cdis pirTa Soris orfaqtoriani sqema da dispersiuli analizi · Web viewcdis pirebs Soris 2x2 sqemis...

cdis pirTa Soris orfaqtoriani sqema da dispersiuli analizi

Tavi XI. cdis pirTa Soris orfaqtoriani sqema da dispersiuli analizi

cdis pirTa Soris 2x2 sqemis magaliTi

faqtoruli sqemis Sedegad miRebuli informacia

ujredis saSualoebi

mTavari efeqtis saSualoebi

damoukidebeli cvladebis urTierTqmedeba

cdis pirTa Soris orfaqtoriani sqemis dispersiuli analizi

monacemTa dayofa

dayofili monacemebisagan gadaxrebis kvadratebis saSualos miReba

F statistikis gamoTvla

statistikuri hipoTezis Semowmeba cdis pirTa Soris orfaqtorian dispersiul analizSi

faqtorebi, romlebic gavlenas axdenen gadaxrebis kvadratebis saSualoebze dispersiul faqtorul analizSi

F statistikaze damyarebuli statistikuri gadawyvetilebebis

miReba

cdis pirTa Soris orfaqtoriani dispersiuli analizis daSvebebi

dispersiis 2x2 faqtoriani dispersiuli analizis axsna

damoukidebeli cvladis martivi efeqti

Sejameba: dispersiuli analizis axsna eqsperimentis magaliTze

Carevis efeqtis siZlieris gazomva dispersiul

faqtorul analizSi

dispersiuli faqtoruli analizis Sedegebis prezentacia

`mravali qceva ganisazRvreba ori an meti erTdroulad moqmedi damoukidebeli cvladis mier. magaliTad, xmauris (damoukidebeli cvladi) gavlena wakiTxulis gaazrebaze (damokidebuli cvladi) gansxvavdeba pirovnebis introvertuli da eqstravertuli tipebisaTvis (meore damoukidebeli cvladi) (Standing, Lynn, & Moxness, 1990). an, Tu sxva magaliTs ganvixilavT, arsebiTi saxelebis wyvilebis (damokidebuli cvladi) damaxsovreba damokidebulia im adamianis warmosaxvis unarze (erTi damoukidebeli cvladi), vinc imaxsovrebs sias, suraTebis tipebze, romelic miewoda adamians (meore damoukidebeli cvladi), da damaxsovrebis drois intervalis xangrZlivobaze (mesame damoukidebeli cvladi) (O’Brien & Wolford, 1982). erTfaqtoriani sqema ar iZleva SesaZleblobas, erTdroulad moxdes erTze meti damoukidebeli cvladiT manipulireba; amitom, imisaTvis, rom Seiswavlon ori an meti damoukidebeli cvladis kombinaciis gavlena, gamoiyeneba faqtoruli analizi.

faqtoruli sqema: kvlevis iseTi sqema, romelSic erTdroulad icvleba ori an meti damoukidebeli cvladi.

faqtoruli sqema aris kvlevis iseTi sqema, romelSic erTdroulad icvleba ori an meti damoukidebeli cvladi. yvelaze martiv faqtorul sqemaSi cvalebadobs ori damoukidebeli cvladi da TiToeul damoukidebel cvlads ori mniSvnelobis (donis) miReba SeuZlia. am sqemas xSirad 2x2 (“ori orze”) sqemas uwodeben. pirveli ‘2’ aRniSnavs, rom arsebobs pirveli damoukidebeli cvladis (romelic ganisazRvreba, rogorc A faqtori) ori mniSvneloba (ori done), xolo meore ‘2’ ki aRniSnavs meore damoukidebeli cvladis (romelic ganisazRvreba, rogorc B faqtori) mniSvnelobebis (doneebis) raodenobas. 2x2x2 sqema warmoadgens samfaqtorian sqemas, sadac faqtorebia A, B da C, da TiToeuli maTgani or mniSvnelobas (dones) iRebs. arsebobs faqtoruli analizis mravali SesaZlo varianti, rogoricaa 2x4 sqema (A faqtoris ori done, B faqtoris 4 done), 3x3x2 sqema (A da B faqtorebis ori done, C faqtoris ori done) da 2x2x2x2 sqema (oTxi faqtori, A, B, C da D, TiToeuls aqvs ori done). faqtoruli analizi aseve SesaZlebelia iyos srulad cdis pirebs Soris, srulad cdis pirebs SigniT an am oris kombinacia, rac Sedegad Sereul sqemas gvaZlevs. am TavSi Cven ganvixilavT mxolod cdis pirebs Soris orfaqtorian sqemas (romelsac aseve uwodeben ormxriv sqemas).

ujredi an Carevis piroba: faqtorul eqsperimentSi TiToeuli damoukidebeli cvladis erTi donisagan warmoqmnili kombinacia.

cdis pirebs Soris 2x2 sqema mosaxerxebelia faqtoruli sqemebis statistikuri monacemebis analizis wardgenisaTvis. cxrili # 11.1 warmoadgens or damoukidebel cvlads an faqtors, romlebic aRniSnulia, rogorc A da B. maTgan TiToeuli iRebs or mniSvnelobas (dones): faqtori A iRebsAA1 da A2 mniSvnelobebs da faqtori B iRebs B1 da B2 mniSvnelobebs. zogadad, arsebobs A faqtoris a mniSvneloba da B faqtoris b mniSvneloba. am magaliTSi a=2 da b=2. ori damoukidebeli cvladis kombinacia cxrilSi qmnis oTx pirobas, romlebsac ujredebs uwodeben. TiToeuli ujredi anu piroba aris kombinacia, romelic iqmneba TiToeuli damoukidebeli cvladis erTi mniSvnelobiT, magaliTad, A1B1, A1B2, A2B1 da A2B2 ujredebi. Cveulebriv, TiToeul ujredSi SemTxveviTad nawildeba cdis pirebis toli raodenoba. amdenad, Tu cdis pirebs Soris 2x2 sqemaSi gamoyenebulia 20 cdis piri da TiToeul ujredSi iqneba xuTi cdis piri. yoveli cdis piri mxolod erT ujredSi xvdeba.

cxrili # 11.1

cdis pirebs Soris 2x2 sqemis gegma. A faqtoris doneebis kombinacia B faqtoris doneebTan qmnis pirobas anu ujreds.

faqtori A

A1 A2

B1

faqtori B

B2

A1B1 piroba

(A1B1 ujredi)

A2B1 piroba

(A2B1 ujredi)

A1B2 piroba

(A1B2 ujredi)

A2B2 piroba

(A2B2 ujredi)

cdis pirebs Soris 2x2 sqemis magaliTi

zogadad adamianebs ar uyvarT sxva adamianebisTvis cudi siaxleebis Setyobineba. am fenomens MUM efeqts uwodeben. am efeqtis asaxsnelad SemoTavazebuli iyo ramdenime hipoTeza. pirovnuli diskomfortis hipoTezis mixedviT, cudi siaxlis momtani adamiani pirovnul diskomforts grZnobs am siaxlis Setyobinebisas da Tavs aridebs am diskomforts imiT, rom ar yveba am siaxles. meore hipoTeza – TviTprezentaciis hipoTeza – amtkicebs, rom individebi ar grZnoben diskomforts cudi siaxlis Setyobinebisas. piriqiT, cudi siaxlis Setyobinebis Seusrulebloba warmoadgens publikaze gaTvlil mcdelobas, SeinarCunon dadebiTi socialuri imiji. bolos da bolos, vis surs, cudi siaxleebis mimtanad iyos cnobili? am hipoTezebis Sesamowmeblad bondma da andersonma (Bond & Anderson, 1987) gamoiyenes cdis pirebs Soris 2x2 sqema. ori damoukidebeli cvladi iyo cdis piris arseboba im adamianis mxedvelobis areSi, visTvisac unda eambnaT cudi ambebi (cdis piris yofna mxedvelobis areSi, faqtori A) da axali ambebis tipi (siaxlis tipi, faqtori B). TiToeuli damoukidebeli cvladi iRebda or mniSvnelobas. cdis piris mxedvelobis areSi yofnis mxriv, igi an ar imyofeboda (mniSvneloba A1) an imyofeboda (mniSvneloba A2) im piris mxedvelobis areSi, visTvisac unda emcnoT axali ambebi. siaxlis tipi iyo an kargi (mniSvneloba B1), an cudi (mniSvneloba B2). eqsmerimentis procedura Semdegi iyo: cdis pirs unda Caetarebina mravlobiTi pasuxis mqone inteleqtis testi sxva pirisaTvis. es piri eqsperimentatoris TanaSemwe iyo, magram cdis pirma ar icoda amis Sesaxeb. cdis piri da TanaSemwe imyofebodnen sxvadasxva oTaxebSi, romelTa Soris calmxrivi SuSa iyo CamontaJebuli. im pirobaSi, romelSic cdis piri ar Canda (mniSvneloba A1), mas eubnebodnen, rom TanaSemwes ar SeeZlo misi danaxva SuSaSi. im pirobaSi, romelSic cdis piri Canda (mniSvneloba A2), mas eubnebodnen, rom TanaSemwes SeeZlo misi danaxva SuSaSi. siaxlis tipis cvla xdeboda TanaSemwes mier testis warmatebuli Tu warumatebeli SesrulebiT. kargi siaxlis dros (mniSvneloba B1), cdis piri TanaSemwes awvdida informacias, rom misi Sedegi testis Sedegebis saukeTeso 20 procentSi xvdeboda. cudi siaxlis pirobaSi (mniSvneloba B1), cdis piri TanaSemwes awvdida informacias, rom misi Sedegi testis Sedegebis yvelaze dabal 20 procentSi xvdeboda. damokidebuli cvladi iyo cdis piris meryeobis periodi (latenturi dro) testis Sedegis Setyobinebisas. es periodi warmoadgenda dros testis dasrulebidan im momentamde, rodesac cdis piri atyobinebda TanaSemwes Tavis Sedegs.

MUM efeqtis Sesaxeb arsebuli ori hipoTeza eqsperimentis gansxvavebul Sedegebs winaswarmetyvelebda. Tu MUM efeqts safuZvlad udevs cdis pirebis pirovnuli diskomforti, maSin cudi siaxlis Setyobinebas ufro didi dro dasWirdeboda, vidre kargi siaxlisa, imisda miuxedavad, aris Tu ara cdis piri TanaSemwes mxedvelobis areSi. sxva sityvebiT, kargi (mniSvneloba B1) da cudi (mniSvneloba B2) siaxleebis pirobebs Soris gansxvaveba ar unda iyos damokidebuli imaze, xedavs Tu ara TanaSemwe cdis pirs. meore mxriv, Tu MUM efeqti ubralod publikaze gaTvlili qmedebaa, maSin latenturi dro cudi siaxlis miwodebisas damokidebuli unda iyos imaze, xedavs Tu ara TanaSemwe cdis pirs. es niSnavs, rom unda moxdes damoukidebeli cvladebis urTierTqmedeba. rodesac xdeba kargi siaxlis Setyobineba, ar unda iyos gansxvaveba latentur droSi im pirobis miuxedavad, xedavs Tu ara TanaSemwe cdis pirs. xolo rodesac cudi siaxlis Setyobineba xdeba, latenturi dro im pirobaSi, rodesac cdis piri ar imyofeba mxedvelobis areSi, unda mniSvnelovnad maRali iyos, vidre latenturi dro im pirobaSi, rodesac cdis piri imyofeba mxedvelobis areSi. Sesabamisad, rodesac cdis piri ar imyofeba mxedvelobis areSi, ar unda iyos gansxvaveba latentur droSi kargi da cudi siaxleebis Setyobinebisas. xolo rodesac cdis piri imyofeba mxedvelobis areSi, cudi ambebis Setyobinebis latenturi dro unda ufro didi iyos, vidre kargi ambebisa.

