The reason I ask is that I keep reading it compares means, yet everywhere people keep using box-plots for visualization, which seems fishy to me.
In more detail I would like to know whether information of the 2 sample means is enough to unambiguously know the "direction"* of a paired t-test p-value?
Are there any theoretical scenarios where looking just at the 2 means would be misleading? (Like many close pairs and a pair with infinite difference..)
*direction: I am lacking the jargon but for example the "direction" of a sign-test points to the group which has more "+". A U-test points to the direction of higher intra-sample mean of inter-sample-ranks and a 'normal' t-test_ind points to the direction of higher mean.
But obviously I know that a boxplot of the differences would be ok!