Sampling without Finding Anything

Abstract

Sampling statistics ordinarily take as their point of departure some finding in a sample. Say the sample consists of artifacts, including some projectile points. We can estimate the proportion of projectile points in the artifact assemblage from which the sample came; we can estimate the mean weight of projectile points for the population of projectile points from which the sample came; we can estimate the proportions of different raw materials of which projectile points in the population were made; and so on. Following the procedures discussed in Chapters 9, 11, and 18, we can attach error ranges for particular confidence levels to these estimates. Sometimes, however, we have particular reason to be interested in some specific category of observation that just does not appear at all in a sample. For example, we may recognize chert, flint, and obsidian as potentially available raw materials from which projectile points could be made, but perhaps our sample includes only chert and flint points. How confidently can we say that obsidian was not used to make projectile points? We certainly know enough about samples by now to know that the fact that we find no obsidian projectile points in a sample does not necessarily mean that there were none at all in the population from which the sample was drawn. This is true no matter how large the sample is. The only way to be certain that there are no obsidian projectile points is to acquire and study the entire population of projectile points. As long as one projectile point remains unexamined, there is at least some possibility that it could be made of obsidian.