davuSvaT, xuTi mamrobiTi sqesis cdis piri SemTxveviTad gadanawilda TiToeul ujredSi da miviReT latenturi drois monacemebi (wamebSi), romlebic warmodgenilia cxrilSi # 11.2. im SemTxvevaSi, Tu Sedegebi saerTod romelime winaswarmetyvelebas Seesabameba, romel hipoTezas miekuTvneba es winaswarmetyveleba - pirovnuli diskomfortis hipoTezas, Tu publikaze gaTvlili qmedebis hipoTezas?

cxrili # 11.2

pasuxis hipoTeturi latenturi dro (wamebSi), rogorc cdis piris mxedvelobis areSi yofnisa da siaxlis tipis funqcia 20 cdis pirisaTvis sanimuSo cdis pirTa Soris 2x2 eqsperimentSi.

cdis piris mxedvelobis areSi yofnis piroba

(faqtori A)

ar Cans (A1) Cans (A1)

siaxlis tipi (faqtori B)

kargi (B1)

97.0

90.0

80.0

107.0

80.0

70.0

87.0

81.0

95.0

90.0

cudi (B2)

68.0

87.0

92.0

80.0

84.0

114.0

96.0

127.0

110.0

115.0

faqtoruli analizis Sedegad miRebuli informacia

cxrilis # 11.2 monacemebi (qulebi) sqematuradaa warmodgenili cxrilSi # 11.3. cdis piris monacemi aRniSnulia Xijk, sadac qveda indeqsebi migvaniSneben Semdeg informaciaze:

i = ujredSi cdis piris nomeri

j = A cvladis done

k = B cvladis done

cxrili # 11.3

cdis pirebs Soris 2x2 sqemaSi monacemTa sqematuri ganawileba, sadac TiToeul damoukidebel cvlads ori done aqvs da yovel ujredSi xuTi cdis piria.

faqtori A

A1 A2

B1

faqtori B

B2

X111

X211

X311

X411

X511

X121

X221

X321

X421

X521

X112

X212

X312

X412

X512

X122

X222

X322

X422

X522

magaliTad, X311 aris mesame cdis piris monacemi A1B1 pirobaSi (80.0 wami cxrilSi # 11.2), X421 aris meoTxe cdis piris monacemi A2B1 pirobaSi (95.0 wami), X211 aris meore cdis piris monacemi A1B2 pirobaSi (87 wami), X522 aris mexuTe cdis piris monacemi A2B2 pirobaSi (115 wami) da a.S. rodesac ar aris aucilebeli konkretuli cdis piris aRniSvna, Cven gamovtovebT ijk indeqsebs da ubralod viyenebT X-s. TiToeuli ujredisaTvis arsebobs nAB cdis pirebis raodenoba, xolo N aris cdis pirebis sruli raodenoba eqsperimentSi. Cvens magaliTSi nAB = 5 da N = 20. monacemebis analizis dros pirveli nabiji centraluri tendenciis sazomis, SerCevis saSualos gamoTvla. cxrilSi # 11.4 naCvenebia ujredisa da mTavari efeqtis saSualoebi, romelTa gamoTvlac SesaZlebelia magaliTis monacemebidan.

cxrili # 11.4

ujredisa da mTavari efeqtis saSualoebi cdis pirebs Soris 2x2 sqemaSi.

_______________________________________________________________________________

a. ujredis saSualo

faqtori A

B1

faqtori B

B2

A1 A2

(XA1B1 (X A2B1

(X A1B2 (X A2B2

(b) mTavari efeqtis saSualo A faqtorisaTvis,(X A1 da(X A2

1

A

X

faqtori A

B1

faqtori B

B1

A1 A2

2

A

X

1

B

X

1

A

X

2

A

X

(g) mTavari efeqtis saSualo B faqtorisaTvis, (X B1 da(X B2

2

B

X

faqtori A

A1 A2

B1

faqtori B

B2

1

2

B

A

X

(X B1

2

2

B

A

X

(X B2

ujredis saSualo: ujredSi nAB qulebis saSualo faqtorul sqemaSi.

ujredis saSualo, romelic simbolurad aRiniSneba(

1

1

B

A

X

,

2

1

B

A

X

,

1

2

B

A

X

, da

2

2

B

A

X

, an, zogadad, rogorc

AB

X

, warmoadgens ujredSi nAB qulebis saSualos (ixileT cxrili # 11.4a). ujredis saSualo aRniSnavs cdis pirebis tipur Sesrulebas am pirobaSi. ujredebis saSualoebis ricxviTi mniSvnelobebi cxrilisaTvis # 11.2 warmodgenilia cxrilSi # 11.5. standartuli gadaxrebi warmodgenilia frCxilebSi. faqtorul sqemaSi standartuli gadaxra, rogorc wesi, gamoiTvleba mxolod ujredis saSualosaTvis.

cxrili # 11.5

ujredisa da mTavari efeqtis saSualoebi qulebisaTvis cxrilidan # 11.2. ricxviTi mniSvnelobebi aris pasuxis latenturi dro wamebSi. ujredis saSualos standartuli gadaxrebi mocemulia frCxilebSi.

cdis piris yofna mxedvelobis areSi (faqtori A)

ar Cans (A1) Cans (A2)

mTavari efeqtis

saSualo siaxlis

tipisaTvis (

B

X

)

kargi (B1)

siaxlis tipi

(faqtori B)

cudi (B2)

mTavari efeqtis

saSualo cdis piris yofnisaTvis mxedvelobis areSi (

A

X

)

90.8 84.6 87.7

(11.56) (9.61)

82.2 112.4 97.3

(9.07) (11.15)

86.5 98.5 sruli saSualo 92.5

mTavari efeqtis saSualo: faqtorul analizSi damoukidebeli cvladis erTi donisaTvis yvela cdis piris saSualo, meore damoukidebeli cvladis doneebis mixedviT klasifikaciis ignorirebiT.

mTavari efeqtis saSualo aRniSnavs yvela cdis piris tipur Sesrulebas damoukidebeli cvladis erTi donisaTvis, meore damoukidebeli cvladis doneebis mixedviT klasifikaciis ignorirebiT. amdenad, arsebobs mTavari efeqtis saSualoebis ori erToblioba – erTi A faqtorisaTvis, xolo meore – B faqtorisaTvis.

A faqtoris mTavari efeqti: gansxvaveba

1

A

X

-sa da

2

A

X

-s Soris, gamoxatuli

1

A

X

-

2

A

X

.

A faqtori

mTavari efeqtis saSualo A faqtorisaTvis aRiniSneba

1

A

X

-iTa da

2

A

X

-iT. es saSualoebi, romelTac xandaxan svetebis saSualoebs uwodeben, miiReba yvela cdis pirisaTvis rogorc A1, aseve A2 doneebis Sesabamisad, imisda miuxedavad, Tu ra mniSvnelobebi miiRes maT B faqtoris mixedviT. B faqtoris doneebis mixedviT monacemebis ignorireba, raTa miRebul iqnes A faqtoris mTavari efeqtis saSualo, naCvenebia cxrilSi # 11.4b. magaliTad, mTavari efeqtis saSualo A faqtorisaTvis, romelic aris cdis piris yofna mxedvelobis areSi cxrilSi # 11.2, damyarebulia im cdis pirebis 10 monacemze, romlebic an imyofebian, an ar imyofebian eqsperimentatoris TanaSemwes mxedvelobis areSi. siaxlis tipi (faqtori B) ignorirebulia, rodesac viTvliT A faqtoris mTavari efeqtis saSualos.

1

A

X

-isa da

2

A

X

-s ricxviTi mniSvnelobebi warmodgenilia cxrilSi # 11.5. A faqtoris mTavari efeqti aris gansxvaveba

1

A

X

-sa da

2

A

X

-s Soris. Tu A faqtors aqvs gavlena damokidebul cvladze, maSin

1

A

X

da

2

A

X

gansxvavebuli iqneba erTmaneTisagan da

1

A

X

-

2

A

X

mniSvneloba ufro didi gaxdeba.

B faqtoris mTavari efeqti: gansxvaveba

1

B

X

-sa da

2

B

X

-s Soris, gamoxatuli

1

B

X

-

1

B

X

.

B faqtori

igive logika gamoiyeneba B faqtorisaTvis mTavari efeqtis saSualos gamoTvlisas. mTavari efeqtis saSualo B faqtorisaTvis (romelsac xandaxan uwodeben striqonebis saSualos) aRiniSneba

1

B

X

-iTa da

2

B

X

-iT da miiReba A faqtoris monacemebis ignorirebiT, rogorc es naCvenebia cxrilSi # 11.4g. B faqtoris, Cvens magaliTSi siaxlis tipis, mTavari efeqtis saSualos gamoTvlisaTvis xdeba cdis pirebis kategorizaciis ignorireba imis mixedviT, imyofebian Tu ara isini mxedvelobis areSi (A faqtori).

1

B

X

-isa da

2

B

X

-s ricxviTi mniSvnelobebi aseve warmodgenilia 11.5 cxrilSi. B faqtoris mTavari efeqti aris sxvaoba

1

B

X

-sa da

2

B

X

-s Soris. Tu B faqtors aqvs gavlena damokidebul cvladze, maSin

1

B

X

da

2

B

X

gansxvavebuli iqneba erTmaneTisagan da

1

B

X

-

2

B

X

mniSvneloba ufro didi gaxdeba.

sruli saSualo

sruli saSualo, romelic aRiniSneba

G

X

, aris cxrilis yvela monacemis saSualo. cxrilis # 11.2 monacemebisaTvis sruli saSualo – 92.5 wami – aris yvela 20 qulis saSualo. Cveulebriv, sruli saSualo ar aris xolme warmodgenili aRweriT statistikaSi, magram am TavSi saWiroa misi ganxilva, raTa movaxdinoT dispersiuli analizi am sqemisaTvis.

damoukidebeli cvladebis urTierTqmedeba

urTierTqmedeba: situacia faqtorul sqemaSi, rodesac erTi damoukidebeli cvladis efeqti damokidebulia masTan kombinaciaSi myofi meore damoukidebeli cvladis mniSvnelobaze.

faqtorul sqemaSi urTierTqmedeba xdeba, rodesac erTi damoukidebeli cvladi (mag., faqtori A) damokidebulia meore damoukidebeli cvladis mniSvnelobaze (mag., an B1 an B2), cvladisa, romelTanac aris kombinaciaSi. magaliTad, Tu urTierTqmedeba xdeba 2x2 sqemaSi, maSin A faqtoris efeqti, gansxvaveba qcevaSi A1 da A2 pirobebs Soris, damokidebulia B faqtoris mniSvnelobaze. amis msgavsad, Tu xdeba urTierTqmedeba, B faqtoris efeqti, gansxvaveba qcevaSi B1 da B2 pirobebs Soris, damokidebulia A faqtoris mniSvnelobaze. urTierTqmedeba xSirad aRiniSneba AxB, rac ikiTxeba ase: “A-sa da B-s urTierTqmedeba”.

publikaze gaTvlili qcevis hipoTezis winaswarmetyvelebis mixedviT, Cvens sanimuSo eqsperimentSi urTierTqmedeba unda momxdariyo. am hipoTezam ivarauda, rom kargi siaxlis tipisaTvis ar iqneboda gansxvaveba pasuxis latentur droSi mxedvelobis areSi yofnis da mxedvelobis areSi aryofnis pirobebis dros (anu ar iqneboda gansxvaveba A1B1 da A2B1 ujredebis saSualoebs Soris). xolo cudi siaxlis tipisaTvis hipoTezam iwinaswarmetyvela mniSvnelovnad grZeli latenturi dro mxedvelobis areSi yofnis pirobisaTvis (A2B2 ujredis saSualo) mxedvelobis areSi aryofnis pirobasTan (A1B2 ujredis saSualo) SedarebiT. miaqcieT yuradReba, rom urTierTqmedebis arseboba gamoiTvleba ujredebis saSualoebs Soris gansxvavebebis SedarebiT, da ara mTavari efeqtebis saSualoebis gansxvavebebis SedarebiT.

