Page "Analysis of variance" Paragraph 90

However, when applied to data from non-randomized experiments or observational studies, model-based analysis lacks the warrant of randomization.

For observational data, the derivation of confidence intervals must use subjective models, as emphasized by Ronald A. 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.