Triggered by this thread, I (again) am thinking about finally using unit tests in my projects. A few posters there say something like "Tests are cool, if they are good tests". My question now: What are "good" tests?

In my applications, the main part often is some kind of numerical analysis, depending on large amounts of observed data, and resulting in a fit function that can be used to model this data. I found it especially hard to construct tests for these methods, since the number of possible inputs and results are too large to just test every case, and the methods themselves are often quite longish and can not be easily be refactored without sacrificing performance. I am especially interested in "good" tests for this kind of method.

The Art of Unit Testing has the following to say about unit tests:


  A unit test should have the following
  properties:
  
  
  It should be automated and repeatable. 
  It should be easy to implement.
  Once it’s written, it should remain for future use.
  Anyone should be able to run it. 
  It should run at the push of a button.
  It should run quickly.
  


and then later adds it should be fully automated, trustworthy, readable, and maintainable.

I would strongly recommend reading this book if you haven't already.

In my opinion, all these are very important, but the last three (trustworthy, readable, and maintainable) especially, as if your tests have these three properties then your code usually has them as well.
