
  "Essentially, all models are wrong, but some are useful."
  
  --- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339.


What exactly is the meaning of the above phrase?  

I think its meaning is best analyzed by looking at it in two parts:

"All models are wrong"  that is, every model is wrong because it is a simplification of reality. Some models, especially in the "hard" sciences, are only a little wrong. They ignore things like friction or the gravitational effect of tiny bodies. Other models are a lot wrong - they ignore bigger things. In the social sciences, we ignore a lot. 

"But some are useful" - simplifications of reality can be quite useful. They can help us explain, predict and understand the universe and all its various components. 

This isn't just true in statistics! Maps are a type of model; they are wrong. But good maps are very useful. Examples of other useful but wrong models abound. 
