Expected Mean Squares For 4-Way Crossed Model With Balanced Correlated Data

HTML
DOWNLOAD

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "Expected Mean Squares For 4-Way Crossed Model With Balanced Correlated Data"

Αμφιτρίτη Γιάνναρης
7 χρόνια πριν
Προβολές:

1 ourn of Bsrh Rsrhs Sns Vo o un Expt n Squrs -Wy ross o Wth Bn rt Dt ZAAB A AKAABAW Dprtnt of thtsog of Sn Unvrsty of Bsrh Bsrh rq Rv // Apt // ABSTRAT n ths stuy w ut th xpt n squrs f -wy ross n o wth rt t n not th fft of th rt t on sttst Th xpt n of squrs f ths stuy s ut usng n pproh s on so spts of nr gr Ky ws Th ross o Anyss of vrn ntrouton AOVA hs o popur sttst prour n w vrty of spns tht th nyss of t fro xprnt sgns s oftn hpr y of thnqu to rt th usu -tst f th fft of rtons Athough th ssupton of th npnn of th osrvtons n AOVA y sn rson ssupton n xnng t usng xprnt sgn Th ssupton of npnnt howvr s rry vrf Gstwrth n Run []Sth n ws [] Pvur n ws [] stuy ths s n xpn tht th rt us wnss of rsuts f th nyss of vrn Pvur n Dvnpt [] stuy th fft of rt t on th nyss of vrn rsuts n on th typ rr f -wy n o Pvur [] stu sp nr o wth rt rr xprsson n not th fft of rt on utp oprson prours f ths o A-Shhry [] stu th fft of rton on sttst n th rton ft f on wy o A-w [] foun th xpt n squrs f n ross two-wy o wth rt t Auh n A-w [] foun th xpt n squrs f n ross -wy o wth rt t A-Kw stu th fft of pnnt t on typ rr rts f utp oprson prours f -wy ross n o [] n ths stuy w hv vop tho f ustng n AOVA n th prsn of rt t wh thr npnn s n ssnt ssupton n AOVA n ton th o shou nr n rr trs shou npnnt n hv nt n struton Th ts hs n opsh y trnng th xpt n squrs f rr n trtnts f th n ross -wy o n rtng th sttsts f tstng th ft ffts Aso ths stuy fouss on th tru typ rr proty n th ffts of prturs fro npnn ssuptons on hypothss n th n ross -wy o nyss of vrn PD rt wth spd PD Wrtr - Tr http//wwwouso

2 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt DEG TE ODE onsr th n ross - wy o wth rt t XB E whr s n vt of osrvtons X s th sgn trx whh s qu to E R whr R s rton trx n s th vrn of h oponnt of osrvtons t B θ α α β β γ γ δ δ αβ αβ αγ αγ αδ αδ βγ [ αγδ βγδ βγδ αβγδ αβγδ ] [ θ α β γ δ αβ αγ αδ βγ βδ γδ αβγ αβδ αγδ βγδ αβγδ ] αγδ suh tht α βγ βγ αβγ βγδ αβγδ β thn µ XB θ βδ βγ γ βγδ αβδ βδ δ βδ γδ αβδ βγδ αβ γδ βδ αβ αβδ αβγδ αβγ γδ αβγ αγ αγδ γδ αβγδ αβδ αγ αγδ αβγ αβγδ αβδ αδ α αγ βδ αγδ β γδ βγδ γ αδ αβγδ αβγ δ βγ αγδ αβ whr s s vt of on n nots th ronr trx prout of two trs Th ronr prout ws fn y Gry ow w hv µ R whr αδ αβγ αβδ PD rt wth spd PD Wrtr - Tr http//wwwouso

3 ourn of Bsrh Rsrhs Sns Vo o un R t s s s s s s s n s s s Pvur thn th rton trx n rwrttn s R Whr PD rt wth spd PD Wrtr - Tr http//wwwouso

4 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt rprsnt th gn vus of th rton trx R rpt rsptvy Ths gn vus r postv onstnts > Sn R s postv fnt trx thn ths gn vus r postv vus urthr h of th trs n s potnt th prout of ny two whh s qu to th zro trx thn thr xsts unqu squr trx R whr R ow y usng R to trnsf th o to n nry nr o R R XB R R XB E Whr E n µ R Suh tht XB XB E R E R E PD rt wth spd PD Wrtr - Tr http//wwwouso

5 ourn of Bsrh Rsrhs Sns Vo o un αβγδ βγδ αγδ αβδ αβγ γδ βδ βγ αδ αγ αβ δ γ β α θ B So E XB ow fn s s A-shhry [ ] ; [ ] ; [ ] ; PD rt wth spd PD Wrtr - Tr http//wwwouso

6 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt [ ] ; ; ; ; ; PD rt wth spd PD Wrtr - Tr http//wwwouso

7 ourn of Bsrh Rsrhs Sns Vo o un ; ; ; ; ; ; AA O VARAE Th osrvton hs n struton wth µ n n vrn thn fro n"s th th tot su of squrs TO to th o n wrttn s TOABDABAS SADBBDDAB ABDADBDABDE Whr PD rt wth spd PD Wrtr - Tr http//wwwouso

