Key findings:

The key findings of the abstract on the study testing the effect of quantitative measurement of risks of fundamental errors on audit efficiency include: quantitative risk measurement impacts audit sample size determination and essential procedures' extent, achieving a balance between audit process efficiency and effectiveness. Statistical inspection complements professional judgment in statistical sampling planning and application.

What is known and what is new?

The known aspect in this abstract is the importance of risk measurement in auditing. The new contribution is the study's focus on the quantitative measurement of fundamental errors' risks and its impact on audit sample size determination and essential procedures, providing insights into the effectiveness of this approach in achieving a balance between audit efficiency and effectiveness.

What is the implication, and what should change now?

The implication of this study is that quantitative risk measurement can improve audit efficiency and effectiveness. Changes needed include adopting this approach in auditing practices, integrating it with professional judgment, and refining the method to enhance its applicability and reliability in various auditing contexts.

1. With the increasing size of economic units and the increasing complexity of the business environment and its impact on its operations, auditing using inspections in most professional engagements is no longer just an option for the auditor. Rather, it has become a necessity that exposes considerations of time and cost، as the auditor usually resorts to using audit samples in conducting tests of compliance with the policies and procedures of the control system. Internal and also in conducting detailed verification tests for balances and operations, where the auditor selects samples based on personal judgments or statistical tools, and the primary goal of the auditor implementing examination procedures and detailed tests is to enable him to evaluate the extent of the possibility of relying on the basic records of the economic unit as a basis for preparing its lists. Finance and expressing a neutral technical opinion on the fairness of what the financial records and statements reflect the result of the economic unit’s activity and its financial position , As he faces External auditor when to examine Financial statements balances resulting from operations Finance numerous and recurring , Usually This will be Processes Supported With a lot from Documents that she has Same characteristics and qualities to Limit What , and when Be a community Auditing homogeneous The examination Comprehensive won't He is Necessary , meaning That we can that We learn using Preview if so He was account or A specific regulatory system may be He was treated In a way Suitable as If it were all the documents may be I checked An examination Inclusive.

2. In light of his evaluation of the sample results, the auditor draws judgments related to society and since statistical sampling is considered one of the most important tools that auditors can use during the audit process, this technique contributes to a portion of the decisions they make, and distances these decisions from individual opinions and provides a basis for audit judgments and reaching conclusions. Regarding the fair presentation of financial statements, this study therefore provides an explanation of the areas of use of statistical sampling by auditors and the mechanism of its application on the ground.

The problem of the current study is that inappropriate assessment of audit risks can lead to an inadequate or inefficient allocation of audit resources, as auditors may overestimate the potential impact of the risks of material misstatement. This results in a loss of audit efficiency as there will be additional processes and elements to be examined. Underestimating risks of material misstatement by auditors can lead to a loss of effectiveness. This is because the audit team may reach incorrect conclusions and issue an inappropriate opinion on the financial statements. Therefore, accuracy in assessing audit risk necessarily requires an appropriate estimate of the risks of material misstatement. It enables auditors to determine the appropriate size of the range of substantive procedures, which in turn work to achieve a balance between the efficiency and effectiveness of the audit process.

As the process of assessing the risks of material misstatement using qualitative measurements used by most auditors is not accurate, this study tries to test the impact of using quantitative measurements for the risks of material misstatement in improving the accuracy of auditing risk assessment. In addition, it tries to identify the significance of differences in the range of substantive procedures resulting from the two methods of measuring qualitative and quantitative errors of the risks of material misstatement. The problem of the study is presented through the following main questions:

Does the quantitative measurement of the risks of material misstatement errors affect the efficiency of determining the audit sample sizes?

Is there a significant difference between the sample sizes resulting from the quantitative measurement of the risks of material misstatement and the sample sizes resulting from the qualitative measurement of the risks of material misstatement?

