This formula_11 is a random variable. A t distribution with a random number of degrees of freedom does not exist. Nevertheless, the Behrens–Fisher "T" can be compared with a corresponding quantile of Student's t distribution with these estimated numbers of degrees of freedom, formula_11, which is generally non-integer. In this way, the boundary between acceptance and rejection region of the test statistic "T" is calculated based on the empirical variances "si"2, in a way that is a smooth function of these.