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.

- random samples from two populations;
- independence within samples and mutual independence between samples;
- measurement scale is ordinal (ranks).

**H**: Distributions of ranks in the two populations are the same._{0}**H**: Distributions of ranks in the two populations are not the same._{1}

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.