This study is considered an extension of previous studies in the field of using statistical sampling in auditing, and the importance of the study lies in the following:

1- The theoretical aspect: It reinforces the academic literature related to assessing audit risk and using statistical sampling in auditing, especially in light of the lack of professional guidelines presented by various regulatory bodies for the auditing profession regarding statistical sampling in auditing and the factors influencing it. 

2- The practical aspect: The study aims to shed light on the areas of using statistical sampling by auditors by outlining the techniques that can be used in this field. It also aims to explain how to apply these techniques in practice through an empirical study of the reality of the procedures followed in selecting samples in auditing firms. It also addresses the practical application of sampling methods and evaluates the impact of applying quantitative measurements of the risks of material misstatement on determining audit sample sizes. This contributes to improving the professional judgment of auditors and effectively allocating audit resources in the planning phase of auditing financial data

The study aims to:

Investigating the impact of quantitative measurement of the risks of material misstatement on improving the efficiency of determining audit sample sizes.

Demonstrating the significance of the differences between audit sample sizes resulting from the quantitative measurements of the risks of material misstatement errors and audit sample sizes resulting from the qualitative measurement of the risks of material misstatement

The current study is based on two basic hypotheses:

H1: The quantitative measurement of the risks of material misstatement does not affect the efficiency of determining audit sample sizes.

H2: There is no significant difference in audit sample sizes resulting from the quantitative measurement of the risks of material misstatement and audit sample sizes resulting from the qualitative measurement of the risks of material misstatement

To achieve the research objectives and test its hypotheses, the descriptive analytical method is adopted through the following steps:

1- Reviewing previous research, studies, and literature related to the subject of the study to form the theoretical framework and the intellectual and theoretical basis for the subject studied.

2- Conducting a field study by designing a questionnaire distributed to a sample of auditors according to the Union of Certified Public Accountants, and then analyzing the results and testing the research hypotheses using the statistical program SPSS

THEORETICAL FRAMEWORK AND PREVIOUS RELEVANT STUDIES:

4.1 Sample Auditing

International Auditing Standard 530 (ISA) adopted a definition of audit sampling which stipulates that audit procedures should be applied to less than 100% of the items within a group of materials relevant to the audit. In this case, all sampling units have the opportunity to be tested to provide a reasonable basis on which the auditor can rely in arriving at conclusions about the entire group.

4.1.1 TYPES OF SAMPLING IN AUDITING ACCOUNTS

This can be classified as follows:

4.1.1.1 ATTRIBUTE SAMPLING

Statistical sampling which concludes a population in terms of incidence through a binomial probability distribution assumes that a random variable can only have two values, success or failure [1]. The attribute sampling answers the question “What is the percentage? It is assumed that the basic test can be answered with a yes or no. Table (1) shows the factors affecting the sample size for tests of control and basic operations.

Table 1: The factors affecting the sample size for tests of control and basic operations.

Source: Prepared by the researchers based on [2,3]

4.1.1.2 SAMPLING OF  DETAILED TESTS

When using audit samples for detailed verification tests, the auditor is interested in whether the monetary values ​​of account balances or the type of transactions include a significant error. Applying the statistical sampling method requires the auditor to take specific steps beginning with planning the sample and ending with documenting the procedures. It is done through selecting the sample items, implementing procedures, and checking and evaluating the sample results [4]. Table (2) shows the factors affecting the sample size for detailed tests:

Table 2: The factors affecting the sample size for detailed tests:

Source: prepared by the researchers depending on [5,3]

Figure 1: shows the sampling stages in the audit and their sub-steps:

Source: Prepared by researchers based on [5]

5. The concept of audit risk and its types

5.1 The Concept of Audit Risk

    Audit risk means that the auditor expresses an unsound opinion when the financial statements contain the risks of material misstatement. Audit risks can be viewed from two different angles [6]

1- The first: Is the risk resulting from incorrect rejection when the financial statements are sound and the auditor rejects them unjustly

2- The second: Is the risk resulting from incorrect acceptance, meaning accepting the client’s financial statements by giving a clean report, knowing that these financial statements contain the risks of material misstatement.

