ABSTRACT
This chapter develops the ideas of samples and populations, and it problematizes the sample-population relationship that plays a major role in statistical inference. The idea of statistical inference is characterized as having a dual logic: One is called its apparent logic: it is limited to understanding the similarity between a sample and a population as the basis for making claims about the latter on the basis of the former. The other is called its inner logic: it corresponds to a richer understanding that takes into account the expected variation in sampling outcomes, were the sampling process hypothetically repeated under the same conditions. This problematizing of the sample-population relationship provides a motivation for further developing variation as an important quantifiable attribute of data collections, including characterizing different types of variation. Moreover, it provides a basis for characterizing statistics as functions that act on data collections and for characterizing the notions of statistic and parameter from the perspective of quantitative reasoning.
