Affected Sampling and Reasoning

Systematic Sampling is Most Affected

Systematic sampling is the type of sampling where a sample is selected by choosing every nth item from the population after a random start. The undetected periodicity in the sampling frame would affect this type of sampling the most.

Reasoning

The reason for this is that the periodicity in the sampling frame can result in the selection of a biased sample. For example, if the periodicity occurs every tenth item, then every tenth item will be selected, resulting in a sample that is not representative of the population. The systematic sampling method relies heavily on the randomness of the starting point and the interval between selections. If there is a pattern in the sampling frame, it can affect the randomness, and the systematic sampling method can become biased.

Other Sampling Methods

The other sampling methods may also be affected by the undetected periodicity in the sampling frame, but to a lesser extent.

- Simple random sampling: This type of sampling method selects items randomly from the population, and the periodicity in the sampling frame may not affect the randomness. However, if the periodicity is detected, the sampling frame can be adjusted to avoid the bias.

- Stratified sampling: This type of sampling method divides the population into different strata based on certain criteria and selects a sample from each stratum. The periodicity in the sampling frame may affect the strata with the periodicity, but the other strata may not be affected.

- Multistage sampling: This type of sampling method involves selecting samples from different stages, such as selecting a sample of cities, then selecting a sample of neighborhoods within the cities. The periodicity in the sampling frame may affect one or more stages, but the other stages may not be affected.

Conclusion

In conclusion, the undetected periodicity in the sampling frame can affect the systematic sampling method the most because it relies heavily on randomness. However, the other sampling methods may also be affected to some extent, and adjustments can be made to avoid bias.