Summary of relevant knowledge points in each chapter of Audit from coarse to fine: audit sampling

First, choose the applicable scope of the test item method.

1. Select all items (for detail test, not for control test)

(1) generally consists of a small number of large projects;

(2) There are special risks and other methods cannot provide sufficient and appropriate audit evidence;

(3) The calculation or other procedures automatically executed by the information system are repetitive, so it is cost-effective to check all items.

2. Select a specific project (applicable to target test)

(1) Large or key projects;

(2) All projects exceeding a certain amount;

(3) Articles used to obtain certain information;

(4) Projects for testing control activities.

3. Audit sampling

(1) concept: audit sampling refers to the audit procedures carried out by certified public accountants for some transactions or events with low account balances, so that all sampling units have the opportunity to be selected; This enables certified public accountants to obtain and evaluate audit evidence related to certain characteristics of selected projects, so as to form or help form an overall conclusion on the samples drawn from them.

(2) Characteristics: Audit sampling should have three basic characteristics:

(1) Implement audit procedures for certain types of transactions or projects with low account balances.

② All sampling units have the opportunity to be selected;

③ The purpose of audit test is to evaluate certain characteristics of account balance or transaction type.

(3) Use in the process of obtaining evidence

① Risk assessment procedures usually do not involve audit sampling;

(2) When the control operation leaves traces, certified public accountants may consider using audit sampling to carry out control tests;

(3) Certified public accountants can use audit sampling to obtain audit evidence when implementing the detail test.

Second, sampling risk and non-sampling risk

1. Impact of sampling risk on audit work

Sampling risk refers to the possibility that the conclusions drawn by certified public accountants based on samples are different from those drawn by implementing the same audit procedures for all overall projects as the samples.

When conducting control tests, certified public accountants mainly face the risks of insufficient trust and excessive trust.

Insufficient trust risk: refers to the risk that the inferred control effectiveness is lower than its actual effectiveness.

Excessive trust risk: refers to the risk that the inferred control effectiveness is higher than its actual effectiveness.

Certified public accountants are mainly faced with the risks of false rejection and false acceptance when testing details.

Misreporting risk: refers to the risk that the certified public accountant infers that there is a major misstatement but actually does not exist.

Misacceptance risk: refers to the actual risk that certified public accountants infer that there is no material misstatement.

Influence of sampling risk on audit work

Test category

Risks affecting audit efficiency

Risks affecting audit effect

Control inspection

Insufficient trust risk

Excessive trust risk

Division test

Risk of false rejection

Take risks by mistake

2. Non-sampling risk

(1) Non-sampling risk refers to the possibility that certified public accountants may draw wrong conclusions due to some factors unrelated to sample size.

(2) Causes that may lead to non-sampling risks

① The overall choice of certified public accountants is not suitable for the test object;

(2) The CPA failed to properly define the control deviation or misstatement, resulting in the CPA failed to find the deviation or misstatement in the sample;

(3) The CPA has chosen an audit procedure that is not suitable for achieving a specific goal;

(4) CPA failed to correctly evaluate the audit results.

(3) Non-sampling risks have a certain impact on the efficiency and effectiveness of audit work.

Three. Statistical sampling and non-statistical sampling

1. Statistical sampling refers to an audit method based on probability theory and mathematical statistics, which combines the method of mathematical statistics with audit work. Certified public accountants can quantify and control the sampling risk through statistical sampling, so that the quality of audit reports is higher.

2. Non-statistical sampling is a method of selecting samples by using professional experience and subjective judgment.

3. Statistical sampling is inseparable from professional judgment. In the process of audit sampling, whether statistical sampling or non-statistical sampling, certified public accountants are required to use professional judgment in designing, implementing and evaluating samples.

4. Audit procedures for selected sample projects are usually irrelevant to sampling methods.

Fourth, sample design.

1. General requirements: When designing audit samples, certified public accountants should consider the objectives of audit procedures and the attributes of the sampling population.

(1) Define population

The padding can include all items that make up a certain type of transaction or account balance, or only some items in a certain type of transaction or account balance.

The overall definition of certified public accountants should have the following two characteristics:

① Appropriateness. Certified public accountants should determine the overall suitability for specific audit objectives, including the direction suitable for testing;

② Integrity. Certified public accountants should determine the integrity of the whole project from the aspects of the overall project content and time involved;

(3) Certified public accountants usually select sample items from objects representing the whole population.

(2) Stratification

(1) Stratification refers to the process of dividing a population into several sub-populations, and each sub-population consists of a group of sampling units with the same characteristics (usually monetary amount);

(2) If there is significant variability in the overall project, certified public accountants should consider stratification;

③ Stratification can reduce the variability of items at each level, thus reducing the sample size without increasing the sampling risk proportionally.

