2022; however, the addresses are distant because the EAs are large. Regardless of its strengths and limitations, this frame is inaccessible as the data is only available on a restricted computer at ArmStat (Pettersson, 2023).

Therefore, our focus is on the latter two datasets, including the 2011 settlement-based frame and the 2023 electoral precinct-based frame, and their advantages and disadvantages are described below.

# **2.1 Census Settlements**

The most granular spatial information in this dataset is “settlement”. There are 1,037 settlements (980 villages, 45 towns, and 12 districts in Yerevan). The main advantage of this frame is that it identifies slightly over 1,000 geographical areas in the country, which is better than having only regions or _marzes_ .

Suppose that 400 settlements were selected in the first stage of the two-stage stratified cluster sampling design as primary sampling units (PSUs), and all 12 districts in Yerevan are likely to be selected via probabilities proportional to size (PPS) approach in the first stage due to the large population in these large districts. Supposedly, if 10 households were randomly selected from each district in the second stage, the sample size from Yerevan would be 120 households, only 3% of the total sample of 4,000 households. However, approximately 35% of the population and 38% of total households live in Yerevan according to the 2011 Armenia Census. One can select a disproportionate number of households from each PSU in the second stage to account for the variations in the size of the PSUs in the first stage. For example, selecting 100 households from each district in Yerevan would yield 1,200 households from Yerevan, which is 30% of the sample.

It is better than having spatial information only at the level of administrative units or strata (strata is defined as a combination of _marz_ and settlement types–urban or rural status–following other official and major surveys) like in several other easily accessible datasets. The primary and more serious disadvantage of this sampling frame, however, is the large-sized settlements, especially in Yerevan. Although the identification information is unavailable, the Census frame from the Committee of the Republic of Armenia (ArmStat) has about 12,000 enumeration areas. The settlements in this frame are thus 12 times larger than the Census enumeration areas on average. Using a few large PSUs would also conceptually undermine the two-stage sampling design, converging to a one-stage design. Large “settlements” thus must be segmented into smaller areas to make workable PSUs.<sup>11</sup> For example, large-sized PSUs were manually segmented into smaller PSUs in the past, such as in Nepal (Central Bureau of Statistics of Nepal, 1996); however, this traditional or manual method is costly and time-consuming in practice. Thus, an innovative technique has been proposed in this paper to divide these large areas into smaller areas.

Another problem with this potential sampling frame is that the population based on the 2011 Census in this sample frame is outdated and misallocated. The outdated data is generally not a severe concern for national sampling frames because any survey fielded before the 2022 Armenia Census could be based on the 2011 Census frame. However, this problem can be significant in Armenia, given that it has been experiencing substantial household displacement and domestic migration due to territorial conflicts in recent years, i.e., the current spatial distribution of the population might be significantly different from that during the

> 11 If these large census settlements were divided into grids, challenges related to the traditional gridded sampling approach would be raised, such as building-cutting boundaries.

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