SeamowmeT Tqveni codna XI.1

1. gansazRvreT: ujredi, ujredis saSualo, svetis saSualo, faqtori, faqtoruli sqema, sruli saSualo, urTierTqmedeba, damoukidebeli cvladis mniSvneloba (done), A faqtoris mTavari efeqti, B faqtoris mTavari efeqti, mTavari efeqtis saSualo, striqonis saSualo, piroba,(XAB,(XA,(XB,(XG.

2. Semdegi faqtoruli sqemebidan TiToeulisaTvis gansazRvreT, ramdeni damoukidebeli cvladi cvalebadobs da miuTiTeT doneebis raodenoba TiToeuli faqtorisaTvis. Semdeg, im daSvebiT, rom gvaqvs cdis pirebs Soris sqema, miuTiTeT, ramdeni cdis piri iqneboda saWiro, Tu yovel pirobaSi monawileoba 10 cdis pirma unda miiRos.

3. sqemis tipi: (a) 3x3, (b) 3x2, (g) 2x3, (d) 6x2, (e) 4x4, (v) 2x2x2, (z) 2x4x3, (T) 3x3x2.

gamoTvaleT ujredebis saSualoebi, mTavari efeqtis saSualoebi da sruli saSualo qvemoT moyvanili TiToeuli cxrilis monacemebisaTvis:

cxrili 1

faqtori A

A1 A2

B1

faqtori B

B2

10 17

13 23

8 17

17 21

12 19

20 24

19 27

13 21

10 16

20 19

22 30

17 24

cxrili 2

faqtori A

A1 A2

B1

faqtori B

B2

23 41

13 22

28 27 11 32

19 26

20 24

18 39

29 28

33 31

18 26

29 34

36 39

47 44

27 35

cdis pirebs Soris orfaqtoriani sqemis dispersiuli analizi

faqtoruli sqemis statistikuri analizi moicavs hipoTezebis Semowmebas, raTa ganisazRvros, mniSvnelovnad gansxvavdeba Tu ara mTavari efeqtis saSualoebi TiToeuli damoukidebeli cvladisaTvis da dadgindes, statistikurad mniSvnelovania Tu ara damoukidebel cvladebs Soris urTierTqmedeba. es Semowmeba xdeba kvlav dispersiuli analizis meSveobiT, romelic monacemebis srul cvalebadobas dayofs cvalebadobis iseT wyaroebad, romlebic erTmaneTisagan damoukidebelia. cdis pirebs Soris erTfaqtoriani dispersiuli analizi (romelic me-10 TavSi ganvixileT) srul cvalebadobas or damoukidebel wyarod yofs: erTi, romelic damoukidebeli cvladis (anu A faqtoris) efeqtis gamo xdeba, da meore, romelic jgufebs SigniT cvalebadobis gamo. cdis pirebs Soris orfaqtorian sqemaSi qulebis sruli cvalebadoba iyofa jgufebs Soris sam wyarod da jgufebs SigniT erT wyarod. jgufebs Soris cvalebadobis wyaroebi Semdegia:

cvalebadoba A faqtoris efeqtis gamo

cvalebadoba B faqtoris efeqtis gamo

cvalebadoba A da B faqtorebs Soris urTierTqmedebis gamo, romelic simbolurad aRiniSneba AxB

jgufebs SigniT cvalebadobis wyaro aris ujredebs SigniT SemTxveviTi cvalebadoba.

Semdeg dispersiuli analizi iyenebs am danawilebas, raTa warmoqmnas kvadratebis oTxi saSualo:

MSA, romelic icvleba A faqtoris efeqtTan erTad

MSB, romelic icvleba B faqtoris efeqtTan erTad

MSAxB, romelic icvleba A da B faqtorebis urTierTqmedebasTan erTad

MSSecdoma, romelic icvleba ujredebs SigniT monacemebis cvalebadobasTan erTad

am etapis Semdeg gamoiTvleba sami F statistika, ori TiToeuli damoukidebeli cvladisaTvis da erTi – urTierTqmedebisaTvis. es Semdegi gziT xdeba:

cvalebadobis wyaro

F statistika

-----------------------------------------------------------------------------------

faqtori A

MSA/ MSSecdoma

faqtori B

MSB/ MSSecdoma

urTierTqmedeba AxB

MSAxB/ MSSecdoma

-----------------------------------------------------------------------------------

TiToeuli am sami F statistikidan gamoiyeneba statistikuri hipoTezebis SemowmebisaTvis, raTa dadgenil iqnes, statistikurad mniSvnelovania Tu ara cvalebadobis is wyaro, romelsac Seesabameba F statistika.

dispersiuli faqtoruli analizis konceptualuri gaazrebisaTvis Semdeg qveTavSi ganvixilavT, rogor miiReba gadaxrebis kvadratebis saSualo, romelic Sedis am F statistikebSi. Tumca, Tu Tqven dagWirdebodaT dispersiuli faqtoruli analizis Catareba monacemTa realur bazaze, Tqven gamoiyenebdiT, gamoTvlis TvalsazrisiT, ufro advil formulebs im gamosaTvleli formulebidan, romlebic moyvanilia am Tavis damatebaSi an mimarTavdiT monacemTa analizis kompiuterul programas.

monacemTa dayofa

dispersiul analizSi sami F statistikisaTvis gadaxrebis kvadratebis saSualoebi gamoiTvleba eqsperimentSi monacemebis sruli cvalebadobis iseT nawilebad dayofiT, romlebic icvleba A faqtorTan (jgufebs Soris), B faqtorTan (jgufebs Soris), AxB urTierTqmedebasTan (jgufebs Soris) da SemTxveviT cvalebadobasTan (jgufebs SigniT) erTad. qulis wardgenis es modeli cdis pirebs Soris orfaqtorian sqemaSi SeiZleba Semdegnairad gamoisaxos:

(11.1)

1

1

B

A

X

= + + +

monacemebis terminebiT es gantoleba SeiZleba Caiweros Semdegnairad:

(X -

G

X

) = (

A

X

-

G

X

) + (

B

X

-

G

X

) + (

AB

X

-

A

X

-

B

X

+

G

X

) + (X -

AB

X

). (11.2)

2

1

B

A

X

Cven ganvixilavT 11.2 gantolebis TiToeul nawils.

sruli cvalebadoba

me-10 TavSi warmodgenili dispersiis erTfaqtoriani analizis msgavsad, monacemis gansxvaveba sruli saSualosagan (anu X -

G

X

) warmoadgens am qulis srul cvalebadobas. rogorc gviCvenebs 11.2 gantoleba, am cvalebadobis nawili xdeba TiToeuli damoukidebeli cvladis efeqtisa da damoukidebeli cvladebis urTierTqmedebis gamo, xolo nawili ki – SemTxveviTi cvalebadobis gamo.

cvalebadoba A faqtoris efeqtisa da SerCevis Secdomis gamo

A faqtoris mTavari efeqtis saSualosa da srul saSualos Soris gansxvaveba (anu

A

X

-

G

X

) icvleba A faqtoris efeqtsa da A faqtoris mTavari efeqtis saSualoebs Soris SerCevis SecdomasTan erTad. misi gamoyeneba orfaqtorian sqemaSi misi cdis pirebs Soris erTfaqtorian sqemaSi gamoyenebis identuria, raTa gaizomos damoukidebeli cvladis gavlena. mosalodnelia, rom A faqtoris nebismieri efeqti yvela cdis pirze Tanabrad moaxdens gavlenas am faqtoris yvela doneze. amdenad, A faqtoris efeqti cvlis mTavari efeqtis saSualoebis mniSvnelobas A faqtorisaTvis. es mTavari efeqtis saSualoebi Semdeg gansxvavebuli iqneba sruli saSualosagan. aqedan gamomdinare, gansxvaveba

A

X

-

G

X

asaxavs A faqtoris nebismier efeqts (pirobis efeqts A faqtorisaTvis 11.1 gantolebaSi). nebismieri pirobis efeqtis garda, mTavari efeqtis saSualoebi A faqtorisaTvis aseve gansxvavebuli iqneba erTmaneTisagan SerCevis Secdomis gamo. amitom,

A

X

-

G

X

sxvaobis mniSvneloba asaxavs rogorc A faqtoris pirobis efeqts, aseve SerCevis Secdomas, romelic gavlenas axdens

A

X

-s mniSvnelobebze. Sesabamisad, is monawileobs MSA.s gamoTvlaSi.

cvalebadoba B faqtoris efeqtisa da SerCevis Secdomis gamo

B faqtoris mTavari efeqtis saSualosa da srul saSualos Soris gansxvaveba (anu

B

X

-

G

X

) icvleba B faqtoris efeqtsa da B faqtoris mTavari efeqtis saSualoebs Soris SerCevis SecdomasTan erTad. iseve, rogorc A faqtoris SemTxvevaSi, mosalodnelia, rom B faqtoris nebismieri efeqti gavlenas moaxdens yvela individze am faqtoris yvela doneze da amdenad Secvlis mTavari efeqtis saSualo mniSvnelobas B faqtorisaTvis, romelic gansxvavebuli gaxdeba sruli saSualosagan. amitom, gansxvaveba

B

X

-

G

X

asaxavs B faqtoris nebismier efeqts (pirobis efeqts B faqtorisaTvis 11.1 gantolebaSi). garda amisa, mTavari efeqtis saSualoebi B faqtorisaTvis aseve gansxvavebuli iqneba erTmaneTisagan SerCevis Secdomis gamo. amitom,

B

X

-

G

X

gansxvaveba asaxavs rogorc B faqtoris pirobis efeqts, aseve SerCevis Secdomas, romelic gavlenas axdens

B

X

-s mniSvnelobebze da, Sesabamisad, monawileobs MSB-s gamoTvlaSi.

cvalebadoba A da B faqtorebis urTierTqmedebis gamo

A da B faqtorebis urTierTqmedeba aris sruli saSualosagan ujredebis saSualoebis darCenili gansxvaveba mas Semdeg, rac TiToeuli damoukidebeli cvladis efeqti gauqmebulia. simbolurad es debuleba SeiZleba Semdegnairad warmovadginoT:

A x B = (

AB

X

-

G

X

) - (

A

X

-

G

X

) - (

B

X

-

G

X

)

2

1

B

A

X

= - -

gantoleba gviCvenebs, rom urTierTqmedeba aris ujredebis saSualoebis cvalebadoba mas Semdeg, rac TiToeuli damoukidebeli cvladis mTavari efeqti gauqmebulia. ujredebis saSualoebis es darCenili cvalebadoba xdeba damoukidebel cvladebs Soris urTierTqmedebisa da ujredebis saSualoebs Soris nebismieri SerCevis Secdomis gamo.

gantolebaSi moyvanili gamoklebis Catarebis Sedegad viRebT urTierTqmedebis gamartivebul gamosaxulebas:

AB

X

-

A

X

-

B

X

+

G

X

urTierTqmedeba am saxiT aris warmodgenili 11.2 gantolebaSi. gantolebis es nawili monawileobs MSAxB-is gamoTvlaSi.

