Solved – Formula to generate Critical t-values for t-test (instead of using a look-up array)

The Student t distribution is essentially an inverse beta function, which is defined in terms of an integral. A good resource for basic formulas for the common functions in statistics is the Numerical Recipes site (nr.com). The older editions, which include code in Fortran and C, are online. For the CDF of the Student t, see section 6.4 of the C version (which should port easily to Java and other C-like languages), p. 228; the inverse beta code is given on the immediately preceding pages.

Some words of experience: porting (or writing) numerical code is fraught with subtle perils and can introduce the nastiest kinds of bugs: those that give only slightly wrong answers and so go undetected. It is essential to create an exhaustive test suite. Consider tabulating a large array of values to high precision using reliable software like R or Mathematica (not a spreadsheet!) and setting up a direct comparison of those values to yours–before you even begin coding. Really stretch the code by evaluating it at endpoints: supplying enormous values for the degrees of freedom, supplying fractional degrees of freedom (you will need this capability for other computations, anyway, such as in a Satterthwaite t-test), infinitesimally small positive values for the limit of integration, and so on. This is especially needed for t distributions because they are often the foundations of other calculations, such as noncentral t distributions, etc., and the algorithms in those calculations might supply surprising values of the arguments in their numerical searches. Robust, defensive coding is essential.

You might consider using a well-tested library instead. 🙂