In　this　article,　we　consider　the　three-factor　unbalanced　nested　design　model　without　the　assumption　of　equal　error　variance.　For　the　problem　of　testing　main　effects　of　the　three　factors,　we　propose　a　parametric　bootstrap　(PB)　approach　and　compare　it　with　the　existing　generalized　F　(GF)　test.　The　Type　I　error　rates　of　the　tests　are　evaluated　using　Monte　Carlo　simulation.　Our　studies　show　that　the　PB　test　performs　better　than　the　generalized　F-test.　The　PB　test　performs　very　satisfactorily　even　for　small　samples　while　the　GF　test　exhibits　poor　Type　I　error　properties　when　the　number　of　factorial　combinations　or　treatments　goes　up.　It　is　also　noted　that　the　same　tests　can　be　used　to　test　the　significance　of　the　random　effect　variance　component　in　a　three-factor　mixed　effects　nested　model　under　unequal　error　variances.