cvalebadoba ujredebs SigniT Secdomis gamo

monacemis gansxvaveba misi ujredis saSualosagan (anu X -

AB

X

) asaxavs mxolod eqsperimentSi ujredebs SigniT SemTxveviT cvalebadobas. amiT gamowveuli Secdoma aris is, rac rCeba monacemis miRma mas Semdeg, rac orive faqtoris mTavari efeqti da maTi urTierTqmedeba gaTvaliswinebul iqna. rogorc dispersiuli erTfaqtoriani analizis dros, Secdoma asaxavs pirovnebis monacemis unikalurobas individebis jgufSi, romelTaganac yvela erTsa da imave pirobaSi iyo. is monawileobs MSSecdomis gamoTvlaSi.

dayofili monacemebidan gadaxrebis kvadratebis saSualos miReba

rogorc ganvixileT me-10 TavSi, dayofis gantoleba gvaZlevs safuZvels, rom miviRoT SS da df, romlebic qmnian kvadratebis saSualos F SefardebisaTvis. pirveli nabijia SS-is miReba cdis pirebis monacemebidan.

kvadratebis jamebis miReba

me-10 TavSi ganxiluli midgomis msgavsad, kvadratebis jamebi (SS) miiReba TiToeuli qulis dayofiT 11.2 gantolebis mixedviT. am dayofis ilustraciisaTvis Cven gamoviyenebT pirveli cdis piris monacems pirobaSi “ar aris mxedvelobis areSi/kargi siaxle” (anu X111) 11.2 cxrilidan, romelic aris 97.0. am monacemisaTvis 11.2 gantoleba iqneba

(X111 -

G

X

) = (

1

A

X

-

G

X

) + (

1

B

X

-

G

X

) + (

1

1

B

A

X

-

1

A

X

-

1

B

X

+

G

X

) + (X111 -

1

1

B

A

X

)

ricxviTi mniSvnelobebis CasmiT viRebT

97.0–92.5 = (86.5 – 92.5) + (87.7 – 92.5) + (90.8 – 86.5 – 87.7 + 92.5) + (97.0 – 90.8)

anu, miviRebT

+4.5 = (-6.0) + (-4.8) + (+9.1) + (+6.2)

es dayofa gvaCvenebs, rom es monacemi gansxvavdeba sruli saSualosagan, radganac adgili aqvs A faqtoris sistematur efeqts (aRniSnulia

1

A

X

-

G

X

= - 6.0 ), B faqtoris sistematur efeqts (aRniSnulia

1

B

X

-

G

X

= - 4.8), A da B faqtorebis urTierTqmedebas (aRniSnulia

1

1

B

A

X

-

1

A

X

-

1

B

X

+

G

X

= 9.1) da ujredebs SigniT SemTxveviTi cvalebadobis arasistematur gavlenebs (aRniSnulia X111 -

1

1

B

A

X

= +6.2). cxrilis # 11.2 yvela sxva monacemis msgavsi dayofa naCvenebia cxrilis # 11.6 pirvel nabijSi. cxrilis danarCen nabijebSi am dayofili monacemebidan gamoTvlilia saSualoebis jamebi. yuradRebiT misdieT TiToeuls am nabijebidan.

nabiji 1. eqsperimentSi monawile yvela 20 cdis piris monacemi

dayofilia 11.2 gantolebis mixedviT.

nabiji 2. TiToeuli monacemisaTvis miRebulia ricxviTi

sxvaobebi.

nabiji 3. me-2 nabijSi miRebuli yoveli dadebiTi da uaryofiTi

sxvaoba ayvanilia kvadratSi.

nabiji 4. eqsperimentis yvela monacemis kvadratSi ayvanili

sxvaobebis mniSvnelobebi dajamebulia. es dajameba miiRweva

ocive mniSvnelobis mimatebiT TiToeul svetSi. Sedegad viRebT

kvadratebis xuT jams:

SSsruli = 4567.000,

SSA = 720.000,

SSB = 460.800,

SSAxB = 1656.200,

SSSecdoma = 1730.000.

SSsruli misi komponentebis jamia, amitom

SSsruli = SSA + SSB + SSAxB + SSSecdoma.

(11.3)

cxrili # 11.6

kvadratebis jamis miReba orfaqtoriani dispersiuli analizisaTvis cxrilis # 11.2 monacemebze dayrdnobiT.

nabiji 1: 20 cdis piris qulebis dayofa Semdegi gantolebis gamoyenebiT:

(X -

G

X

) = (

A

X

-

G

X

) + (

B

X

-

G

X

) + (

AB

X

-

A

X

-

B

X

+

G

X

) + (X -

AB

X

)

__________________________________________________________________

97.0 - 92.5 = (86.5 - 92.5) + (87.7 - 92.5) + (90.8 - 86.5 - 87.7 + 92.5) + (97.0 - 90.8)

90.0 – 92.5 = (86.5 – 92.5) + (87.7 - 92.5) + (90.8 - 86.5 - 87.7 + 92.5) + (90.0 - 90.8)

monacemebi 80.0 - 92.5 = (86.5 - 92.5) + (87.7 - 92.5) + (90.8 - 86.5 - 87.7 + 92.5) + (80.0 - 90.8)

A1B1-Si 107.0 - 92.5 =(86.5 - 92.5) + (87.7 - 92.5) + (90.8 - 86.5 - 87.7 + 92.5) + (107.0 - 90.8)

80.0 - 92.5 = (86.5 - 92.5) + (87.7 - 92.5) + (90.8 - 86.5 - 87.7 + 92.5) + (80.0 - 90.8)

70.0 - 92.5 = (98.5 - 92.5) + (87.7 - 92.5) + (84.6 - 98.5 - 87.7 + 92.5) + (70.0 - 84.6)

87.0 - 92.5 = (98.5 - 92.5) + (87.7 - 92.5) + (84.6 - 98.5 - 87.7 + 92.5) + (87.0 - 84.6)

monacemebi 81.0 - 92.5 = (98.5 - 92.5) + (87.7 - 92.5) + (84.6 - 98.5 - 87.7 + 92.5) + (81.0 - 84.6)

A2B1-Si 95.0 - 92.5 = (98.5 - 92.5) + (87.7 - 92.5) + (84.6 - 98.5 - 87.7 + 92.5) + (95.0 - 84.6)

90.0 - 92.5 = (98.5 - 92.5) + (87.7 - 92.5) + (84.6 - 98.5 - 87.7 + 92.5) + (90.0 - 84.6)

68.0 - 92.5 = (86.5 - 92.5) + (97.3 - 92.5) + (82.2 - 86.5 – 97.3 + 92.5) + (68.0 - 82.2)

87.0 - 92.5 = (86.5 - 92.5) + (97.3 - 92.5) + (82.2 - 86.5 – 97.3 + 92.5) + (87.0 - 82.2)

monacemebi 92.0 - 92.5 = (86.5 - 92.5) + (97.3 - 92.5) + (82.2 - 86.5 – 97.3 + 92.5) + (92.0 - 82.2)

A1B2-Si 80.0 - 92.5 = (86.5 - 92.5) + (97.3 - 92.5) + (82.2 - 86.5 – 97.3 + 92.5) + (80.0 - 82.2)

84.0 - 92.5 = (86.5 - 92.5) + (97.3 - 92.5) + (82.2 - 86.5 – 97.3 + 92.5) + (84.0 - 82.2)

114.0 - 92.5 = (98.5 - 92.5) + (97.3 - 92.5) + (112.4 - 98.5 - 97.3 + 92.5) + (114.0 -112.4)

96.0 - 92.5 = (98.5 - 92.5) + (97.3 - 92.5) + (112.4 - 98.5 - 97.3 + 92.5) + (96.0 - 112.4)

monacemebi 127.0 - 92.5 = (98.5 - 92.5) + (97.3 - 92.5) + (112.4 - 98.5 - 97.3 + 92.5) + (127.0 -112.4)

A2B2-Si 110.0 - 92.5 = (98.5 - 92.5) + (97.3 - 92.5) + (112.4 - 98.5 - 97.3 + 92.5) + (110.0 -112.4)

115.0 - 92.5 = (98.5 - 92.5) + (97.3 - 92.5) + (112.4 - 98.5 - 97.3 + 92.5) + (115.0 -112.4)

nabiji 2: CavataroT pirvel nabijSi miTiTebuli gamokleba, raTa miviRoT ricxviTi sxvaobebi TiToeuli cdis pirisaTvis.

+ 4.5 = - 6.0 + - 4.8 + + 9.1 + + 6.2

- 2.5 = - 6.0 + - 4.8 + + 9.1 + - 0.8

monacemebi - 12.5 = - 6.0 + - 4.8 + + 9.1 + - 10.8

A1B1-Si +14.5 = - 6.0 + - 4.8 + + 9.1 + + 16.2

_ 12.5 = - 6.0 + - 4.8 + + 9.1 + - 10.8

- 22.5 = + 6.0 + - 4.8 + - 9.1 + - 14.6

- 5.5 = + 6.0 + - 4.8 + - 9.1 + + 2.4

monacemebi - 11.5 = + 6.0 + - 4.8 + - 9.1 + - 3.6

A2B1-Si + 2.5 = + 6.0 + - 4.8 + - 9.1 + + 10.4

- 2.5 = + 6.0 + - 4.8 + - 9.1 + + 5.4

- 24.5 = _ 6.0 + + 4.8 + - 9.1 + - 14.2

- 5.5 = _ 6.0 + + 4.8 + - 9.1 + + 4.8

monacemebi - 0.5 = _ 6.0 + + 4.8 + - 9.1 + + 9.8

A1B2-Si - 12.5 = _ 6.0 + + 4.8 + - 9.1 + - 2.2

- 8.5 = _ 6.0 + + 4.8 + - 9.1 + + 1.8

+ 21.5 = + 6.0 + + 4.8 + + 9.1 + + 1.6

+ 3.5 = + 6.0 + + 4.8 + + 9.1 + - 16.4

monacemebi + 34.5 = + 6.0 + + 4.8 + + 9.1 + + 14.6

A2B2-Si + 17.5 = + 6.0 + + 4.8 + + 9.1 + _ 2.4

+ 22.5 = + 6.0 + + 4.8 + + 9.1 + + 2.6

cxrili # 11.6 (gagrZeleba)

nabiji 3: kvadratSi aiyvaneT TiToeuli sxvaoba:

(X -

G

X

)2 (

A

X

-

G

X

)2 (

B

X

-

G

X

)2 (

AB

X

-

A

X

-

B

X

+

G

X

)2 (X -

AB

X

)2

-----________________________________________________________________

20.25

36.0

23.04

82.81

38.44

6.25

36.0

23.04

82.81

0.64

monacemebi 156..2536.0

23.04

82.81

116.64

A1B1-Si 210.2536.0

23.04

82.81

262.44

156..2536.0

23.04

82.81

116.64

506.2536.0

23.04

82.81

213.16

30.25

36.0

23.04

82.81

5.76

monacemebi 132.2536.0

23.04

82.81

12.96

A2B1-Si 6.25

36.0

23.04

82.81

108.16

6.25

36.0

23.04

82.81

29.16

600..2536.0

23.04

82.81

201.64

30.25

36.0

23.04

82.81

23.04

monacemebi 0.25

36.0

23.04

82.81

96.04

A1B2-Si 156..2536.0

23.04

82.81

4.84

72.25

36.0

23.04

82.81

3.24

462.25

36.0

23.04

82.81

2.56

12.25

36.0

23.04

82.81

268.96

monacemebi 1190..25

36.0

23.04

82.81

213.16

A2B2-Si 306.25

36.0

23.04

82.81

5.76

506.25

36.0

23.04

82.81

6.76

nabiji 4: daajameT kvadratSi ayvanili sxvaobebi TiToeuli dayofisaTvis yvela cdis piris mixedviT.

