What is the relationship between expected deviation rate and sample size?

The relationship between expected deviation rate and sample size is fundamental in audit sampling. When the expected deviation rate is lower, auditors can rely on a smaller sample size to conclude whether the population is likely to meet the desired control level. This is because a low expected deviation implies that the controls are likely to function effectively, meaning that fewer instances of deviations are anticipated. As a result, the auditor can obtain sufficient evidence with a smaller sample, as there is a higher probability that the sample will reflect the population's low degree of deviation.

In contrast, a higher expected deviation rate suggests that controls may not be effective and that more instances of errors are anticipated. This would generally necessitate a larger sample size to achieve the same level of confidence and assurance regarding the population as a whole. A larger sample can help ensure that the auditor identifies any significant issues.

Consequently, the assertion that lower expected deviations require smaller samples underscores the principle that an auditor's confidence in control effectiveness directly influences the size of the sample needed to test those controls.