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I am following A.W. van der Vaart, asymptotic statistics (1998). He talks of statistical experiments, claiming that they are different from a statistical model, but he defines neither. My question:

What is

  1. a statistical experiment,
  2. a statistical model and
  3. what is the key ingredient which always will make the statistical experiment distinct from any statistical model?
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    $\begingroup$ For future readers: While the answers below seem to discuss the more commonplace and colloquial distinction between "models" and "experiments", I think they misunderstand what is meant by a "statistical experiment" in van der Vaart's book, which is a formal mathematical concept, having little to do with the comments below. $\endgroup$
    – JohnA
    Jul 9, 2019 at 13:25
  • $\begingroup$ Where does he claim that they are different? In the intro to chapter 7 he states "In the context of the present chapter we shall speak of a statistical experiment, rather than of a statistical model." I.e., it is just a terminological difference. I agree with @JohnA that the answers below are referring to a related but different sense of the term than van der Vaart is using. $\endgroup$
    – sayda
    Apr 29, 2022 at 20:09

3 Answers 3

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Another way to think about this is that the statistical experiment is the protocol we follow to generate data and the statistical model is the protocol we use to analyze these data.

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    $\begingroup$ Isabella: That is a nice way to put it where protocol means instruction by a mathematical formula.. $\endgroup$
    – Michael R. Chernick
    Apr 8, 2018 at 21:41
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A statistical experiment is a design that describes how the data will be collected in a statistically valid way. A statistical model is a description of relationships between variables that are measured in the experiment and/or the parametric form of the distribution of those variables.

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What @Michael Chernick said is correct from a statistician's viewpoint.

I'm a physicist, and in science, "model" can also mean a predictive description. You would say something like "if you set up the following situation, for example, place a small drop of ink in a glass of milk, then at time t you would expect the statistical distribution of ink molecules in space to be P[x, t]."

I suspect this meaning is becoming more ubiquitous. For instance, to be apropos, one might tell a potential client "if we target a certain population with such and such advertising, we would anticipate a voting increase of 4 ± 1 % for your candidate." This might be a purely empirical result, or it might be based on a predictive statistical model built on a theory combined with the results of statistical experiments.

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