Editing Analysis of variance (section)

====Statistical models for observational data====
However, when applied to data from non-randomized experiments or [[observational study|observational studies]], model-based analysis lacks the warrant of randomization.<ref>
Kempthorne (1979, pp 125–126, 
"The experimenter must decide which of the various causes that he feels will produce variations in his results must be controlled 
experimentally. Those causes that he does not control experimentally, because he is not cognizant of them, he must control by the device of randomization." "[O]nly when the treatments in the experiment are applied by the experimenter using the full randomization procedure is the chain of inductive inference sound. It is ''only'' under these circumstances that the experimenter can attribute whatever effects he observes to the treatment and the treatment only. Under these circumstances his conclusions are reliable in the statistical sense.") 
</ref> For observational data, the derivation of confidence intervals must use ''subjective'' models, as emphasized by [[Ronald Fisher]] and his followers. In practice, the estimates of treatment-effects from observational studies generally are often inconsistent. In practice, "statistical models" and observational data are useful for suggesting hypotheses that should be treated very cautiously by the public.<ref>Freedman {{full citation needed|date=November 2012}}</ref>