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Hagaman and Wutich (2016) showed that to be the case. They analyzed semistructured ethnographic interviews from a cross-cultural study on water issues in four research sites: one each in Bolivia, Fiji, New Zealand, and the United States. The question was how many interviews were necessary to reach data saturation for themes and metathemes within and across sites. Hagaman and Wutich operationalized saturation as having identified a theme in three separate interviews. Most themes appeared for the first time quickly – only 3–5 interviews – but it generally took up to 10 interviews for the second instance of a theme and 16 for the third. These numbers are just averages. Hagaman and Wutich found that even 30 interviews wasn’t enough in the U.S. site and that, to identify metathemes cross-culturally, it took up to 39 interviews. These findings underscore the principle that the more heterogeneous the population, the larger the sample you will need.

Cultural consensus theory (Romney et al. 1986) formalizes the relationship between heterogeneity and sample size. The theory draws on a cognitive view of culture as shared and socially transmitted knowledge; it then provides a formal model for measuring the extent to which knowledge is shared or contested. The implication for sample size is that the higher the sharing, the smaller the sample necessary to detect consensual beliefs. If we wanted to know how Americans carve up the calendar into days of the week, a handful of informants would do, because this cultural knowledge is widely shared. But if we wanted to understand how days of the week relate to more complex domains – eating, drinking, family life, or sources of stress – we would need a larger sample to capture the variation. Consensus theory formalizes this intuition, and Weller (2007) provides tables for calculating necessary sample sizes to achieve desired levels of accuracy and validity, given varying levels of agreement among informants. To use this table in designing a study, you’d have to make some assumptions about how much agreement you expect to find.