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Audit sampling methodologies are techniques used by auditors to select a representative sample of data or transactions for testing during an audit. Sampling allows auditors to draw conclusions about the entire population based on the examination of a subset, making the audit process more efficient while still providing reasonable assurance about the accuracy and completeness of the information being audited. Here are some common audit sampling methodologies:

1. **Statistical Sampling**:
   - Statistical sampling involves using probability theory to select a sample that is statistically representative of the population being audited. This methodology allows auditors to quantify sampling risks and determine sample sizes based on desired confidence levels and precision levels. Statistical sampling techniques include:
     - **Simple Random Sampling**: Each item in the population has an equal chance of being selected for the sample.
     - **Stratified Sampling**: The population is divided into homogeneous subgroups (strata), and samples are selected from each stratum based on predetermined criteria.
     - **Systematic Sampling**: Items are selected at regular intervals from the population, such as every nth item.
     - **Probability Proportional to Size (PPS) Sampling**: Items are selected with probabilities proportional to their sizes or values within the population.

2. **Non-Statistical Sampling**:
   - Non-statistical sampling involves selecting a sample based on auditor judgment and professional judgment rather than statistical principles. While non-statistical sampling does not provide quantifiable measures of sampling risk, it may be appropriate for audits where statistical sampling is not feasible or practical. Non-statistical sampling techniques include:
     - **Haphazard Sampling**: Items are selected based on the auditor's judgment without following a specific sampling plan.
     - **Block Sampling**: Items are selected in contiguous groups or blocks from the population, such as selecting all transactions within a specific time period or range.
     - **Judgmental Sampling**: Items are selected based on auditor judgment to focus on high-risk areas, unusual transactions, or specific criteria identified during the audit planning process.
     - **Convenience Sampling**: Items are selected based on convenience or availability, without consideration of representativeness or randomness.

3. **Attribute Sampling vs. Variables Sampling**:
   - Attribute sampling is used to test the occurrence or non-occurrence of specific attributes or characteristics within a population (e.g., the presence of control deficiencies).
   - Variables sampling is used to measure the numerical values or amounts of specific attributes within a population (e.g., the accuracy of financial statement amounts).

4. **Sample Size Determination**:
   - Sample sizes are determined based on factors such as the desired confidence level, the acceptable level of risk, the variability of the population, and the precision required for audit conclusions. Sample size determination may be based on statistical formulas, professional judgment, or regulatory requirements.

5. **Evaluation of Sample Results**:
   - After testing the sample, auditors evaluate the results to draw conclusions about the entire population. This may involve extrapolating sample findings to the population, assessing the sufficiency and appropriateness of audit evidence, and considering any errors or exceptions identified in the sample.

By employing appropriate audit sampling methodologies, auditors can efficiently gather sufficient and relevant evidence to support their audit conclusions while minimizing sampling risks and ensuring the reliability of audit findings. The selection of the most suitable sampling approach depends on factors such as the audit objectives, the nature of the population being audited, and the available resources.