful of the fact that data mining may identify meaningless relationships and patterns

Although it may be technically feasible to apply numerous data mining tests, such resource limitations require the forensic accountant to use discretion in identifying the most efficient and effective tests.

The efficiency of data mining can be evaluated in terms of the true signals it identifies (such as an error or fraud occurrence) relative to false signals, also described as false positives or noise.
In statistics, a false positive is called a Type I error, whereas a miss—that is, failure to identify a true signal—is called a Type II error.
There is a trade-off between Type I and Type II errors: Decreasing the occurrence of one increases the occurrence of the other.
One might think it best to cast a wide net by designing tests to minimize misses. This is accomplished by increasing the test’s power, defined as its discriminatory capability to distinguish a true signal from other unusual variations in the data set.

Another limitation of data mining is the tendency for forensic accountants to focus on findings that are consistent with the working hypothesis, while ignoring other relevant findings.

For example, although preexisting knowledge and data profiles are useful for creating focused tests, they may also hinder the exploratory quality of a comparative analysis.
This is why analysts must remain open to the possibility that the wrong (or not the best) data profile has been selected for comparison or that the data profile has changed.

Finally, the forensic accountant must be mindful of the fact that data mining may identify meaningless relationships and patterns.

With large data sets, a comprehensive search will always suggest patterns that are merely the product of random fluctuations. If the pattern is not meaningful, we cannot expect it to be repeated, which means it has no predictive value.

25 of 39

Identify Examples of Data Analysis Software, and Explain the Advantages and Disadvantages of Each

Learning Objective 4

26 of 39

Data Analysis Software

Basic programs: Microsoft Excel, Microsoft Access, which are included in the Microsoft Office suite that is distributed with many personal computers
Advantages

Affordability
Ease of use
Flexibility of application

Disadvantages

Allow data to be altered without record
Errors can be easily introduced
Cannot accommodate data in certain formats

Two basic data analysis programs are Microsoft Excel and Microsoft Access, which are included in the Microsoft Office suite that is distributed with many personal computers.
These programs store and display data (numbers, text, or images) in cells, which are arranged in columns and rows.
Advantages:

In addition to affordability, the primary advantages of these basic programs are their ease of use and flexibility of application.

A variety of functions are available, ranging from simple arithmetic to complex statistical calculations.
This multifunctionality, combined with an intuitive user interface, facilitates use across individuals of diverse skill levels.
Based on their specific needs, users can combine the individual functions into unique formulas and templates.
This flexibility supplies a seemingly endless variety of possible applications.

The flexibility of Microsoft Excel and Access can also be a disadvantage in certain contexts.
These programs allow data to be altered, either intentionally or unintentionally, without record.
Moreover, errors can be easily introduced, commonly through formulas, the copy/paste function, incorrect cell references, or improperly defined cell ranges.
Another weakness is that they cannot accommodate data in certain formats, in which case the data must be converted. This conversion process introduces yet another opportunity for the integrity of the data to be compromised.

27 of 39

Excel or Access?

both are suitable for forensic accounting engagements that require data mining
Excel is more popular among practitioners
Access forces structure on data analysis project

Excel allows more flexibility

Access has a useful feature—database

Creates complete record of its contents and allows user to create explanatory notes

Because Excel and Access have similar capabilities, both are suitable for forensic accounting engagements that require data mining.
Excel is more popular among practitioners, probably due to their past experience with the program for general accounting tasks.
A key difference between the two programs is that Access forces some structure on the data analysis project, while Excel allows more flexibility.

For example, in Excel, either a number or a formula can be entered into a cell. If a number appears in a cell, you will not know whether it is a data point or a calculation (that is, the result of a formula) until you click on the cell.
Similarly, column headings can be duplicated, and there is no requirement that consistency be maintained between column headings and the type of data contained in the column.

