In any statistical test, variability needs to be overcome by sample size in order to detect any real effect that may be present. BecauseTo the extent that a paired design has less variability than a corresponding two-sample experiment, it will require fewer subjects in order to give useful results.
In most cases, if a paired experiment requires $n$ pairs ($2n$ exam administrations), in order to have the same ability to detect an AM/PM difference in ability, a two-sample experiment will require many more than $n$ people in
the AM group and $n$ others in the PM group. So for all the difficulties in getting subjects to show up twice for testing, a paired experiment may really be easier
to conduct than an equally-powerful two-sample experiment.
Generally, experienced experimenters always use paired experiments in preference to two-sample experiments, provided that a paired experiment is feasible. In drug testing, it is often possible to do paired experiments for pain relievers because the effect of a pain-relieving drug is temporary and second (independent) administration of a different drug is feasible. By contrast, a trial comparing drugs
to slow the progress of a cancer often has to be a two-sample experiment.
