Data Sampling › Limitations and Considerations {#limitations-and-considerations}

While probability-based sampling provides a rigorous framework for statistical inference, practical implementations face numerous challenges that can compromise the idealized theory. Real-world sampling frames rarely perfectly enumerate the target population. For example, phone survey sampling frames leave out people without phones, and online panels may underrepresent individuals with limited or no access to the internet. Administrative databases can also contain outdated or incomplete information. These coverage gaps mean that even perfectly random selection from a sampling frame may yield biased estimates for the true population of interest.

Nonresponse poses another challenge. When selected individuals decline to participate or cannot be reached, and if these nonrespondents differ systematically from respondents, bias enters the results. Low response rates affect many modern surveys, and weighting adjustments can only partially compensate when the characteristics driving nonresponse are not fully understood or measured.

The law of diminishing returns applies to sample size: doubling sample size reduces standard errors by only about 29% (since standard error decreases with the square root of sample size), while potentially doubling costs. Very large samples reduce sampling error to negligible levels, but this offers little value if non-sampling errors like measurement bias or systematic nonresponse bias dominate. Resources might be better spent improving data quality than simply collecting more observations.

Temporal considerations matter when populations evolve over time. A sample drawn from a customer database represents the population at that moment, but if customer characteristics change, inferences drawn from that sample may not apply to future periods. Trends and seasonal or sudden shifts can all affect the representativeness of samples drawn at specific times.

Sampling theory provides tools for statistical inference but cannot substitute for clear thinking about causal relationships and study design. Representative samples enable us to estimate population characteristics accurately, but they do not by themselves establish causation or ensure that observed associations reflect meaningful relationships rather than confounding factors.