4567.000

=720.000+460.800+1656.200

+1730.000

SSsruli

SSA

SSB

SSAxB SSSecdoma

es gantoleba gvaCvenebs, rom eqsperimentSi monacemebis sruli cvalebadoba (SSsruli) im cvalebadobis Sedegia, romelic oTxi damoukidebeli wyaros gamo xdeba: A faqtori, B faqtori, A da B faqtorebis urTierTqmedeba da ujredebs SigniT Secdoma.

Tavisuflebis xarisxis gamoTvla

kvadratebis saSualo (MS) miiReba TiToeuli SS-is gayofiT Tavis Tavisuflebis xarisxze. gaixseneT, rom Tavisuflebis xarisxebi ganisazRvreba, rogorc monacemebis (qulebis) raodenoba, romelic Tavisuflad icvleba statistikis gamoTvlisas. gamoviyenoT es gansazRvreba 11.3 gantolebaSi TiToeuli SS-isaTvis df–is gamosaTvlelad.

Tavisuflebis sruli xarisxi. SSsruli -s gamosaTvlelad unda vicodeT sruli saSualo

G

X

. radganac kvadratebis sruli jami damokidebulia eqsperimentSi yoveli monacemis sxvaobaze sruli saSualosagan (anu X -

G

X

), amdenad monacemebis srul raodenobaze erTiT naklebs SeuZlia Tavisufali cvlileba SSsruli -s gamoTvlisas. amitom

Tavisuflebis sruli xarisxi = dfsruli = N – 1,

sadac N aris eqsperimentSi monacemTa sruli raodenoba. rodesac N = 20, dfsruli = 20 – 1 = 19.

Tavisuflebis xarisxi SSA.-isaTvis. SSA gamoiTvleba

G

X

–sagan A faqtoris mTavari efeqtis saSualoebis gamoklebiT (anu Cvens magaliTSi

1

A

X

da

2

A

X

). faqtorul sqemaSi, sadac A faqtors ori done aqvs, Tu viciT

G

X

, maSin A faqtoris mxolod erT mTavari efeqtis saSualos SeuZlia Tavisuflad cvlileba. zogadad, df SSA.-isaTvis (dfA) udris erTiT naklebs, vidre A faqtoris doneebi, anu

Tavisuflebis xarisxi SSA.-isaTvis = dfA = a – 1,

sadac a aris A damoukidebeli cvladis doneebis raodenoba. Cvens magaliTSi, rodesac a = 2, amitom dfA = 2 – 1 = 1.

Tavisuflebis xarisxi SSB-isaTvis. SSB gamoiTvleba

G

X

–sagan B faqtoris mTavari efeqtis saSualoebis gamoklebiT (anu Cvens magaliTSi

1

B

X

da

2

B

X

). faqtorul sqemaSi, sadac B faqtors ori done aqvs, Tu viciT

G

X

, maSin B faqtoris mxolod erT mTavari efeqtis saSualos SeuZlia Tavisuflad cvlileba. zogadad, df SSB-isaTvis (dfB) udris erTiT naklebs, vidre B faqtoris doneebi, anu

Tavisuflebis xarisxi SSB-isaTvis = dfB = b – 1,

sadac b aris B damoukidebeli cvladis doneebis raodenoba. Cvens magaliTSi, rodesac b = 2, amitom dfB = 2 – 1 = 1.

Tavisuflebis xarisxi SSAxB-isaTvis. SSAxB gamoiTvleba TiToeuli ujredis saSualosagan Sesabamisi mTavari efeqtis saSualoebis gamoklebiT. 2x2 sqemisaTvis, Tu cnobilia TiToeuli mTavari efeqtis saSualo, maSin mxolod erT ujredis saSualos SeuZlia Tavisufali cvlileba. rodesac viciT erTi ujredis saSualo da A da B faqtorebis mTavari efeqtebis saSualoebi, SegviZlia vipovoT danarCeni sami ujredis saSualoebi. zogadad,

Tavisuflebis xarisxi SSAxB-isaTvis = dfAxB = (a - 1) (b – 1)

2x2 sqemaSi a = 2 da b = 2, amitom

dfAxB = (2 - 1) (2 – 1) = 1

Tavisuflebis xarisxi SSSecdomisaTvis. SSSecdoma gamoiTvleba yoveli

AB

X

-is gamoklebiT ujredis yvela monacemidan, eqsperimentis yvela ujredisaTvis. amdenad, yoveli pirobisaTvis, mas Semdeg, rac napovnia

AB

X

, mxolod nAB – 1 monacemebs SeuZliaT Tavisufali cvalebadoba am ujredSi. magaliTad, cxrilSi # 11.2 xuTi monacemidan mxolod oTxs SeuZlia Tavisufali calebadoba TiToeul ujredSi, Tu cnobilia TiTeuli

AB

X

. radganac arsebobs oTxi ujredi da TiToeulSi Tavisufali cvlileba oTx qulas SeuZlia, SSSecdomisaTvis arsebobs 16 df. zogadad, rodesac a aris A faqtoris doneebis raodenoba, b – B faqtoris doneebis raodenoba, xolo nAB ki qulebis raodenoba TiToeuli ujredis SigniT,

Tavisuflebis xarisxi SSSecdomisaTvis = dfSecdoma = ab (nAB - 1)

Tavisuflebis xarisxis aditiuroba. faqtorul analizSi Tavisuflebis xarisxebi imave gziT jamdeba, rogorc erTfaqtorian dispersiul analizSi. amdenad

dfsruli = dfA + dfB + dfAxB + dfSecdoma

(11.4)

es damokidebuleba sruldeba Cvens magaliTSic, radgan dfsruli =19, dfA =1, dfB =1, dfAxB =1, dfSecdoma =16.

MS-is miReba SS-is da df-is saSualebiT.

11.3 gantolebaSi TiToeuli SS-is gayofa mis Sesabamis df-ze warmoqmnis kvadratebis oTx saSualos, romlebic saWiroa cdis pirebs Soris orfaqtoriani dispersiuli analizisaTvis:

MSA =

A

A

df

SS

-

MSB =

B

B

df

SS

-

MSAxB =

AxB

AxB

df

SS

MSSecdoma =

Secdoma

Secdoma

df

SS

Cven ar vangariSobT MSsruls, radganac is ar gamoiyeneba am analizSi romelime F Sefardebis misaRebad.

cxrilis # 11.2 monacemebisaTvis SSA=720.000, SSB=460.800, SSAxB=1656.200 da SSSecdoma =1730.000. ufro metic, dfA=1, dfB=1, dfAxB=1 da dfSecdoma =16. Sesabamisad,

MSA =

1

000

.

720

= 720.000

MSB =

1

800

.

460

= 460.800

MSAxB =

1

200

.

1656

= 1656.200

MSSecdoma =

16

000

.

1730

= 108.125

F statistikis gamoTvla

F Sefardeba iqmneba kvadratebis ori saSualos SefardebiT, erTi MS-isa, romelic icvleba damoukidebeli cvladis efeqtTan erTad da aseve SerCevis SecdomasTan erTad, da meore MS_isa, romelic icvleba mxolod Secdomis cvalebadobasTan erTad eqsperimentSi. orfaqtorian cdis pirebs Soris dispersiul analizSi, MSA icvleba A faqtorTan erTad, MSB – B faqtorTan erTad, MSAxB – A da B faqtorebis urTierTqmedebasTan erTad da MSSecdoma ki – mxolod ujredebs SigniT SemTxveviT cvalebadobasTan erTad. ase rom, viRebT sami saxis F statistikas. maTgan TiToeuli asaxavs cvalebadobis erT sistematur wyaros eqsperimentSi:

cvalebadobis wyaro

F

-------------------------------------------------------------------------------------------

faqtori A

Secdoma

MS

MS

A

faqtori B

Secdoma

MS

MS

B

A da B urTierTqmedeba

Secdoma

MS

MS

AxB

------------------------------------------------------------------------------------

gadaxrebis kvadratebis saSualoebis ricxviTi mniSvnelobebis CasmiT viRebT Semdeg F statistikebs:

cvalebadobis wyaro

F

-------------------------------------------------------------------------------------------------

faqtori A

125

.

108

000

.

720

= 6.66

faqtori B

125

.

108

800

.

460

= 4.26

A da B urTierTqmedeba

125

.

108

200

.

1656

= 15.32

---------------------------------------------------------------------------------------------------

mokled ganvixiloT, Tu rogor gamoviyenoT da rogori axsna mivceT TiToeul F-s.

cxrilSi # 11.7 moyvanilia cvalebadobis wyaroebi cdis pirebs Soris orfaqtorian dispersiul analizSi da formulebi TiToeuli SS-isTvis, df-isTvis, MS-isTvis da F statistikisaTvis. cxrilis # 11.2 monacemebis dispersiuli analizis Sejamebis Sedegebi mocemulia cxrilSi # 11.8.

cxrili # 11.7

cdis pirebs Soris orfaqtoriani dispersiuli analizSi gamoyenebuli ganmartebiTi formulebis Sejameba.

------------------------------------------------------------------------------------------------------------------------------------------------

wyaro

SS

dfa

MS

F

-----------------------------------------------------------------------------------------------------------------------------------------------------

A faqtori ‡

å

å

å

(

A

X

-

G

X

)2

A.1

A

A

df

SS

Secdoma

MS

MS

A

B faqtori

å

å

EMBED Equation.3

å

(

B

X

-

G

X

)2

b-1

B

B

df

SS

Secdoma

MS

MS

B

A da B

urTierTqmedeba

å

å

EMBED Equation.3

å

(

AB

X

-

A

X

-

B

X

+

G

X

)2(A.1)(b-1)

AxB

AxB

df

SS

Secdoma

MS

MS

AxB

Secdoma

å

å

EMBED Equation.3

å

(X -

AB

X

)2

ab(nAB-1)

Secdoma

Secdoma

df

SS

sul

å

å

EMBED Equation.3

å

(X -

G

X

)2

N-1

ar gamoiTvleba

-------------------------------------------------------------------------------------------------------------------------------------------------------

aa = A faqtoris doneebis raodenoba; b = B faqtoris doneebis raodenoba; nAB = qulebis raodenoba TiToeul ujredSi; N = qulebis sruli raodenoba.

-------------------------------------------------------------------------------------------------------------------------------------------------------

cxrili # 11.8

cxrilis # 11.2 hipoTeturi qulebis dispersiuli analizis gamoTvlis Sedegebi.

wyaro

SS

df

MS

F

subieqtis yofna

mxedvelobis areSi (A)

720.000

1

720.000

6.66*

siaxlis tipi (B)

460.800

1

460.800

4.26

A x B

1656.2001

1656.200

15.32**

Secdoma

1730.000

16

1656.200

sul

4567.000

19

* p < .05

** p < .01


1. gansazRvreT monacemebis (qulebis) cvalebadobis wyaroebi cdis pirebs Soris orfaqtorian sqemaSi.

2. dawereT gantoleba, romlis mixedviTac xdeba qulebis dayofa dispersiis orfaqtorian cdis pirebs Soris analizSi.

3. axseniT, ratom icvleba

A

X

-

G

X

mniSvneloba A faqtoris efeqtTan erTad faqtorul eqsperimentSi.


B

X

-

G

X

mniSvneloba B faqtoris efeqtTan erTad faqtorul eqsperimentSi.


AB

X

-

A

X

-

B

X

+

G

X

mniSvneloba A da B faqtorebs Soris urTierTqmedebis efeqtTan erTad faqtorul eqsperimentSi.

6. axseniT, ratom icvleba X -

AB

X

mniSvneloba mxolod ujredebs SigniT SemTxveviT cvalebadobasTan erTad faqtorul eqsperimentSi.

