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I always read phrases such as "empirical data" and "empirical study." What does it mean when a study is empirical?

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A good definition from Wikipedia is

Empirical research is a way of gaining knowledge by means of direct and indirect observation or experience. Empirical evidence (the record of one's direct observations or experiences) can be analyzed quantitatively or qualitatively.

Another good resource is EricDigests.com is a further resource that goes through in detail the steps to empirical research, the 7 that are defined from that link are:

  1. Randomisation
  2. Control
  3. Reliability
  4. Validity
  5. Implementation of Treatment Variable
  6. Analysis Issues
  7. Implementation issues

(The full details are on the 2nd link - too much to fit here)

Hope this helps answer your question.

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In computer science, this terminology is often used to indicate that an algorithm has been run on real (or simulated) data sets, and observations are made as to how it behaves (how fast does it run, does it solve the problem correctly, and so forth). The experimental procedures are usually not so much of an issue here, because the testing environment can be so well-controlled (i.e. you can generate infinite amounts of random test data).

This is to be contrasted with analyses which are based on mathematical proof, i.e. proving that your algorithm has certain behaviors (e.g. proving it is always correct).

Some times you will see papers in between these two poles.

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