Behrens Fisher problem: The difficulty of testing for the equality of the means of the two normal distributions which do not have the equal variance. Various test statistics have been planned, even though none of them are completely satisfactory. The one which is most commonly used can be given as
where x1; x2; s21; s2 2; n1 and n2 are the variances, means and sizes of samples of observations from each population. Under the hypothesis or the assumption that the population means are equal, t has a Student's t-distribution with v degrees of freedom where
and