The first case is referred to as (Risk of Type I - Alpha Risk /α/) because the auditor rejects a real assumption in reality, and this risk results in a loss of efficiency. The second case is referred to as (Risk of Type II -Beta Risk /β/), because the auditor accepts an assumption that is not realistic in reality, and this risk results in a loss of effectiveness [5]

5.1.2   Components of Audit Risk

Audit risk consists of three basic components: inherent risks, control risk, and detection risk. The following is the explanation of each of these components [7-9]

1- Inherent risks: This represents a measure of the auditor’s estimate of the possibility of material misstatements before the effectiveness of internal control is taken into account.

2- Control risks: International standards define control risks as risks represented in the error that may occur in the confirmation process regarding a category of transactions, account balance, or disclosure, which may be material, either alone or when combined with other errors.

It is worth noting that international auditing standards call inherent risks and control risks together with what is known as the risks of material misstatement. They consider them risks specific to the economic unit being audited because the auditor cannot change the actual level of these two risks and all the auditor can do is evaluate them to determine the nature, timing, and range of the substantive procedures.

3- Detection risks: International standards define them as the risks of procedures performed by the auditor to reduce audit risks to an acceptable low level that will not reveal an existing error which may be a fundamental error. What distinguishes detection risks is that they are within the scope of the auditor’s control and he/she can control and modify them according to the results of the assessment of underlying risks and control risks by intensifying or reducing substantive procedures.

5.1.3 Assessing Inherent Risks and Control Risks

    The assessment of inherent risks and control risks is considered the basic step in the audit risk assessment process, as it is based on a set of procedural steps and ends with arriving at an estimate of the value of both latent risks and control risks [10].As for qualitative measurement, it refers to the method by which the value of risks is estimated using qualitative (non-numeric) terms to express the level of assessed risks. This method does not require mathematically estimating the probability of risks occurring but only gives judgmental estimates of them [11]. Concerning risks in general, the risk classification technique issued by the General Accounting Office (GAO) in the United States of America is the most common. The technique is based on an intersection of the level of risk assessed (high, medium, low, very low) with the probability of its occurrence (always, possible, Sometimes, rarely, unlikely) and then classify it into the following three qualitative categories [1]

1- Very high risk: requires immediate corrective action.

2- High risk: requires taking corrective action, while allowing some overlook.

3- Moderate risk: requires review by management.

6. Applied Study

6.1 Methodology of the Study

    To achieve the objectives of the study and test the hypotheses, the researchers rely on the inductive approach, where the researchers apply the quantitative measurement of the risks of material misstatements. The second step includes statistical sampling, conducting statistical analysis, testing the study hypotheses, and using the data available from the auditing companies under study to apply statistical sampling. After that the researchers compare the results resulting from both the application of quantitative measurement and the results resulting from the qualitative measurement of the risks of material errors, test the study hypotheses statistically, generalize the results, and propose recommendations.

6.2 Data of the Study

    The study has been applied to data for audits conducted by an auditing company (the name of the company will not be mentioned as requested by the company itself)

6.2.1 Data Sources Used in the Study

    The first source: this includes data extracted from the records and documents of the economic units under audit. Five sectors are included (industrial, commercial, service, banking, and insurance companies).

The second source: comprises historical data stored by auditing companies.

Table 3: The customers of each company are distributed according to the sector to which they belong.

Source: Authors’ construction 

6.2.2 Data Collection 

The researchers have relied mainly on working papers, which are documents, papers, and audit evidence of the companies under study.

6.2.3 Methods and Tools Used in Data Analysis

Several types of mathematical methods and statistical tools are used in the study. During the application of statistical sampling, the Excel program and the SPSS program are mainly relied upon to conduct the following tests:

1- Descriptive Statistic Measures

2- Test of Inferential Statistics

3- One-Way ANOVA

4- Logistic Regression Analysis

5- Paired-Samples T-Test

6.3 Analysis of the sales cycle and receipts in the study company

6.3.1 Sales

First: Table (4) displays the steps of examining the characteristics of the sales cycle in the company sample of the study.