7. daasruleT Semdegi tolobebi cdis pirebs Soris orfaqtoriani dispersiuli analizisaTvis:

a. dfA =

b. dfB =

g. dfAxB =

d. dfSecdoma =

e. dfsruli =

v. MSA =

z. MSB =

T. MSAxB =

i. MSSecdoma =

8. ras udris SSsrulis mniSvneloba, Tu SSA =40.00, SSB =70.00, SSAxB =30.00 da

SSSecdoma =100.00?

9. ras udris SSA–is mniSvneloba, Tu SSsruli = 224.00, SSB =14.00, SSAxB =64.00 da

SSSecdoma =101.00?

10. ras udris SSAxB–is mniSvneloba, Tu SSsruli = 302.00, SSA =75.00, SSB =19.00 da

SSSecdoma =153.00?

11. ras udris SSSecdomis mniSvneloba, Tu SSsruli = 98.00, SSA =14.00, SSB =7.00 da SSAxB =17.00?

12. ipoveT dfA, dfB, dfAxB, dfSecdoma da dfsruli 2x3 cdis pirebs Soris dispersiuli analizisaTvis, sadac TiToeul ujredSi eqvsi cdis piria.

13. ipoveT dfA, dfB, dfAxB, dfSecdoma da dfsruli 3x2 cdis pirebs Soris dispersiuli analizisaTvis, sadac TiToeul pirobaSi 13 qulaa.

14. ras udris dfsrulis mniSvneloba, Tu dfA=3, dfB=1, dfAxB=3 da dfSecdoma = 72?

15. gamoTvaleT gadaxrebis kvadratebis saSualoebis ricxviTi mniSvnelobebi Semdegi SS-isa da df-isaTvis: SSA =14.00, SSB =26.00, SSAxB =44.00, SSSecdoma = 480.00, dfA=1, dfB=2, dfAxB=2 da dfSecdoma = 60.

16. davuSvaT, Tqven CaatareT 2x2 faqtoruli eqsperimenti, sadac TiToeul ujredSi sami cdis piria da miiReT Semdegi qulebi:

faqtori A

A1 A2

B1

faqtori B

B2

30 34

32 36

28 32

28 38

30 34

26 36

a. dayaviT es qulebi cxrilSi # 11.6 naCvenebi midgomis mixedviT. gamoTvaleT SSsruli, SSA, SSB, SSAxB, SSSecdoma da Sesabamisi Tavisuflebis xarisxebi yoveli dayofisaTvis. Semdeg SeqmeniT ricxviTi Sejamebis cxrili MS-isa da F-is mniSvnelobebiT.

b. ratom aris SSB nulis toli am magaliTSi?

17. cxrilebi # 1 da 2 cdis pirebs Soris orfaqtoriani dispersiuli analizis dausrulebeli cxrilebia. dauSviT, rom TiToeul ujredSi qulebis toli raodenobebia. TiToeul cxrilSi SeavseT gamotovebuli mniSvnelobebi SS-isa da df-is cxrilebSi # 11.3 da 11.4 mocemuli kavSiris gamoyenebiT. Semdeg TiToeuli cxrilisaTvis upasuxeT Semdeg kiTxvebs:

a. A faqtoris ramdeni done iyo gamoyenebuli?

b. B faqtoris ramdeni done iyo gamoyenebuli?

g. ramdeni cdis piri gaizoma TiToeul ujredSi?

d. ramdeni cdis piri monawileobda kvlevaSi?

cxrili # 1

wyaro

SS

df

MS

F

A faqtori

____

2

16.00

------

B faqtori

24.00

1

---------

3.00

A x B

--------

------

12.00

-------

Secdoma

---------

------

---------

sul

560.00

65

-------------------------------------------------------------------------------------------------------------------------------------------------------

cxrili # 2

wyaro

SS

df

MS

F

A faqtori

____

2

---------

4.50

B faqtori

24.00

4

---------

1.50

A x B

160.00

------

---------

5.00

Secdoma

---------

------

4.00

sul

---------

224

-------------------------------------------------------------------------------------------------------------------------------------------------------

statistikuri hipoTezis Semowmeba cdis pirTa Soris orfaqtorian dispersiul analizSi

imisaTvis, rom gavigoT, Tu rogor xdeba statistikuri hipoTezebis Semowmeba F statistikis gamoyenebiT, romelic miiReba dispersiuli faqtoruli analizis Sedegad, unda vicodeT, Tu ra axdens gavlenas MSA.ze, MSB-ze, MSAxB-sa da MSSecdomaze.

faqtorebi, romlebic gavlenas axdenen gadaxrebis kvadratebis saSualoebze dispersiul faqtorul analizSi

faqtorul analizSi yovel MS-ze gavlenas axdens cvalebadobis gansxvavebuli wyaroebi. Tu damokidebul cvladze arc erT damoukidebel cvlads ar aqvs gavlena da aseve ar arsebobs urTierTqmedeba damoukidebel cvladebs Soris, maSin yoveli MS asaxavs mxolod SemTxveviT cvalebadobas. aseT pirobebSi oTxive kvadratebis saSualo daaxloebiT erTi da imave mniSvnelobis unda iyos da aCvenebdes mxolod SerCevis Secdomis gavlenas. magram, Tu romelime an orive damoukidebel cvlads aqvs mTavari efeqti an Tu isini urTierTqmedeben, maSin efeqti zrdis Sesabamisi MS-is mniSvnelobas. magaliTad, Tu A faqtori qmnis mTavar efeqts, maSin MSA gaizrdeba MSSecdomasTan SedarebiT, magram es mTavari efeqti ar moaxdens gavlenas MSB-ze, MSAxB-ze da MSSecdomaze. msgavsi situacia iqneba, Tu B faqtors aqvs mTavari efeqti. Tu B faqtori qmnis mTavar efeqts, maSin MSB gaizrdeba MSSecdoma -sTan SedarebiT, magram es mTavari efeqti ar moaxdens gavlenas MSA.ze, MSAxB-ze da MSSecdoma -ze. Tu damoukidebeli cvladebi urTierTqmedebaSia, maSin izrdeba MSAxB, magram MSA.ze, MSB-ze da MSSecdoma -ze gavlena ar aris. MSSecdoma -ze gavlenas ar axdens arc mTavari efeqtebi da arc damoukidebeli cvladebis urTierTqmedeba. is asaxavs mxolod ujredebs SigniT SemTxveviT cvalebadobas eqsperimentSi. amdenad, TiToeuli MS-is mniSvneloba damoukidebelia sxva kvadratebis saSualoebis mniSvnelobebisagan.

kvadratebis oTxi saSualo da cvalebadobis wyaroebi, romlebic maTze axdenen gavlenas, SeiZleba Semdegnairad Sejamdes:

kvadratebis saSualo

masze gavlenas axdens:

MSAA faqtoris gamo arsebuli sistematuri cvalebadoba

SerCevis Secdoma

MSBB faqtoris gamo arsebuli sistematuri cvalebadoba

SerCevis Secdoma

MSAxBA da B faqtorebis interaqciis gamo arsebuli sistematuri cvalebadoba

SerCevis Secdoma

MSSecdoma

ujredebs SigniT SemTxveviT cvalebadoba

imisaTvis, rom yvelaferi zemoT Tqmuli davukavSiroT sam F Sefardebas

cxrilidan # 11.8, miaqcieT yuradReba, rom yoveli F Sefardeba iyenebs

MSSecdomas, rogorc mniSvnels da damoukidebeli cvladis an

urTierTqmedebis Sesabamis MS-s, rogorc mricxvels. Tu konkretuli F Sefardebis gamoTvlaSi MS-ze gavlenis mqone damoukidebel cvlads ara aqvs efeqti, maSin es F Sefardeba daaxloebiT 1-s unda udrides, radganac rogorc mricxvelis, aseve mniSvnelis MS zomavs mxolod SemTxveviT cvalebadobas eqsperimentSi. magram Tu damoukidebel cvlads aqvs efeqti, maSin MS-is mniSvneloba am cvladisaTvis izrdeba da F-is mniSvneloba am faqtorisaTvis 1.0-ze meti xdeba. es dasabuTeba me-10 TavSi dispersiuli erTfaqtoriani analizisaTvis moyvanili dasabuTebis identuria.

F statistikaze damyarebuli statistikuri gadawyvetilebebis

miReba

axla, rodesac viciT, Tu rogor axdens gavlenas faqtorebi F Sefardebis TiToeul mniSvnelobaze, Cven mzad varT, gamoviyenoT TiToeuli F hipoTezebis Semowmebisas. saWiro nabijebi igivea, rac me-10 TavSi.

a. TiTeuli F SefardebisaTvis yalibdeba nulovani hipoTeza, H0, da alternatiuli hipoTeza, H1;

b. im daSvebiT, rom H0 sworia, F-is TiTeuli mniSvnelobisaTvis gamoiTvleba F-is SerCeviTi ganawileba. es ganawileba mocemulia cxrilSi # A.3;

g. xdeba mniSvnelovnobis donis SerCeva;

d. F-is kritikuli done, romelic aRiniSneba Fkritikuli,

TiToeuli F SefardebisaTvis F–is SerCeviTi ganawilebidan gamoiTvleba, romelic mocemulia cxrilSi # A.3;

e. F–is SerCeviT ganawilebaSi TiToeuli F-isaTvis gamoiyofa uaryofis are;

v. SerCevis monacemebidan gamoiTvleba sami F-is sami mniSvneloba, romlebic aRiniSneba, rogorc Frealuri;

z. gadawyvetileba imis Taobaze, uarvyoT Tu ara H0 TiToeuli FrealurisaTvis, miiReba imaze dayrdnobiT, xvdeba Tu ara Frealuri uaryofis areSi.

statistikuri hipoTezebi

cdis pirebs Soris orfaqtoriani dispersiuli analiziT mowmdeba sami gansxvavebuli nulovani hipoTeza, TiTo yoveli Frealuri-saTvis. 2x2 faqtorul dispersiul analizSi nulovani (H0) da alternatiuli (H1) hipoTezebi yoveli F-isaTvis Semdegia:

F statistika

statistikuri hipoTezebi

A faqtorisaTvis

H0: ( A1 = ( A2

H1: ( A.ebi ar aris toli

B faqtorisaTvis

H0: ( B1 = ( B2

H1: ( B-ebi ar aris toli

A x B

H0: ((AB - ( A - ( B + ( G) = 0

H1: yvela ((AB - ( A - ( B + ( G) ar udris 0

mTavari efeqtebi. A da B faqtorebis mTavari efeqtebis nulovani da alternatiuli hipoTezebi formiT identuria erTfaqtoriani analizis statistikuri hipoTezebisa. damoukidebeli cvladis mTavari efeqtis SemTxvevaSi dispersiuli faqtoruli analizi monacemebs ganixilavs ise, TiTqos isini miRebulia erTfaqtoriani sqemidan, rogorc naCvenebia cxrilSi # 11.4. populaciis saSualoebis raodenoba, romelic ganisazRvreba H0-Si, rogorc A, aseve B faqtorisaTvis, Seesabameba eqsperimentSi am faqtoris doneebis raodenobas. magaliTad, Tu eqsperimenti moicavs A faqtoris sam dones, maSin H0 A faqtorisaTvis ase gamoisaxeba:

H0: ( A1 = ( A2 = ( A3,

xolo H1 ki ase:

H1: yvela ( A.-ebi ar aris erTmaneTis toli.

nulovani hipoTeza TiToeuli faqtorisaTvis aris situacia, romelic arsebobs, Tu damoukidebel cvlads ar aqvs efeqti. Tu nulovani hipoTeza sworia, maSin nebismieri aRmoCenili gansxvaveba mTavari efeqtebis Sesabamis saSualoebs Soris mxolod SerCevis Secdomis gamoa.

alternatiuli hipoTeza amtkicebs, rom populaciis saSualoebi ar aris erTmaneTis toli. es situacia arsebobs maSin, Tu damoukidebel cvlads aqvs efeqti.

urTierTqmedeba. urTierTqmedebis nulovani hipoTeza amtkicebs, rom Tu populaciaSi urTierTqmedeba ar xdeba, ujredebis saSualoebis, (AB, gansxvaveba sruli saSualosagan, (G, nulis toli iqneba, mas Semdeg, rac mas gamovaklebT TiToeuli damoukidebeli cvladis mTavar efeqts (anu (( A - ( G) da (( B - ( G)). sxva sityvebiT, es H0 amtkicebs, rom Tu damoukidebel cvladebs Soris urTierTqmedeba ar arsebobs, damoukidebeli cvladebis mTavari efeqtebidan SesaZlebelia zustad viwinaswarmetyveloT TiToeuli ujredis saSualos mniSvneloba. alternatiuli hipoTeza amtkicebs, rom es ase ar aris da SeuZlebelia ujredebis saSualoebis cvalebadobis winaswarmetyveleba mxolod mTavari efeqtebidan.