(3) Factors affecting the sample size

influencing factor

Control inspection

Division test

According to the sample size

relationship

Acceptable sampling risk

Acceptable risk of excessive trust

Acceptable risk of false acceptance

Reverse change

Tolerance error

Allowable deviation rate

Tolerable false positive

Reverse change

Estimated total error

Estimated total deviation rate

Expected overall misstatement

Co-directional change

Overall variability

Overall variability

Co-directional change

Overall scale

Overall scale

Overall scale

The impact is not great.

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Sample selection of verbs (abbreviation of verb)

1. General requirements:

Certified public accountants should make all sampling units in the population have the opportunity to be selected.

2. Selection method

(1) Sampling with random number table or computer-aided auditing technology (random rules, used for statistical and non-statistical sampling);

(2) Systematic sampling (random rules for statistical and non-statistical sampling);

(3) Random sampling (non-random rules, used for non-statistical sampling).

Evaluation of sample results of intransitive verbs

1. Analyze sample error

(1) Control the deviation rate during the test;

(2) falsely reporting the quantity during the detailed test;

2. Infer the total error

(1) When carrying out control inspection, because the error rate of the sample is the overall inference error rate, the CPA does not need to infer the overall error rate;

(2) When implementing the detailed test, the certified public accountant shall infer the total error amount according to the error amount found in the sample, and consider the influence of the inference error on the specific audit objectives and other aspects of the audit.

3. Form an audit conclusion

(1) Evaluation of sample results in quality control test

In the control test, the CPA should compare the overall deviation rate with the allowable deviation rate, but the sampling risk must be considered.

I. Statistical sampling

Relationship between the upper limit of total deviation rate and allowable deviation rate

(1) below, acceptable;

② greater than or equal to, unacceptable; (Revise the risk assessment level of material misstatement, increase the number of substantive procedures, and test other controls that affect the risk assessment level of material misstatement to support the planned risk assessment level of material misstatement. )

(3) Below but close to, consider whether to accept the whole and whether to expand the test scope, so as to further confirm the control effectiveness and risk level of material misstatement of the planned evaluation)

B, non-statistical sampling

Sample deviation rate and allowable deviation rate

(1) greater than, unacceptable; (same as above)

② Below but close, acceptable;

(3) much lower than that, acceptable;

④ It is not too big or too small, whether to consider expanding the sample size for further evidence collection.

(2) Evaluation of sample results in detailed testing.

In the detail test, the certified public accountant must first ask the audited entity to adjust the book record amount according to the actual misstatement found in the sample. After deducting the misstatement corrected by the audited entity from the inferred overall misstatement amount, the certified public accountant shall compare the adjusted inferred overall misstatement with the tolerable misstatement of this kind of transaction or account balance, but the sampling risk must be considered.

Upper limit of overall misstatement = inferred overall misstatement+sampling risk tolerance

I. Statistical sampling

(1), there is no material misstatement, which is acceptable;

(2) greater than or equal to, there is a material misstatement, which is unacceptable.

B, non-statistical sampling

(1) is greater than, and there is a significant misstatement, which is unacceptable;

(2) It is below but very close, and there is a major misstatement, which is unacceptable;

(3) far less than, no material misstatement, acceptable;

(4) Not too big or too small, consider whether it is acceptable or not, and consider whether to expand the scope of detail testing.

Seven, the concept of sampling risk in control testing.

1. Acceptable risk of excessive trust

The samples selected in the control test are intended to provide evidence of the effectiveness of the control operation.

As the control test is the main evidence source to control the effective operation, the acceptable risk of over-trust should be determined at a relatively low level.

2. Allowable deviation rate

Tolerable error is manifested as tolerable deviation rate in control test, which refers to the deviation rate of setting control that certified public accountants are willing to accept without changing the control effectiveness of their plan evaluation and thus the risk level of major misstatement of their plan evaluation.

3. Control effectiveness of planned estimation

When determining the allowable deviation rate, certified public accountants should consider the control effectiveness of plan evaluation. The lower the control effectiveness of plan evaluation, the higher the allowable deviation rate determined by certified public accountants, and the smaller the sample size required. A high allowable deviation rate usually means that the operation of control will not greatly reduce the degree of relevant substantive procedures, and may not require specific control tests.

4. Estimated total error

Estimated total error refers to the estimated total deviation rate in control test.

Eight, commonly used sampling methods in control testing

1, fixed sample size sampling

In fixed sample size sampling, certified public accountants check samples of a certain size, and then make audit conclusions after all samples of a certain size are selected and rechecked.

Determine the size of the sample

There are three key factors in the sample size formula:

① Expected deviation rate

② Trust risk coefficient is too large.

③ Allowable deviation rate

(2) Select a sample

(3) Review samples

(4) Analyze the sample error (consider whether the control operation is effective);

(5) Inferring the overall error

① Calculate the overall deviation rate.

② Analyze the nature and reasons of deviation.

(6) form an audit conclusion

It is appropriate for certified public accountants to estimate and evaluate the effectiveness of control operation and the risk level of material misstatement.

2. Stop to take samples.

Stop-and-go sampling is a special form of fixed sample size sampling.

