The test statistic can then be compared against the critical values of the theoretical distribution.

But T can also be used as a test statistic in one of two ways:

Counts are taken as before and used to estimate the test statistic.

The test statistic follows the F distribution with and degrees of freedom.

Right so if we had a test statistic greater than one point seven zero on a T ratio.

Right, so if we had a test statistic greater than three point eight it would reject our null hypothesis.

The test statistic is found by counting the number of inversions (I).

(which, in applications, would be used as a test statistic).

Moreover, it becomes questionable whether the same test statistic ought to be used.

A small p-value often corresponds to a high test statistic.