Table 4: The steps of examining the characteristics of the sales cycle in the company

Source: Prepared by the researcher based on the worksheets of the company under this study.

Second: Table (5) displays the steps for planning the attribute sampling of the sales cycle in the company sample of the study.

Table 5: Planning the attribute sampling of the company

Source: Prepared by the researcher based on PwC’s worksheets.

Third: The following table presents the identification of planned control risks and the sample size in the company's study sample.

Table 6: Planned control risks and identifying the planned sample size in the study company

Source: prepared by the researcher based on PwC’s worksheets.

Fourth: Choosing the sample items through the following steps: Giving a number to each item in the population, using the Excel program. This is done through the following function (Rand between), which generates random digits between two numbers.

Fifth: Table (7) displays the deviations discovered for each attribute of the sales cycle of the study sample company.

Table 7: Deviations for each attribute and sum deviations for the study sample company

Source: Prepared by the researcher based on the worksheets of (PwC).

Sixth: Table (8) presents the maximum deviation and control risk according to the new evaluation for each sales cycle objective in the study company sample.

Table 8: The maximum deviation and control risk evaluation for the study sample company.

Source: Prepared by the researcher based on PwC’s worksheets.

Table 9: Quantitative risk matrix at the evidence level for the study sample company.

Source: Prepared by the researcher based on the outputs of tables (4) to (8)

    Based on the audit risk model, the planned detection risk value can be calculated at the evidence level for the research sample company through Table (10)

PDR = Planned Detection Disk

AAR = Acceptable Audit Risk

IR= Inherent Risks

CR= Control Risk

RMM = Risks of material misstatement

Table 10: Planned detection risks at the evidence level for the study company

Source: Prepared by the researcher based on the outputs of Table (9) and the audit risk model.

    After obtaining the acceptable level of the “Acceptable Risk of Incorrect Acceptance (ARIA)”, the acceptable level of “Acceptable Risk of Incorrect Rejection (ARIR)” using Conventional Variable Sampling (CVS) and using the “Monetary Unit Sampling (MUS)” method; It becomes possible to determine the range of the substantive procedures necessary for each cycle of the accounting information system for the company of the research sample. 

6.3.2 Cycle of Sales and Receivables

6.3.2.1 Traditional Variables Sampling

First: The following table displays the population size, the acceptable deviation, the expected deviation, and the planned standard deviation of the sales and receipts cycle for establishment (A):

Table 11: Population size, acceptable deviation, expected deviation, and planned standard deviation for establishment (A) – cycle of sales and receipts

Source: Prepared by the researcher based on Tupac’s worksheets.

Notes:

1- It was taken from the data of the company being audited, likewise for the rest of the accounting system cycles

2- It was obtained by estimating the relative importance, likewise the rest of the accounting system cycles

3- This was obtained based on the audit team’s assessment in the previous year and according to the acceptable deviation, likewise for the rest of the accounting system cycles

4- This was obtained based on the audit team’s assessment in the previous year, likewise for the rest of the accounting system cycles

Second: The following table displays the risk that can be accepted for incorrect acceptance, the risk that can be accepted for incorrect rejection, and the confidence factor for the sales and receipts cycle of the establishment (A):

Table 12: The risk that can be accepted for incorrect acceptance, the risk that can be accepted for incorrect rejection, and the confidence factor for establishment (A) – the cycle of sales and receipts.

Source: Prepared by the researcher based on TPwC’s worksheets.

Notes: 

1- Taken from Table (10) “The planned detection risks”, likewise for the rest of the accounting system cycles

2- It is obtained from special tables, likewise for the rest of the accounting system cycles

3- Obtained from Table (10), “The planned detection risks”, likewise for the rest of the cycles of the accounting system

4- Taken from special tables, likewise for the rest of the accounting system cycles

Third: The following table displays the sample size and sampling unit for the sales and receipts cycle for establishment (A):

Table 13: Sample size and sampling unit for establishment (A) – cycle of sales and receipts.

