Let $n$ individuals in a statistical population be identified by $p.id \in \{1, 2, ..., n\}$ where the order is randomised. Assume, for simplicity, that all individuals are included in the sampling frame and could, in principal, be sampled. Also for simplicity, assume there is no complex survey design (no clustering or stratification) but merely a simple random sample.
The researcher initially thinks that $10\%$ of the invited individuals will respond to the survey and hopes to get around $100$ respondents. So she invites the first $1000$ individuals ($p.id \in \{1, ..., 1000\}$) from the sampling frame to participate.
After two weeks, only $5\%$ of the invited participants has responded. So the researcher invites the next set of $1000$ individuals ($p.id \in \{1001, ..., 2000\}$) to participate.
Given the random order of the individuals in the sampling frame, it can be argued that this is a probability sample. However, the decision to continue sampling after a low response rate sounds very similar to quota sampling, which is a type of non-probability sampling.
- Is the described procedure probability sampling?
- How does the answer depend on whether there is non-response bias or not?
- How does the answer depend on whether there is clustering or stratification?
- What is the sampling probability of $p.id \in \{1, ..., 1000\}$?
- What is the sampling probability of $p.id \in \{1001, ..., 2000\}$?
- What are the problems with quota sampling which make it non-probability based?
- Are there any problems with the procedure described above?
