Chapter 2 Basic concepts in household surveys
Household surveys are one of the main tools for understanding the social and economic reality of a population. They provide essential information on living conditions, employment, education, health, and other aspects that guide public policy formulation and evidence-based decision-making. Rigorous analysis of these surveys is fundamental for studying the social, economic, and demographic reality of a population. However, the validity of the results depends not only on sample size or the quality of data collection, but also on how the survey was designed and how that design is incorporated into the statistical analysis. Ignoring the sample design and applying traditional analysis methods that assume a simple random sample can lead to biased estimates, inferential errors, and incorrect conclusions. For this reason, the analysis of household surveys cannot be separated from their selection design, since that design is the foundation that supports the validity and representativeness of the information produced.
In practice, household surveys often use complex designs that combine stratification with the selection of informants in several stages. These designs seek to optimize resources and improve the precision of estimates, although they may generate unequal inclusion probabilities. Ignoring these characteristics can lead to biased estimates, incorrect standard errors, and erroneous conclusions. As Särndal et al. (2003) and Gutiérrez (2016) point out, every survey starts from three fundamental concepts: the target population, the sampling frame, and the selected sample. These elements form the basis of the survey design and are essential for ensuring the validity of inferences and the representativeness of the results.
In this context, a fundamental aspect is the proper consideration of the sample design. To obtain valid conclusions about the population, it is necessary to adopt a design-based inference approach, which recognizes that the sample does not come from just any random selection, but from a carefully defined probability plan. In this scheme, each unit in the population has a known and nonzero probability of being selected, which is the main guarantee that the results can be generalized to the reference population.
Under this approach, it is possible to show that the estimates are unbiased (or approximately unbiased) with respect to the sampling design, without needing to assume specific distributions for the variable of interest. This feature gives design-based inference a robust and widely accepted character in the analysis of household surveys. A central component of this process is the sampling weights, which indicate how many population units are represented by each selected unit. These weights make it possible to adjust estimates to the particular features of the design, ensuring that the results adequately reflect the structure of the population.
As Korn & Graubard (1995) show, weighted and unweighted estimates can differ substantially, which demonstrates the importance of using analysis methods that are consistent with the survey design. Consequently, properly accounting for sampling weights, stratification, and selection units is not a secondary technical issue, but an essential requirement for ensuring the credibility of the results.
United Nations Statistics Division (2026) mentions the following example. Suppose a country is made up of two regions: Region A, with 100 inhabitants and an average income of $10,000, and Region B, with 900 inhabitants and an average income of $2,000. The true average income of the population is:
\[ \theta = \frac{(100 \times 10.000) + (900 \times 2.000)}{100 + 900} = 2.800 \]
If 50 people are selected in each region and the sampling design is ignored, assigning the same weight to all observations, the estimated average would be:
\[ \hat{\theta} = \frac{(50 \times 10.000) + (50 \times 2.000)}{100} = 6.000 \]
In this case, the estimate considerably overestimates national income, since Region A, which represents only 10% of the population, ends up having as much influence as Region B, which contains 90%. By contrast, when weights proportional to population size are applied (1 for Region A and 9 for Region B), the following estimate is obtained:
\[ \hat{\theta} = \frac{(1 \times 50 \times 10.000) + (9 \times 50 \times 2.000)}{(1 \times 50) + (9 \times 50)} = 2.800 \]
This result matches the true population value and shows how the proper use of weights corrects the bias introduced by an analysis that ignores the sample design.