Average Sample Number

TL;DR

• ASN indicates how many samples, on average, are required to reach a specified accuracy in a survey.
• It is computed as the ratio of the total number of samples to the total number of units in the population.
• ASN helps choose an appropriate sample size and is affected by population size, desired accuracy, and sampling method.

Definition

Average Sample Number (ASN) is a statistical measure used to determine the average number of samples needed to obtain a specified level of accuracy in a sample survey. It is calculated by dividing the total number of samples by the total number of units in the population.

$$\text{ASN} = \frac{\text{total number of samples}}{\text{total number of units in the population}}$$

Explanation

ASN quantifies, on average, how many samples are required to achieve a specified accuracy for survey results. A larger ASN means more samples are needed to reach the same accuracy because larger samples provide more information and reduce random error.

Factors affecting ASN described in the source:

• Population size: Generally, larger populations require larger sample sizes to obtain the same level of accuracy, since larger populations tend to be more diverse and variable.
• Level of accuracy (confidence level): A higher confidence level requires a larger sample size to ensure sample results fall within the desired margin of error more frequently (for example, a 95% confidence level).
• Sampling method: Different sampling methods have differing accuracy and therefore different sample size requirements. For example, simple random sampling is relatively simple and provides good accuracy but may require a larger sample size than other methods.

Examples

Example from source:

• If a population consists of 100 units and a sample size of 10 is selected, the ASN would be:

$$\text{ASN} = \frac{10}{100} = 0.1$$

This is interpreted in the source as meaning that, on average, 0.1 samples are needed to obtain a specified level of accuracy in the sample survey.

Use cases

• ASN is used by researchers to determine the appropriate sample size for a study and to understand how many samples are needed on average to reach a specified accuracy.

Notes or pitfalls

• A larger ASN implies more samples are needed to achieve the specified accuracy.
• Larger populations and higher desired confidence levels both generally increase the required sample size.
• Different sampling methods require different sample sizes to achieve the same accuracy; simple random sampling may require a larger sample than some other methods.

Related terms

• Confidence level
• Simple random sampling
• Sample size