Hi,
I just did a little bit mathematics and checked the relative magnitude of unpaired and paired T statistics. It seems to me that the paired T statistic could be greater or smaller than, or even equal to, the unpaired T, depending on the specific datasets.
Whether paired T should be used is based on an assumption that the two datasets are pairwise correlated. And if you check the mathematics, the difference between the two formulae exactly reflects the assumption: If the two datasets are positively linearly correlated, unpaired T value is smaller than the paired; if the two are negatively linearly correlated, unpaired T value is greater than the paired; if their covariance is zero, then the two statistics are equal.
Gang