F–is mniSvnelobaze damyarebuli gadawyvetilebebis miReba

hipoTezebis samive tipis Sesaxeb gadawyvetilebebis miReba Frealuris mniSvnelobebze dayrdnobiT msgavsia im procesisa, romelic mimdinareobs erTfaqtoriani dispersiuli analizis dros. (-s mniSvneloba, romelic gansazRvravs uaryofis ares, arCeulia analizis Catarebamde. H0 hipoTezis pirobebSi F -is SerCeviTi ganawileba ganisazRvreba samive F SefardebisaTvis da uaryofis are arsebobs samive SerCevis ganawilebaSi. es nabiji moiTxovs Fkritikulis sami mniSvnelobis moZebnas Sesabamisi mricxveli da mniSvneli df-ebiT A.3a an b cxrilSi, imis mixedviT, Tu ra aris arCeuli (-s mniSvneloba. Semdeg, TiToeuli FrealurisaTvis, Tu Frealuri udris an metia, vidre misi Sesabamisi Fkritikulis mniSvneloba, H0 am FrealurisaTvis uaryofilia da miRebulia H1. Frealuris am mniSvnelobaSi Semaval saSualoebs Soris sxvaoba statistikurad mniSvnelovania. Tu Frealuri naklebia, vidre misi Sesabamisi Fkritikulis mniSvneloba, maSin gadawyvetileba isaa, rom cvalebadobis am wyarosaTvis ver uarvyofT H0–s da ver miviRebT H1–s. Frealuris am mniSvnelobaSi Semaval saSualoebs Soris gansxvaveba ar aris statistikurad mniSvnelovani. orfaqtorian dispersiul analizSi TiToeuli FrealurisaTvis arsebuli gadawyvetilebebis ori jgufi Sejamebulia cxrilSi # 11.9. gadawyvetilebis miRebis ilustracias movaxdenT cxrilSi # 11.2 sanimuSo monacemebis dispersiuli analizis meSveobiT, rac Sejamebulia cxrilSi # 11.8. am cxrilSi, TiToeul Frealurs aqvs 1 df mricxvelad da 16 df mniSvnelad. amitom TiToeul Frealurs aqvs Fkritikulis erTi da igive mniSvneloba da, Sesabamisad, erTi da igive uaryofis are. es mimarTeba aucileblad ar aris aseTi faqtoruli analizis yvela SemTxvevaSi. TiToeuli damoukidebeli cladis doneebis raodenobis mixedviT, SesaZlebelia, rom TiToeul Frealurs mricxvelad hqondes gansxvavebuli df da, Sesabamisad, gansxvavebuli uaryofis are.

cxrili # 11.9

dispersiis orfaqtorian analizSi statistikuri gadawyvetilebebis Sejameba

-------------------------------------------------------------------------------------------------------------------------------------------------------

F Sefardeba:

Frealuri-s mniSvneloba

statistikuri gadawyvetileba

A faqtorisaTvis

Fkritikulze naklebi

ver uarvyofT H0-s

ver viRebT H1-s

A faqtoris mTavari efeqti ar aris mniSvnelovani.

Fkritikulis toli an masze meti

uarvyofT H0-s

viRebT H1-s

A faqtoris mTavari efeqti statistikurad mniSvnelovania.

B faqtorisaTvis

Fkritikulze naklebi

ver uarvyofT H0-s

ver viRebT H1-s

B faqtoris mTavari efeqti ar aris mniSvnelovani.


uarvyofT H0-s

viRebT H1-s

B faqtoris mTavari efeqti statistikurad mniSvnelovania.

A x B

Fkritikulze naklebi

ver uarvyofT H0-s

ver viRebT H1-s

A da B faqtorebis urTierTqmedeba ar aris mniSvnelovani.


uarvyofT H0-s

viRebT H1-s

A da B faqtorebis urTierTqmedeba statistikurad mniSvnelovania.

rodesac (=.05, Fkritikuli 1,16 df-iT aris 4.49 (aRebulia cxrilidan # A.3a). aqedan gamomdinare, cxrilSi # 11.8 TiToeuli FrealurisaTvis uaryofis are Sedgeba Frealuris mniSvnelobebisagan, romlebic udris an metia 4.49-ze. dispersiis am analizidan Semdeg gadawyvetilebebs viRebT:

wyaro:

Frealuri

xvdeba uaryofis areSi

statistikuri gadawyvetileba

A faqtorisaTvis

6.66

ki

uarvyofT H0-s

viRebT H1-s

A faqtoris mTavari efeqti statistikurad mniSvnelovania.

B faqtorisaTvis

4.26

Aara

ver uarvyofT H0-s

ver viRebT H1-s

B faqtoris mTavari efeqti ar aris mniSvnelovani.

A x B

15.32

ki

uarvyofT H0-s

viRebT H1-s

A da B faqtorebis urTierTqmedeba statistikurad mniSvnelovania.

cdis pirTa Soris orfaqtoriani dispersiuli analizis daSvebebi

cdis pirTa Soris dispersiuli faqtoruli analizi damyarebulia imave sam daSvebaze eqsperimentSi miRebuli monacemebis (qulebis) Sesaxeb, rac cdis pirTa Soris erTfaqtorian analizSi:

1. monacemebi TiToeul SerCevaSi SemTxveviTad aris aRebuli populaciis monacemebidan da TiToeuli qula damoukidebelia yvela sxva qulisagan;

2. im populaciaSi, saidanac aris aRebuli SerCeva, monacemebi normaluradaa ganawilebuli;

3. monacemebis dispersiebi populaciebSi tolia.

rogorc aRvniSneT, erTfaqtorian analizTan dakavSirebiT, Tu gvsurs, gamoviyenoT cdis pirTa Soris dispersiuli analizi, unda Sesruldes pirveli daSveba monacemebis damoukideblobis Sesaxeb. TiTeul cdis pirs mxolod erTi qulis mocema SeuZlia eqsperimentSi. Tumca, ar aris aucilebeli, eqsperimentis monacemebSi Sesruldes meore da mesame daSvebebi. mosalodnelia, rom normaluridan gadaxra da dispersiebis tolobis daSvebis darRveva minimalur gavlenas moaxdens I gvaris Secdomis daSvebis albaTobaze, Tu sruldeba Semdegi pirobebi:

1. cdis pirebis raodenoba yovel ujredSi tolia;

2. TiToeul pirobaSi qulebis ganawilebis forma daaxloebiT erTnairia da ganawilebebi arc Zalian wamaxvilebulia, arc Zalian brtyeli;

3. mniSvnelovnobis done aris .05.


a. gansazRvreT faqtorebi, romlebsac aqvs gavlena yovel MS-ze cdis pirTa Soris dispersiul faqtorul analizSi.

b. axseniT, Tu ratom izrdeba MSA.-is mniSvneloba, Tu A faqtors aqvs efeqti faqtorul eqsperimentSi.

g. axseniT, Tu ratom izrdeba MSB-is mniSvneloba, Tu B faqtors aqvs efeqti

faqtorul eqsperimentSi.

d. axseniT, Tu ratom izrdeba MSAxB-is mniSvneloba, Tu A da B faqtorebi

urTierTqmedeben faqtorul eqsperimentSi.

e. axseniT, Tu ratom ar aqvs gavlena MSSecdomis mniSvnelobaze arc A da B

faqtorebs, arc maT urTierTqmedebas faqtorul eqsperimentSi.

v. ra aris mosalodneli, rom daemarTos Frealuris mniSvnelobas A faqtorisaTvis,

Tu A faqtors aqvs efeqti eqsperimentSi?

z. ra aris mosalodneli, rom daemarTos Frealuris mniSvnelobas AxB-saTvis, Tu

damoukidebeli cvladebi urTierTqmedeben eqsperimentSi?

T. gansazRvreT statistikuri Semowmebis nabijebi dispersiul faqtorul analizSi.

i. dawereT statistikuri hipoTezebi SemdegisaTvis:

c. 2x4 cdis pirTa Soris dispersiuli analizi

d. 3x2 cdis pirTa Soris dispersiuli analizi

b. 3x3 cdis pirTa Soris dispersiuli analizi

k. am savarjiSoSi mocemulia ramdenime cdis pirTa Soris orfaqtoriani sqemis

dispersiuli analizis Sejamebis cxrilebi. TiToeuli FrealurisTvis ipoveT Fkritikuli 0.5 mniSvnelovnobis donisaTvis cxrilidan # A.3a da miuTiTeT, xvdeba Tu ara Frealuri uaryofis areSi. Semdeg daafiqsireT Tqveni gadawyvetileba H0-Tan da H1-Tan dakavSirebiT. Tu dfSecdomisaTvis cxrilSi ar aris mocemuli zusti df, gamoiyeneT cxrilSi qvemoT miTiTebuli momdevno mniSvneloba.

cxrili 1

cxrili 2

wyaro

df

Frealuri

A faqtori

1

4.63

B faqtori

3

2.11

A x B

3

3.97

Secdoma

56

sul

63

wyaro

df

Frealuri

A faqtori

3

1.42

B faqtori

2

3.51

A x B

6

2.37

Secdoma

144

sul

155

cxrili 3

wyaro

df

Frealuri

A faqtori

2

4.12

B faqtori

4

2.83

A x B

8

1.87

Secdoma

150

sul

164

2x2 faqtoruli dispersiuli analizis interpretacia

faqtoruli sqemis Sedegebis axsnis Sesaxeb diskusias daviwyebT im nabijebiT, romlebic saWiroa statistikurad mniSvnelovani urTierTqmedebis axsnisaTvis. Semdeg ki avxsniT statistikurad mniSvnelovan mTavar efeqtebs.

damoukidebeli cvladis martivi efeqti

damoukidebeli cvladis martivi efeqti: faqtorul sqemaSi erTi damoukidebeli cvladis efeqti meore damoukidebeli cvladis mxolod erTi donis dros.

ori damoukidebeli cvladis urTierTqmedeba xdeba, rodesac erTi damoukidebeli cvladis efeqti damokidebulia masTan kombinaciaSi myofi meore damoukidebeli cvladis doneze. Sesabamisad, dispersiul analizSi statistikurad mniSvnelovani urTierTqmedebis interpretacia xdeba eqsperimentSi ujredebis saSualoebs Soris sxvaobebis SedarebiT. ujredebis saSualoebs Soris sxvaobebi gviCveneben damoukidebeli cvladebis martiv efeqtebs. damoukidebeli cvladis martivi efeqti (romelsac xandaxan martiv mTavar efeqtsac uwodeben) faqtorul sqemaSi aris am damoukidebeli cvladis efeqti meore damoukidebeli cvladis mxolod erTi donis dros. cxrilSi # 11.10 moyvanilia oTxi martivi efeqti, iseve, rogorc ori mTavari efeqti 2x2 sqemaSi. TiToeuli damoukidebeli cvladis martivi efeqti gansazRvrulia marTkuTxedebSi ujredebs Soris. 2x2 sqemaSi mxolod ori martivi efeqti arsebobs TiToeuli damoukidebeli cvladisaTvis.

cxrili # 11.10

martivi da mTavari efeqtebi 2x2 cdis pirebs Soris dispersiuli analizSi.

