“”All models are wrong”: what did George Box actually mean?
There are so many quotes out there that we repeat and assume to understand, and then all of a sudden, we discover them in their wider context, and they gain a completely new meaning⦠Thatās what happened to me with George E. P. Boxās quote:
āAll models are wrong, but some are usefulā. (1987, p. 424)

Confession time: I used to use this quote as a reason to dismiss most psychological models. They can in no way reflect the complexity of the human mind or spiritātherefore, wrong, therefore, dispensable⦠After all, if a renowned statistician admits models are wrong, why should I bother? Yes, I admit, it was a relatively cynical view.
What Box actually meant
But then I got curious about that quote and discovered that earlier in his book, on page 74, Box wrote:
āRemember that all models are wrong; the practical question is how wrong do they have to be to not be useful.ā
Reading the p.424 quote in light of p.74 reframes it entirelyāat least for me. Hereās how I now understand Boxās words:
Models are a simplification of a phenomenon so it can be somewhat grasped by our limited brain cells and become practical. Think of our models for the human body and how it functions; the universe; and so on.
āAll models are wrongā
Obviously. They have to be wrong by definition, as they are a simplification of the āreal thingā and as such do not represent or encompass the whole thing in its full form or complexity⦠ergo, all models are wrong. And yet we need models to be able to somewhat comprehend ourselves and the world we live in.
So, knowing that models are just thatāmodelsāBox goes on to ask: āthe practical question is how wrong do they have to be to not be useful.ā In other words, how far off from the real thing do they have to be to no longer serve their intended purpose?
One could argue that Box is not questioning models per se, but rather inviting us to think about what margin of error we are willing to acceptāand when a gap to reality becomes too wide to be of any use. It seems to me that Box was really a pragmatist, advocating we use the models we have until better ones come along.
Nowāanother confession: I am neither a statistician, nor a mathematician, nor a George E. P. Box expert. But I love quotes and am always curious where they actually come from. Which is probably why I kept digging and found this, in a journal from 1976, p. 792:
Worry selectively
āSince all models are wrong the scientist cannot obtain a ‘correct’ one by excessive elaboration. (ā¦) 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 mediocrityā
Followed by:
āWorry selectively. 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.ā
In other words, overcomplicating a model or trying to make it as ācompleteā as possible is unhelpful. But also, that not all errors in a model deserve equal attentionāwe should focus on the ones that actually matter instead. Interesting thoughts, especially for someone like me who loves to get lost in the details of things.
Four statements, same author, same thread of thoughtāeach one adding a layer to the others. Together, they paint a portrait of a rigorous but deeply pragmatic mind. Love it!
Now itās your turn
šĀ Whatās your experience of Boxās quote? How would you interpret it?
šĀ Any other quotes youāve come across that took on a completely different meaning once you explored their original context?
With love,
Dina š«¶š½
PS: All em dashes are my own.
References:
Box, George E. P. (1976),Ā “Science and statistics”Ā (PDF),Ā Journal of the American Statistical Association,Ā 71Ā (356):Ā 791ā799,Ā doi:10.1080/01621459.1976.10480949.)
Box, George E. P.; Draper, Norman Richard (1987).Ā Empirical model-building and response surfaces. Wiley series in probability and mathematical statistics. Page 424. New York: Wiley.Ā ISBNĀ 978-0-471-81033-9. –> “The fact that the polynomial is an approximation does not necessarily detract from its usefulness because all models are approximations. Essentially, all models are wrong, but some are useful.”


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