"Statistical criteria should (1) be sensitive to change in the specific factors tested, (2) be insensitive to changes, of a magnitude likely to occur in practice, in extraneous factors." (George E P Box, 1955)
"The method of least squares is used in the analysis of data from planned experiments and also in the analysis of data from unplanned happenings. The word 'regression' is most often used to describe analysis of unplanned data. It is the tacit assumption that the requirements for the validity of least squares analysis are satisfied for unplanned data that produces a great deal of trouble." (George E P Box, "Use and Abuse of Regression", 1966)
"To find out what happens to a system when you interfere with it you have to interfere with it (not just passively observe it)." (George E P Box, "Use and Abuse of Regression", 1966)
"A man in daily muddy contact with field experiments could not be expected to have much faith in any direct assumption of independently distributed normal errors." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"For the theory-practice iteration to work, the scientist must be, as it were, mentally ambidextrous; fascinated equally on the one hand by possible meanings, theories, and tentative models to be induced from data and the practical reality of the real world, and on the other with the factual implications deducible from tentative theories, models and hypotheses." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"One important idea is that science is a means whereby learning is achieved, not by mere theoretical speculation on the one hand, nor by the undirected accumulation of practical facts on the other, but rather by a motivated iteration between theory and practice." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"Since all models are wrong the scientist cannot obtain a ‘correct’ one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." (George E P Box, "Empirical Model-Building and Response Surfaces", 1987)
"The fact that [the model] is an approximation does not necessarily detract from its usefulness because models are approximations. All models are wrong, but some are useful." (George E P Box, 1987)
"Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics." (George E P Box, Commentary, Technometrics 32, 1990)
"The central limit theorem says that, under conditions almost always satisfied in the real world of experimentation, the distribution of such a linear function of errors will tend to normality as the number of its components becomes large. The tendency to normality occurs almost regardless of the individual distributions of the component errors. An important proviso is that several sources of error must make important contributions to the overall error and that no particular source of error dominate the rest." (George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2nd Ed., 2005)
"Two things explain the importance of the normal distribution: (1) The central limit effect that produces a tendency for real error distributions to be 'normal like'. (2) The robustness to nonnormality of some common statistical procedures, where 'robustness' means insensitivity to deviations from theoretical normality." (George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2nd Ed., 2005)
"All models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind." (George E P Box & Norman R Draper, "Response Surfaces, Mixtures, and Ridge Analyses", 2007)
"In my view, statistics has no reason for existence except as the catalyst for investigation and discovery." (George E P Box)
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