In contrast, Access has a well-defined structure that includes tables, queries, and reports.
Data are stored in tables, which have a layout similar to an Excel spreadsheet.
Each row in the table contains data for a single record (such as a transaction), the discrete components of which are stored in fields (columns).
Importantly, each field can store only one type of data for all the records.
All data-related functions are applied through the creation of queries, the results of which are displayed in reports.
Thus, with Access, it is always clear whether you are looking at data (input) or results (output).
Finally, Access has a useful feature known as the Database, which creates a complete record of the database contents and allows the user to create explanatory notes regarding tables, queries, and reports.
This record facilitates review of the database by another user or by the same user at a later time.

28 of 39

Generalized Audit Software

Specialized software, known as generalized audit software (GAS), has been developed for use in auditing and fraud investigation engagements
GAS programs are designed to analyze financial data in an auditing environment
Generalized Audit is Software enables Auditors to have direct access to computerized records and to deal effectively with large quantities of data.
Generalized audit software (GAS) is the tool use by auditors to automate various audit tasks
Two common examples of GAS are

Audit Command Language (ACL)
Interactive Data Extraction Analysis (IDEA)
GAS programs are designed to analyze financial data

Specialized software, known as generalized audit software (GAS), has been developed for use in auditing and fraud investigation engagements.
Two common examples of GAS are:

Audit Command Language (ACL) and
Interactive Data Extraction Analysis (IDEA).

The primary advantage of these programs is their user-interface attributes, which are customized for specific tasks.
In contrast to the basic programs described previously, which can facilitate data analysis for a variety of purposes but less efficiently, GAS programs are designed to analyze financial data in an auditing environment.
Specialized software programs address the weaknesses of Microsoft Excel and Access that were previously identified.
They can process data in a wide variety of formats, which eliminates the need for conversion.
Moreover, if the data reside in a database, specialized software can directly access and analyze the data inside the database.
This is a read-only operation, in which the data cannot be altered.
Such features help ensure the integrity of the data, which is critical in forensic accounting engagements.
A final advantage of specialized software programs is their ability to record the analytics that have been performed, thus creating an audit trail or log.
This record is important for a number of reasons.

First, it allows the forensic accountant to review the analysis that has already been completed, for the purpose of guiding future efforts and avoiding duplication of past efforts.
Next, it facilitates the creation of a template that can be used in future engagements, another productivity-enhancing feature.
Finally, a complete record of the data analysis process provides essential context for the results of the analysis.

Major disadvantages of GAS programs are their high cost compared to basic programs and the extensive training required to use them effectively.

A single-user license of IDEA or ACL costs several times more than ActiveData for Excel (assuming that one already has Excel).
Thus, such programs are usually used in larger firms, where the cost can be shared among multiple users.
A large user community also helps to minimize the need for formal training.

29 of 39

�Two common examples of GAS are�

Audit Command Language (ACL)

A data analysis software program that helps
auditors remain current with changing technology.
Its primary usefulness lies in its ability to perform
analysis and audit tests on 100% of the data
available rather than merely sampling the data.
The ability to audit 100% of the available data
assists auditors with identifying potential fraud
patterns and data irregularities.

30 of 39

�Two common examples of GAS are�

Interactive Data Extraction and Analysis (IDEA) is
a leading eAudit data-analytics software package.
IDEA provides audit, finance and compliance
professionals in industry and practice with an
efficient and effective solution for high
performance audits.
IDEA is also used by tax authorities throughout the
world (including the Revenue Commissioners) to
interrogate taxpayer transaction and system data.

31 of 39

Generalized Audit Software can accomplish the following audit tasks:

Footing and balancing entire files or selected data items.
Selecting and reporting detailed data contained on files.
Selecting stratified statistical samples from data files.
Formatting results of tests into reports.
Printing confirmations in either standardized or special wording.
Screening data and selectively including or excluding items.
7. Comparing two files and identifying any differences.
8. Recalculating data fields.

