ABSTRACT
This chapter addresses some of the vexing problems and the most challenging conceptual errors that applied researchers face. It considers that the phrase "standard error" is meaningful solely in terms of capturing a consequence of a data generating process. The chapter interprets the standard error as reflecting the variation in a statistic due to the possibility of obtaining different data sets from a data generating process. It explains notational conventions, and addresses key issues of measure theory that can help us to sort out. The chapter identifies two types of indices, one that applies to variables, which denotes distinct variables, and one that applies to values, which denotes arbitrary elements of a variable's domain. It elaborates upon within the context of a research problem. The research problem may lead to conclude that random effects cannot be applied when a data generating process includes inherent fixed units.
