Numerical algorithms for computing special functions are adopted from the Numerical Recipes in C: The Art of Scientific Computing, Second Edition, by William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery. The graphs of the density functions are taken from the Wikipedia. Please send questions, corrections and suggestions about this page to Alex Kasiukov.
Combinatorics computations (including those for exact statistics of Wilcoxon-Mann-Whitney U-Test) will push your JavaScript engine to its limit (and likely beyond). Expect long delays. Sometimes you will have to press "Continue" button when the browser pops up a warning about slow script. Opera performs best on those tasks, Firefox is in the middle, and Internet Explorer is the worst.
Clicking the button next to a field will compute the value of that field based on the other inputs you have provided. For example, if you enter 1 into the Test Statistic (z-value) field for the Two-Tailed Z-test, clicking on the button next to the p-value will compute the p-value based on the supplied z-value. Conversely, if you enter 0.01 into the p-value field, clicking the button next to the Test Statistic field will compute the z-value for the supplied p-value.
Standard Normal Approximation of the p-value is using the (two-tailed) Z-Test without corrections for ties or continuity. It can be used to rule out significance in very pronounced cases or as the approximation to the exact p-value if both samples > 10.