8 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt TO A B D h h AB A AD B BD D AB ABD AD BD PD rt wth spd PD Wrtr - Tr http//wwwouso

9 ourn of Bsrh Rsrhs Sns Vo o un ABD E h h Th grs of fro f ABDABAADB BDDABABDADBD ABDE n TO r n - rsptvy EXPETED EA SQUARES ES ow w ut th xpt n squrs wth rt t f SE SA SB S SD SAB SA SAD SB E SE h h SBD SD SAB SABD SAD SBD n SABD Sn h h n PD rt wth spd PD Wrtr - Tr http//wwwouso

10 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt So E E Ο Ο Ο [ ] Ο E y usng onvrtr o n usng th rtons R µ y usng th rton ut f onvrtr o E y susttutng th rton n th rton w gt on y th susttutng th rton n th rton n y usng th rton E E E E E By usng rtons n y usng th n y n th ppnx n sn s potnt trx so E X R η R µ µ η µ η rprsnts th non ntr prtr f h-squr struton ss s ss s s s pvur y usng rtons n sn α β γ δ PD rt wth spd PD Wrtr - Tr http//wwwouso

11 ourn of Bsrh Rsrhs Sns Vo o un η µ E µ R X µ R E E y usng th rton n E E µ K E E E E SE E Aso A SA Sn ow n so Ο Ο Ο Ο PD rt wth spd PD Wrtr - Tr http//wwwouso

12 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt y susttutng rtons n th rton n y usng th rton thn A y usng th rton ut f onvrtr o n usng th rtons A y susttutng rton n th rton n y usng th rtons thn A R R A A A y usng th rtons th y n th ppnx n sn th trx s potnt trx η X A µ µ µ η η rprsnt non ntr prtr f h-squr struton y usng th rtons R R α α α µ µ µ µ η So X A α uy usng n n th ppnx A E α y usng rtons n A E α α A E A E SA E Sry w otn tht PD rt wth spd PD Wrtr - Tr http//wwwouso

13 ourn of Bsrh Rsrhs Sns Vo o un E SB β E S γ E SD δ E SAB αβ E SA αγ E SAD αδ E SB βγ E SBD βδ E SD γδ E SAB αβγ E SABD αβδ E SAD αγδ E SBD βγδ n E SABD αβγδ Thrf th nyss of vrn t AOVA n wrttn s t -TEST Aftr fnng AOVA f stuyng os w n suss ftn ss f nu α α β β f so f so hypothss to now tht f th ft vs n s qu n ths hypothss r PD rt wth spd PD Wrtr - Tr http//wwwouso

14 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt so f γ γ so f δ δ so f αβ αβ so f αγ αγ so f αδ αδ so f βγ βγ so f βδ βδ so f γδ γδ so f αβγ αβγ ; so f αβδ αβδ so f αγδ αγδ so f βγδ βγδ so f αβγδ αβγδ fro th foowng rtons X E X A α X γ X D δ X AB αβ X B β PD rt wth spd PD Wrtr - Tr http//wwwouso

15 ourn of Bsrh Rsrhs Sns Vo o un A X αγ AD X αδ B X βγ BD X βδ D X γδ AB X αβγ ABD X αβδ AD X αγδ BD X βγδ ABD X Aso fro th rtons E A B D AB A AD B BD D AB αβγδ PD rt wth spd PD Wrtr - Tr http//wwwouso

16 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt ABD AD BD ABD n Sn th trs r potnt n th prout of ny two s zro trx y usng pont fro th thn ABD BD AD ABD AB D BD B AD A AB D B A E n pnnt thrf w n wrt th struton f tst to qu ft vs n s whr E A E A whr E B E B whr E E whr E D E D whr E AB E AB whr E A E A whr E AD E AD whr E B E B PD rt wth spd PD Wrtr - Tr http//wwwouso

17 ourn of Bsrh Rsrhs Sns Vo o un BD BD E E whr D D E E whr AB AB E E whr ABD ABD E E whr AD AD E E whr BD BD E E whr ABD ABD E E whr Aftr fnng sttsts w fn t vus fro -struton t wth sgnfn v α n gr of fro n opr twn ths vus ORRETG OR ORREATO Th rt fts K y t on of th foowng ss - rt ft - rt ft> - rt ft< whn th vu of rt ft s qu to on thn thr s not n to th rton tst But whn th rt ft s not qu to on thn w n rtons A-Shhry Ts shows th vus of tru α f vrty of vus f sgnfn v of α ws ut f so hypotht vus f K To ut th tru α n ts fro to w us th fu X X X X whr _ X X rprsnts sgnfn vs whh t fro th ts n th sttst struton n nown rprsnts th vus rsponng to sprsht X X n PD rt wth spd PD Wrtr - Tr http//wwwouso

