▁body ▁of ▁mathematical ▁theory ▁that ▁expl ores ▁the ▁consequences ▁of ▁making ▁the ▁allocation ▁of ▁units ▁to ▁treat ments ▁by ▁means ▁of ▁some ▁random ▁mechanism ▁( such ▁as ▁tables ▁of ▁random ▁numbers , ▁or ▁the ▁use ▁of ▁random ization ▁devices ▁such ▁as ▁playing ▁cards ▁or ▁dice ). ▁Ass ign ing ▁units ▁to ▁treat ments ▁at ▁random ▁tends ▁to ▁mit ig ate ▁conf ounding , ▁which ▁makes ▁effects ▁due ▁to ▁factors ▁other ▁than ▁the ▁treatment ▁to ▁appear ▁to ▁result ▁from ▁the ▁treatment . ▁ ▁The ▁ris ks ▁associated ▁with ▁random ▁allocation ▁( such ▁as ▁having ▁a ▁serious ▁im bal ance ▁in ▁a ▁key ▁characteristic ▁between ▁a ▁treatment ▁group ▁and ▁a ▁control ▁group ) ▁are ▁calcul able ▁and ▁hence ▁can ▁be ▁managed ▁down ▁to ▁an ▁acceptable ▁level ▁by ▁using ▁enough ▁experimental ▁units . ▁However , ▁if ▁the ▁population ▁is ▁divided ▁into ▁several ▁sub pop ulations ▁that ▁somehow ▁differ , ▁and ▁the ▁research ▁requires ▁each ▁sub pop ulation ▁to ▁be ▁equal ▁in ▁size , ▁strat ified ▁sampling ▁can ▁be ▁used . ▁In ▁that ▁way , ▁the ▁units ▁in ▁each ▁sub pop ulation ▁are ▁random ized , ▁but ▁not ▁the ▁whole ▁sample . ▁The ▁results ▁of ▁an ▁experiment ▁can ▁be ▁generalized ▁reli ably ▁from ▁the ▁experimental ▁units ▁to ▁a ▁larger ▁statistical ▁population ▁of ▁units ▁only ▁if ▁the ▁experimental ▁units ▁are ▁a ▁random ▁sample ▁from ▁the ▁larger ▁population ; ▁the ▁probable ▁error ▁of ▁such ▁an ▁ext rap olation ▁depends ▁on ▁the ▁sample ▁size , ▁among ▁other ▁things . ▁ ▁Statist ical ▁rep lication ▁Me asure ments ▁are ▁usually ▁subject