ABSTRACT
Good science often requires the detailed planning of experiments, observational studies and data collection procedures. A major component of standard frequentist statistics is the theory of design of experiments, a detailed study of how to incorporate randomness and resulting probability into planning a scientific study. The analysis of variance model serves as the basis for decomposing variation when the entire experiment is completely replicated as a component of the overall planned experimental design. Replication as a component of experimental design allows for better modeling of random variation in the response of interest and helps clarify the significance of results. Path analysis examines collections of potentially correlated variables in terms of their relation to the response of interest. G. G. Simpson's paradox can occur when the analysis is applied to various subgroups and the identified path networks differ in structure from the overall path analysis.
