In this paper, we examined a test statistic for testing ordered alternative hypothesis under unequal group variances. The
proposed modified t-test statistic obtained by replacing the pooled sample variance with the corresponding harmonic
mean of variances in other to avoid the Behren - Fisher's problem. The distribution of the sample of harmonic mean of
variances which is known to be generalized Beta is approximated by the chi-square using a condition that is easily
satisfied.
The result shows that the modified t-test statistic is found to be appropriate for the data set obtained from Kwara
Agricultural Development Project (KWADP) where the crop yields of the treatment means were known to be in a particular
order because of ecological conditions.
