The Concept of A Family
Within the statistical framework, there are several definitions for the term "family":
- First of all, a distinction must be made between exploratory data analysis and confirmatory data analysis: for exploratory analysis – the family constitutes all inferences made and those that potentially could be made, whereas in the case of confirmatory analysis, the family must include only inferences of interest specified prior to the study.
- Hochberg & Tamhane (1987) define "family" as "any collection of inferences for which it is meaningful to take into account some combined measure of error".
- According to Cox (1982), a set of inferences should be regarded a family:
- To take into account the selection effect due to data dredging
- To ensure simultaneous correctness of a set of inferences as to guarantee a correct overall decision
To summarize, a family could best be defined by the potential selective inference that is being faced: A family is the smallest set of items of inference in an analysis, interchangeable about their meaning for the goal of research, from which selection of results for action, presentation or highlighting could be made (Benjamini).
Read more about this topic: Familywise Error Rate
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