Select the TWO options that are TRUE statements about survey sampling.
Select one or more:
(1)Cluster sampling usually increases the sampling error compared to a simple random sample of the same size.
(2)In stratified sampling, each member of the population must be in exactly one stratum.
(3)Cluster sampling requires a complete list of the whole target population before the sampling can begin.
(4)Within each stratum in stratified sampling, individuals should be as different as possible from one another with respect to the subject under investigation.
(5)If a survey uses clustering, it must not use stratification as well.
1 and 2
To determine the true statements about survey sampling, let's analyze each option:
(1) Cluster sampling usually increases the sampling error compared to a simple random sample of the same size.
To select if this statement is true or false, let's consider that cluster sampling involves dividing the population into groups or clusters, and then randomly selecting a few clusters to gather data from. This method can lead to an increase in sampling error compared to a simple random sample because individuals within the same cluster often share similar characteristics, which can introduce bias. Therefore, this statement is true.
(2) In stratified sampling, each member of the population must be in exactly one stratum.
To verify the accuracy of this statement, let's review the concept behind stratified sampling. Stratified sampling involves dividing the population into several non-overlapping subgroups called strata based on relevant characteristics, and then selecting a sample from within each stratum. In this method, each individual in the population falls into one and only one stratum. Consequently, this statement is true.
(3) Cluster sampling requires a complete list of the whole target population before the sampling can begin.
To determine if this statement is true, let's examine the nature of cluster sampling. Cluster sampling involves selecting clusters or groups rather than individuals from the population. It does not require a complete list of the whole target population before sampling can begin since sampling is done at the cluster level and not individual level. Therefore, this statement is false.
(4) Within each stratum in stratified sampling, individuals should be as different as possible from one another with respect to the subject under investigation.
To establish the validity of this statement, let's consider the purpose of stratified sampling. Stratified sampling seeks to create subgroups (strata) within the population based on specific characteristics relevant to the investigation. Ideally, individuals within each stratum should be as similar as possible to each other with respect to the subject under investigation, but not necessarily different. For greater precision, individuals within a stratum should be more alike than individuals in other strata. Therefore, this statement is false.
(5) If a survey uses clustering, it must not use stratification as well.
To evaluate this statement correctly, it's important to understand that clustering and stratification are different sampling techniques and can be used simultaneously or individually, depending on the survey design and objectives. Both methods have their own advantages and disadvantages and can complement each other in certain scenarios. Therefore, this statement is false.
Based on the analysis above, the true statements about survey sampling are:
- Cluster sampling usually increases the sampling error compared to a simple random sample of the same size.
- In stratified sampling, each member of the population must be in exactly one stratum.