18 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt X Tru ph rsptvy n nown so whr rprsnts th vu of OUSOS - Ths o s n xtnson of so os stu rr y ny uths But unr rtn onton w y gt th s os suss f y pvur A- n Dvnpt [ ] w [ ] n Auh A-w [ ] - Ts show tht th tru ph v nft ft whn th rton onstnt < > APPEDX t X rno vt wth n vt µ vrn trx Σ - t AX Th E Aµ n OV AΣA - E X µ trσ whr tr Σ s th tr of Σ t n µ whr µ µ µ n n > s sr Thn th r npnnt n µ µ µ X n Th t n µ Σ Σ > Thn - Σ X µ Σ µ n sttst sprsht t th v α utp y rton ft n ths s to hv sr ggr rton rgon f th opt nu hypothss on tstng fts - Ths stuy y xtn to n- wy o - Th o whh s unr stuyng n xtn to unn o whr n h - µ Σ µ X n Th t n µ > t A n B p n n s n trs n t n D n n nonngtv fnt trs Thn - A n B r npnnt f n ony f A B -f A thn A n r npnnt -f D thn n D r npnnt y t n µ > f A s potnt n rn A P thn µ Aµ A X p thth y too fro Arno PD rt wth spd PD Wrtr - Tr http//wwwouso

19 ourn of Bsrh Rsrhs Sns Vo o un PD rt wth spd PD Wrtr - Tr http//wwwouso

20 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt T tru α f ffrnt vus of PD rt wth spd PD Wrtr - Tr http//wwwouso

21 ourn of Bsrh Rsrhs Sns Vo o un n T tru α f ffrnt vus of n T tru α f ffrnt vus of n T tru α f ffrnt vus of n T tru α f ffrnt vus of α n T tru α f ffrnt vus of n T tru α f ffrnt vus of n T tru α f ffrnt vus of n T tru α f ffrnt vus of PD rt wth spd PD Wrtr - Tr http//wwwouso

22 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt n T tru α f ffrnt vus of n T tru α f ffrnt vus of n n T tru α f ffrnt vus of n T tru α f ffrnt vus of n T tru α f ffrnt vus of n T tru α f ffrnt vus of PD rt wth spd PD Wrtr - Tr http//wwwouso

23 ourn of Bsrh Rsrhs Sns Vo o un PD rt wth spd PD Wrtr - Tr http//wwwouso

24 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt PD rt wth spd PD Wrtr - Tr http//wwwouso

25 ourn of Bsrh Rsrhs Sns Vo o un PD rt wth spd PD Wrtr - Tr http//wwwouso

26 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt PD rt wth spd PD Wrtr - Tr http//wwwouso

27 ourn of Bsrh Rsrhs Sns Vo o un REEREES - A Auh Z A Auh "Expt n Squrs -Wy ross o wth rt Dt" ourn of og of Euton unvrsty of A- ustnsry O - - A Gry " trs wth Apptons n Sttsts " Ws Wth ntrnton Group Bont fn - Sth T O ws "Dtrnng Th Effts of ntrss rton on t Exprnts" ountons n Sttsts Prt A Vo - - Gstwrth Run "Efft of Dpnn of v of So On-Sp Tst" ASA Vo - - tr W Wssrnn" App nr Sttst os" RW - G A-Shhry "Dtrnng th Expt n Squrs f Bn Onwy o wth rt Dt" S Thss unvrsty of A-ustnsry - R Pvur "Typ Err Rts f utp oprson Prours wth Dpnnt Dt" ASA Vo - - R Pvur Dvnpt " Th rg Efft of S rtons n AOVA n rton Prours " Arn ourn of tht n ngnt Sns Vo n - - R Pvur T O ws " Tst Prours f th Anyss of Exprnt Dsgns wth rt on Dt" oon Sttst Th th - - S Arno "Th Thy of nr os n utvrt Anyss " Wy w - Z A A-w " Th Efft of Dpnnt Dt on Typ Err Rts f utp oprson Prours f - wy ross Bn o" Bsrh ourn of Sn Ston A Vo o- - Z A A-Kw "Dtrnng th Expt n Squrs f Bn ross two-wy o wth rt Dt" S Thss unvrsty of Bsrh rq حساب توقع معدلات المربعات لنموذج ذي ا ربعة اتجاهات متقاطع متوازن لبيانات مترابطة الخلاصة في هذا البحث تم حساب توقع معدلات المربعات لنموذج ذي ا ربعة اتجاهات متقاطع متوازن لبيانات مترابطة ولاحظنا التا ثير للترابط بين البيانات على الا حصاي ية وتم عمل كل ذلك باستخدام بعض مفاهيم الجبر الخطي PD rt wth spd PD Wrtr - Tr http//wwwouso

28 AKAABAW Expt n Squrs -Wy ross o Wth Bn rt PD rt wth spd PD Wrtr - Tr http//wwwouso

Σχετικά έγγραφα

δ β β γ δ ββ γ α β α α α α α α α α δ δ γ γ δ δ δ δ β β α α α α α α α α β γδ α β γ δ α βγδ αβγδ δγ βα α β γ δ O α β γ δ αγ α γ α γ δ αγδ α αγ γ γ δ γ α γ β β β β β β β α γ β β β β β μ μ β β