When sampling with a fixed sample size, if the expected overall deviation rate is much higher than the actual deviation rate, the result will be that too many samples are selected and the efficiency of audit work will be reduced.

Stop-and-go sampling starts with zero expected total deviation rate, and the audit work is completed through sampling and evaluation. First, certified public accountants take a certain number of samples for inspection. If the result is acceptable, he will stop sampling and draw a conclusion. If the result is unacceptable, he will expand the sample size and continue to test until he comes to a conclusion.

3. Discovery sampling

Discovery sampling is another special form of sampling with fixed sample size, which is different from fixed sample size sampling in that discovery sampling directly sets the expected overall deviation rate to 0%, and determines the sample size according to the acceptable risk and tolerable deviation rate of over-trust, as shown in the textbook P268, table 12-4. When checking the selected samples, once the deviation is found, stop sampling immediately. If no deviation is found in the sample, an overall acceptable conclusion can be drawn. Discovery sampling is suitable for discovering major fraud or illegal acts.

Nine, variable sampling

Variable sampling mainly includes mean estimation sampling, difference estimation sampling and ratio estimation sampling. 、

1. mean estimation sampling

(1) definition

Mean estimation sampling refers to a variable sampling method that determines the average value of samples through sampling review, and then infers the average value and total value of the population according to the average value of samples.

(2) Step:

(1) Calculate the average of the approved amounts of all projects in the sample;

(2) multiplying the average value of the sample by the total size to obtain the estimated value of the total quantity;

③ The difference between the overall estimated amount and the overall book amount is the inferred overall misstatement.

(3) the application of the principle of materiality;

2. Variance estimation sampling

(1) definition

Difference estimation sampling is a method to estimate the average difference between the actual amount and the book amount of the sample, and then multiply the average difference by the overall size to find out the difference between the actual amount and the book amount (that is, the overall misstatement).

(2) Step

(1) Calculate the average false alarm rate of the sample;

② Overall misstatement of estimated amount data;

③ Compare the estimated value of overall false alarm with tolerable false alarm.

(3) the application of the principle of materiality;

3. Ratio estimation sampling

(1) definition

Ratio estimation sampling refers to a sampling method that estimates the ratio relationship between the total actual amount and the book amount by the ratio relationship between the actual amount and the book amount of the sample, and then multiplies the ratio by the total book amount to obtain the estimated total actual amount.

(2) Step

① Calculate the ratio of the approved amount of the sample to the book amount of the sample;

② Estimated actual total amount = total book amount x ratio;

Inferred overall misstatement = estimated overall actual amount-overall book amount.

(3) the application of the principle of materiality;

(4) Consider the allowable limit of sampling risk.

Probability proportional sampling method

1.PPS sampling meaning

PPS sampling is a method of selecting samples with paper money as the sampling unit.

In fact, CPA does not check the monetary units in the population, but checks the balances or transactions that contain the selected monetary units. The balance or transaction checked by a certified public accountant is called a "logical unit".

PPS sampling is a variant of attribute sampling, and it is a method to infer the overall false alarm rate by using the sample false alarm rate, and then infer the overall false alarm amount.

In PPS sampling, CPA pays attention to the size of the error, not the error rate. It calculates the upper limit of error according to the sampling results and compares it with the set allowable error to infer the overall value. This method is suitable for the situation that the transaction amount or account balance is overvalued.

PPS sampling is also called "monetary unit sampling" or "meta unit sampling" because its sampling unit is meta unit.

PPS sampling is also called "cumulative monetary amount sampling" because it needs to calculate the cumulative amount of each overall project.

PPS sampling is also called "comprehensive attribute variable combination sampling" because it combines mathematical attributes with variable conclusions.

2. Advantages:

(1)PPS sampling is generally easier to use than traditional variable sampling.

(2) The sample size of PPS sampling does not need to consider the expected variability of the audited amount.

(3) The probability that an item is selected in the 3)PPS sampling is directly proportional to its monetary amount, so the generated sample is automatically stratified.

(4) In PPS sampling, if the project amount exceeds the sampling interval, PPS system will automatically identify all single major projects through sampling.

(5) Without the expected misstatement of certified public accountants, the sample size of PPS sampling is usually smaller than the traditional variable sampling method.

(6)PPS samples are easier to design, and samples can be selected before obtaining a complete population.

3. Disadvantages:

(1) When using PPS sampling, it is generally assumed that the audit amount of the sampling unit should not be less than zero or greater than the book amount.

(2) If CPA finds underestimation in PPS samples, it needs special consideration when evaluating the samples.

(3) The choice of zero balance or negative balance needs special consideration in the design.

(4) When misstatement is found, if the risk level is certain, PIS sampling may overestimate the impact of sampling risk when evaluating samples, which may lead to the possibility that certified public accountants may reject an acceptable overall book amount.

(5) In PPS sampling, CPAs usually need to accumulate the total amount one by one.

(6) When the overall misstatement amount is expected to increase, the sample size required for PPS sampling will also increase.