Source: Prepared by the researcher based on TPwC’s worksheets.

7. A comparison between the results of applying quantitative and qualitative measurements of the risks of material misstatement by the auditing company (X)

1-The following table shows a comparison between the sample sizes resulting from applying the quantitative measurement of the risks of material misstatement and from applying the qualitative measurement used by the auditing company (X)

First: The range of the substantive procedures:

Table 14: The range of the substantive procedures resulting from quantitative and qualitative measurement by the company (X):

Source: Prepared by the researcher based on the applied study and the program (Microsoft Excel-10)

●             It is noted from the previous table that:

The total range of substantive actions resulting from the application of quantitative measures amounted to 5526 items, representing 12.40% of the total size of the original population (44566). The total range of the substantive procedures resulting from the qualitative measurement followed by Company (X) reached (3303), representing (7.41%) of the total size of the original population (44566). To conclude, the use of quantitative measurement has led to an increase in the total range of substantive procedures by (67.30%) over what it was under the use of qualitative measurement. 

The following figure shows the change caused by the use of quantitative measurement in the range of substantive actions:

Figure 2: A comparison between the range of substantive procedures using quantitative measurement and qualitative measurement (Company X)

Source: Authors’ construction 

The following figure also shows the change caused by the use of quantitative measurement in the range of fundamental procedures according to the type of sector:

Figure 3: A comparison between the range of substantive procedures of the use of quantitative measurement and qualitative measurement according to the type of sector (Company X)

Source: Authors’ construction 

The following table shows a comparison between the range of essential measures resulting from the use of quantitative and qualitative measurement:

Table 15: Results of the T-test for paired samples - range of essential measures

Source: prepared by the researcher based on the outputs of the SPSS-Ver. 23 program

It is noted from the previous table that the significance level of the statistical test reached (Sig = 0.003), which is smaller than the significance level (α = 0.05). This means that these differences are statistically significant, and therefore there is a significant difference between the range of the substantive measures resulting from the use of quantitative measurement and the qualitative measure.

Depending on data taken from audits of clients from different sectors, the researcher conducted a variance test (ANOVA) to study the difference between the range of the substantive procedures resulting from both statistical sampling and non-statistical sampling depending on the type of sector. The following results are obtained: 

Table 16: Results of the ANOVA test on the differences in the range of substantive procedures (non-statistical sampling) according to the type of sector

Source: Prepared by the researcher based on the outputs of the SPSS-Ver. 23 program

It is noted from the previous table, regarding the range of essential measures resulting from non-statistical sampling, that the variance test function (F = 3.370) corresponds to the calculated significance level (Sig = 0.013), which is smaller than the significance level (α = 0.05). There are statistically significant differences depending on the type of sector to which the client belongs regarding the range of the substantive procedures for non-statistical sampling.

8.1 FINDINGS

1- The use of quantitative measurement has led to an increase in the total range of substantive measures by (67.30%) over what it was under the use of qualitative measurement.

2- The use of quantitative measurement of the risks of material misstatement affects the efficiency of determining the sizes of audit samples by determining the appropriate size for the range of substantive procedures that work to achieve a balance between the efficiency and effectiveness of the audit process.

3- There is a significant difference in the sizes of audit samples resulting from the quantitative measurement of the risks of material misstatement and the sizes of the audit samples resulting from the qualitative measurement of the risks of material misstatement.

8.2 RECOMMENDATIONS

In light of the previous results, the researcher recommends the following:

1- Applying qualitative measurement by audit practitioners instead of qualitative measurement of the risks of material misstatement.

2- Including a working mechanism within international auditing standards to become a guide for auditors on how to apply quantitative measurement of the risks of material misstatement.

3-Working to increase the application of statistical sampling and mathematical methods in calculating the sizes of audit samples.

The authors declare that they have no conflict of interest

No funding sources

The study was approved by the University of Fallujah, Iraq, 31002.

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