Discovery sampling, also known as exploratory sampling, is a statistical method used primarily in auditing and quality control. It ensures that the proportion of units with a particular attribute, such as an error, is not in excess of a pre-specified percentage of the entire population.
Core Determinants of Discovery Sampling
Size of Population
The population size, denoted as \(N\), is the total number of units under consideration. It is essential because it impacts the sample size required to achieve the desired confidence level and the accuracy of the sample’s representativeness.
Minimum Unacceptable Error Rate
The minimum unacceptable error rate, denoted as \(p\), is the threshold proportion of errors within the population that is considered unacceptable. This parameter is critical in setting the standard for acceptable quality or accuracy.
Confidence Level
The confidence level, often expressed as \(1 - \alpha\), where \(\alpha\) is the significance level, indicates the degree of confidence that the sample correctly represents the population. Common confidence levels include 90%, 95%, and 99%.
Sample Size Determination
The required sample size can be obtained from a sampling table or calculated using statistical formulas derived from binomial distribution models. The sample size ensures that there is a high probability that at least one error will be found if the actual error rate exceeds the minimum unacceptable error rate.
Application and Conclusion
In practice, if none of the random samples exhibit the error, the auditor can conclude, with a given level of confidence, that the actual error rate in the population is below the minimum unacceptable error rate.
Example
Imagine an auditor is examining invoices. With a population of 1000 invoices (N), a minimum unacceptable error rate of 5% (p), and a 95% confidence level, the auditor uses a sampling table to determine the required sample size. If a sample of 59 invoices is tested and no errors are found, the auditor concludes with 95% confidence that the error rate in the population is less than 5%.
Historical Context
Discovery sampling has evolved from early inspection methods in manufacturing and quality control. Its formalization as a statistical method has broadened its application to areas like auditing and compliance.
Applicability
Discovery sampling is applicable in various fields:
- Auditing: To ensure financial records accuracy.
- Quality Control: To verify product defect rates are within acceptable limits.
- Compliance: To check adherence to regulatory standards.
Comparisons and Related Terms
Systematic Sampling
Systematic sampling involves selecting samples at regular intervals from a sorted list. Unlike discovery sampling, it does not specifically focus on detecting error rates.
Statistical Significance
Although related, statistical significance focuses on whether results could have occurred by chance and not specifically on the rate of errors in a population.
Confidence Interval
A confidence interval provides a range of values within which the true population parameter lies, whereas discovery sampling aims to directly assess the population error rate against a threshold.
FAQs
What is the main goal of discovery sampling?
How is the sample size determined in discovery sampling?
What happens if errors are found in the samples?
References
- Cochran, W. G. (1977). Sampling Techniques. John Wiley & Sons.
- Arkin, H. (1974). Handbook of Sampling for Auditing and Accounting. McGraw-Hill.
Summary
Discovery sampling provides an effective technique for assessing error rates within a population, ensuring high levels of accuracy in quality control, auditing, and compliance practices. Through a defined process involving population size, unacceptable error rate, and confidence levels, it helps professionals make informed conclusions about the integrity and quality of the population under study.
