▁un cor related ▁and ▁independently ▁distributed ▁if ▁the ▁data ▁are ▁normal . ▁Because ▁of ▁this ▁independence , ▁each ▁orthogonal ▁treatment ▁provides ▁different ▁information ▁to ▁the ▁others . ▁If ▁there ▁are ▁T ▁treat ments ▁and ▁T ▁– ▁ 1 ▁orthogonal ▁contrast s , ▁all ▁the ▁information ▁that ▁can ▁be ▁captured ▁from ▁the ▁experiment ▁is ▁obtain able ▁from ▁the ▁set ▁of ▁contrast s . ▁ ▁F actor ial ▁experiments ▁Use ▁of ▁factor ial ▁experiments ▁instead ▁of ▁the ▁one - factor - at - a - time ▁method . ▁ ▁These ▁are ▁efficient ▁at ▁evalu ating ▁the ▁effects ▁and ▁possible ▁interactions ▁of ▁several ▁factors ▁( in dependent ▁variables ). ▁Analysis ▁of ▁experiment ▁design ▁is ▁built ▁on ▁the ▁foundation ▁of ▁the ▁analysis ▁of ▁variance , ▁a ▁collection ▁of ▁models ▁that ▁partition ▁the ▁observed ▁variance ▁into ▁components , ▁according ▁to ▁what ▁factors ▁the ▁experiment ▁must ▁estimate ▁or ▁test . ▁ ▁Example ▁ ▁This ▁example ▁of ▁design ▁experiments ▁is ▁attributed ▁to ▁Harold ▁Hot elling , ▁building ▁on ▁examples ▁from ▁Frank ▁Y ates . ▁The ▁experiments ▁designed ▁in ▁this ▁example ▁involve ▁combin atorial ▁designs . ▁ ▁We ights ▁of ▁eight ▁objects ▁are ▁measured ▁using ▁a ▁pan ▁balance ▁and ▁set ▁of ▁standard ▁weights . ▁ ▁Each ▁we igh ing ▁measures ▁the ▁weight ▁difference ▁between ▁objects ▁in ▁the ▁left ▁pan ▁and ▁any ▁objects ▁in ▁the ▁right ▁pan ▁by ▁adding ▁cal ibr ated ▁weights ▁to ▁the ▁l ighter ▁pan ▁until ▁the ▁balance ▁is ▁in ▁equilibrium . ▁Each ▁measurement ▁has ▁a ▁random ▁error . ▁ ▁The ▁average ▁error ▁is ▁zero ; ▁the ▁standard ▁devi