32 of 39

Generalized Audit Software

Advantages:

The primary advantage of these programs is their user-interface attributes customized for specific tasks
Specialized software programs address weaknesses of Microsoft Excel and Access
Ability to record analytics performed, creating audit trail
Relatively easy to learn and use
Improved efficiencies by automating manual procedures
Reduced risk by testing entire populations reducing reliance on sampling
GAS can be applied to wide variety of clients with

minimal customization

33 of 39

Generalized Audit Software

Advantages:

This record is important for a number of reasons
First, it allows the forensic accountant to review the analysis that has already been completed, for the purpose of guiding future efforts and avoiding duplication of past efforts
Next, it facilitates the creation of a template that can be used in future engagements, another productivity-enhancing feature
Finally, a complete record of the data analysis process provides essential context for the results of the analysis

34 of 39

Generalized Audit Software

Major disadvantages of GAS programs are their
High cost compared to basic programs and
The extensive training required to use them effectively.
A single-user license of IDEA or ACL costs several times more than Active Data for Excel (assuming that one already has Excel)
Thus, such programs are usually used in larger firms, where the cost can be shared among multiple users
A large user community also helps to minimize the need for formal training

35 of 39

Explain Benford’s Law and Describe Specific Digital Analysis Tests

Learning Objective 5

36 of 39

Digital Analysis—Benford’s Law

Digital analysis is funded on oppose intuitive observation that individual digits of multidigit numbers are not random, but follow a pattern

Describes expected frequencies of digits in numbers —that is, the probability that any given digit in a number will take a certain value

Posits that distribution of first digits is positively skewed, or more heavily weighted toward smaller numbers

37 of 39

Applications of Benford’s Law

Number series must follow a geometric sequence in which each successive number is calculated as a fixed percentage increase over the previous number

Each successive number calculated as a fixed percentage increase over previous number

Many research studies have used Benford’s Law to examine various types of accounting data:

Net income: Analyzing net income data for New Zealand companies
Earnings per share
Income tax
Fraud detection:Nigrini (1994) was the first to use digital analysis for fraud detection

To conform to Benford’s Law, a number series must approximately follow a geometric sequence, in which each successive number is calculated as a fixed percentage increase over the previous number.
Almost all natural numbers display such a geometric tendency, including city populations, sizes of geologic objects, and accounting numbers.
Examples of numbers that do not follow Benford’s Law are data sets with built-in maximums or minimums and assigned numbers. In each of these cases, there is some unnatural (external) influence on the numbers that stifles the development of a geometric pattern.
Many research studies have used Benford’s Law to examine various types of accounting data:

Net income. Analyzing net income data for New Zealand companies, Carslaw (1988) found an excess of second-digit 0s and a shortage of second-digit 9s. Based on this evidence, he concluded that companies with income just below certain thresholds have a tendency to round the income number up. Thomas (1989) and Nigrini (2005) found a similar pattern in U.S. net income data.
Earnings per share. Thomas (1989) found that that EPS numbers in the United States displayed unusually high frequencies of 5- and 10-cent multiples, providing additional evidence of deliberate rounding by management.
Income tax. Christian and Gupta (1993) identified a tendency among individuals to claim additional deductions for the purpose of decreasing taxable income to fall within the next-lowest tax bracket. Nigrini (1996) examined interest income and interest expense reported on tax returns, finding evidence of understatement in the former and overstatement in the latter.
Fraud detection. Nigrini (1994) was the first to use digital analysis for fraud detection. Examining numbers from a known instance of a long-term payroll fraud, he compared the actual digital frequencies of the payroll data to the expected frequencies determined by Benford’s Law. Consistent with his expectation that invented numbers are unlikely to conform to the expected profile, his comparative analysis identified the fraudulent payroll data and showed that the deviations increased over time.

38 of 39

Size of Data Set

Important consideration in the determination to employ a Benford test

Close conformity to Benford’s Law requires a large data set with numbers having at least four digits
The size of the data set is important because it is more difficult to identify significant deviations from Benford’s profile in small data sets

1 of 39

2 of 39

3 of 39

4 of 39

5 of 39

6 of 39

7 of 39

8 of 39

9 of 39

10 of 39

11 of 39

12 of 39

13 of 39

14 of 39

15 of 39

16 of 39

17 of 39

18 of 39

19 of 39

20 of 39

21 of 39

22 of 39

23 of 39

24 of 39

25 of 39

26 of 39

27 of 39

28 of 39

29 of 39

30 of 39

31 of 39

32 of 39

33 of 39

34 of 39

35 of 39

36 of 39

37 of 39

38 of 39

39 of 39