2

2

B

A

X

A faqtori

A1 A2

mTavari efeqtis saSualoebi B faqtorisaTvis

B1

B faqtori

B2

1

1

B

A

X

1

1

B

A

X

1

2

B

A

X

2

1

B

A

X

2

2

B

A

X

1

B

X

2

B

X

mTavari efeqtis saSualoebi A faqtorisaTvis

1

A

X

2

A

X

A faqtoris martivi efeqti

A faqtoris martivi efeqti B1 doneze

1

1

B

A

X

da

1

2

B

A

X

ujredebis saSualoebs Soris gansxvavebiTaa mocemuli (anu

1

1

B

A

X

-

1

2

B

A

X

). es gansxvaveba asaxavs A faqtoris efeqts B faqtoris B1 doneze. amis msgavsad, A faqtoris martivi efeqti B faqtoris B2 doneze

2

1

B

A

X

da

2

2

B

A

X


2

1

B

A

X

-

2

2

B

A

X

). es gansxvaveba asaxavs A faqtoris efeqts B2 doneze. martivi efeqtebis ricxviTi mniSvnelobebis gamoTvlisas mniSvnelovania, SevinarCunoT Sedarebebis mimarTulebis SeTanxmebuloba da efeqtis niSani (+ an _).

B faqtoris martivi efeqti

B faqtoris martivi efeqti A1 doneze

1

1

B

A

X

da

2

1

B

A

X


1

1

B

A

X

-

2

1

B

A

X

), xolo B faqtoris martivi efeqti A2 doneze

1

2

B

A

X

da

2

2

B

A

X


1

2

B

A

X

-

2

2

B

A

X

). TiToeuli martivi efeqti miuTiTebs B faqtoris efeqts A faqtoris mxolod erT doneze.

martivi da mTavari efeqtebis ricxviTi magaliTi. cxrilis # 11.5 saSualoebisagan martivi da mTavari efeqtebis ricxviTi mniSvnelobebis sxvaobebi mocemulia cxrilSi # 11.11. saSualoebs Soris mTavari efeqtis da martivi efeqtis gansxvavebebi naCvenebia marTkuTxedebSi. magaliTad, kargi siaxlis mosmenisas cdis piris mxedvelobis areSi yofnis/ar yofnis martivi efeqti (A faqtoris martivi efeqti B1 doneze) aris

1

1

B

A

X

-

1

2

B

A

X

, rac udris 90.8-84.6, anu +6.2 wams. amis msgavsad, siaxlis tipis martivi efeqti im pirobisaTvis, rodesac cdis piri ar imyofeba mxedvelobis areSi (B faqtoris martivi efeqti A1 doneze) aris

1

1

B

A

X

-

2

1

B

A

X

, rac udris 90.8-82.2, anu +8.6 wams.

cxrili # 11.11

pasuxis latenturi drois (wamebSi) mTavari efeqtisa da martivi efeqtis sxvaobebi cdis piris mxedvelobis areSi yofnisa da siaxlis tipisaTvis sanimuSo eqsperimentSi.

subieqtis yofna mxedvelobis areSi (A)

1

2

B

A

X

Cans (A1) ar Cans (A2)

mTavari efeqtis saSualoebi siaxlis tipisaTvis (B)

kargi (B1)

siaxlis tipi

(B)

cudi (B2)

90.8 84.6

82.2 112.4

87.7

97.3

mTavari efeqtis saSualoebi subieqtis mxedvelobis areSi yofnisaTvis (A)

86.5 98.5

martivi efeqtebis axsna, rodesac vlindeba statistikurad mniSvnelovani urTierTqmedeba

Tu dispersiuli analizisas xdeba damoukidebeli cvladebis statistikurad mniSvnelovani urTierTqmedeba, maSin faqtoris ori martivi efeqti ar aris erTmaneTis toli an am faqtoris mTavari efeqtis toli. amitom, Tu xdeba statitikurad mniSvnelovani urTierTqmedeba, A faqtoris martivi efeqti B1 doneze,

1

1

B

A

X

-

1

2

B

A

X

, ar udris A faqtoris martiv efeqts B2 doneze,

2

1

B

A

X

-

2

2

B

A

X

. garda amisa, A faqtoris arc erTi martivi efeqti ar udris A faqtoris mTavar efeqts, romelic ganisazRvreba

1

A

X

-

2

A

X

.

Tu am mimarTebas mivusadagebT magaliTis Sedegebs cxrilSi # 11.11, aRmovaCenT, rom kargi siaxlis mosmenisas cdis piris mxedvelobis areSi yofnis martivi efeqti (efeqtia +6.2 wami) ar udris cudi siaxlis mosmenisaTvis cdis piris mxedvelobis areSi yofnis martiv efeqts (efeqtia –30.2 wami), da arc erTi martivi efeqti ar udris cdis piris mxedvelobaSi yofnis mTavar efeqts (efeqtia –12.0 wami).

msgavsi urTierToba axasiaTebs B faqtoris martiv efeqtebsac. Tu xdeba statistikurad mniSvnelovani urTierTqmedeba, maSin B faqtoris martivi efeqti A1 doneze,

1

1

B

A

X

-

2

1

B

A

X

, ar udris B faqtoris martiv efeqts A2 doneze,

1

2

B

A

X

-

2

2

B

A

X

; da arc erTi martivi efeqti ar udris B faqtoris mTavar efeqts, romelic ganisazRvreba

1

B

X

-

2

B

X

.

Tu am mimarTebas mivusadagebT magaliTis Sedegebs cxrilSi # 11.11, naTelia, rom siaxlis tipis martivi efeqti im pirobaSi, rodesac cdis piri ar imyofeba mxedvelobis areSi (efeqtia +8.6 wami) ar udris siaxlis tipis martiv efeqts im pirobaSi, rodesac cdis piri imyofeba mxedvelobis areSi (efeqtia –27.8 wami), da arc erTi efeqti ar udris siaxlis tipis mTavar efeqts (efeqtia –9.6 wami).

mravlobiTi Sedarebis kriteriumebi statistikurad mniSvnelovani urTierTqmedebisaTvis. martivi efeqtebis TiToeuli Sedareba cxrilebSi # 11.10 da 11.11 warmoadgens wyvilTaSoris Sedarebas. erTmaneTs vadarebT ori ujredis saSualos. imis gansasazRvrad, mniSvnelovnad gansxvavdeba Tu ara erTmaneTisagan ori ujredis saSualo, gamoiyeneba mravlobiTi Sedarebis kriteriumi, raTa dadgenil iqnes kritikuli gansxvaveba (CD) martivi efeqtisaTvis. Tu martivi efeqtis realuri mniSvneloba tolia an aRemateba CD–s, maSin ujredebis saSualoebs Soris gansxvaveba statistikurad mniSvnelovania.

aqac, martivi efeqtebis saboloo SedarebisaTvis xSirad gamoiyeneba tukis (Tukey) HSD kriteriumi. am kriteriumisaTvis CD ase gamoiTvleba:

CD = q

AB

n

MS

Secdoma

q-s mniSvneloba gamoiTvleba cxrilidan # A.4 da damokidebulia martivi efeqtis Casatarebeli Sedarebebis raodenobaze da dfSecdomaze. radgan cxrili # A.4 Sedegil iqna erTfaqtoriani sqemisaTvis, Cven cxrilSi viyenebT Semdeg gardaqmnas:

cxrilidan # A.4 gamoiyeneT q, romelic

moTavsebulia svetSi damoukidebeli

sqemis tipi

cvladis _____ doneebisaTvis

______________________________________________________

2 x 2

3

2 x 3

5

3 x 2

5

3 x 3

7

2 x 4

8

4 x 3

8

4 x 4

10

______________________________________________________

MSSecdoma aris MSSecdomis mniSvneloba, gamoTvlili dispersiis faqtorul analizSi da nAB aris qulebis raodenoba TiToeul ujredSi.

am gamoTvlis ilustraciisaTvis 2x2 eqsperimentSi cdis piris mxedvelobis areSi yofnisa da siaxlis tipis efeqtebisaTvis, viyenebT svets a=3 cxrilidan # A.4, raTa vipovoT q. radganac MSSecdomis df aris 16 (cxrilidan # 11.8) da ( = .05, q-s mniSvneloba (3, 16) aris 3.65. cxrilSi # 11.8 MSSecdoma =108.125 da nAB, qulebis raodenoba, romlebic Sedis TiToeuli ujredSi, aris 5. aqedan gamomdinare, tukis CD-s ricxviTi mniSvneloba aris

CD = 3.65

5

125

.

108

= 17.0 wami, damrgvalebuli erT meaTedamde.

nebismieri martivi efeqti cxrilidan # 11.11, romelic absoluturi mniSvnelobiT tolia an aRemateba 17.0-s, statistikurad mniSvnelovania .05 doneze. martivi efeqtebi cdis piris mxedvelobis areSi yofnisaTvis cudi siaxlis mosmenis pirobaSi (anu - 30.2 wami) da siaxlis tipisaTvis cdis piris mxedvelobis areSi yofnis pirobaSi (anu -27.8 wami) aRemateba absoluturi mniSvnelobiT CD-s, romelic aris 17.0 wami. es martivi efeqtebi gviCvenebs statistikurad mniSvnelovan gansxvavebebs ujredebis saSualoebs Soris. martivi efeqtebi cdis piris mxedvelobis areSi yofnisTvis kargi siaxlis mosmenis pirobaSi (anu + 6.2 wami) da siaxlis tipisaTvis cdis piris mxedvelobis areSi aryofnis pirobaSi (anu + 8.6 wami) absoluturi mniSvnelobiT naklebia, vidre CD, romelic 17.0 wamia. es martivi efeqtebi ar aris mniSvnelovani da monawile ujredebis saSualoebi gansxvavdeba mxolod SerCevis Secdomis gamo.

mTavari efeqtebis axsna, rodesac xdeba urTierTqmedeba

rodesac xdeba statistikurad mniSvnelovani urTierTqmedeba, damoukidebeli cvladebis mTavari efeqtebi SeiZleba ver gamoviyenoT raime mniSvnelobis mqone axsnisaTvis. es xdeba imis gamo, rom damoukidebeli cvladis mTavari efeqti aris am cvladis martivi efeqtebis saSualo. magaliTad, yvela ujredSi cdis pirebis toli raodenobis arsebobisas, cdis piris mxedvelobis areSi yofnis mTavari efeqti (-12.0 wami) cxrilSi # 11.11 aris kargi da cudi siaxleebisTvis cdis piris mxedvelobis areSi yofnis martivi efeqtebis saSualo (anu [(+6.2) + (-30.2)]/2 = _12.0 wami). msgavsi damokidebulebaa siaxlis tipis mTavari efeqtisaTvis, -9.6 wami. es aris saSualo martivi efeqtebisa siaxlis tipisaTvis cdis piris mxedvelobis areSi aryofnis pirobaSi, +8.6 wami, da cdis piris mxedvelobis areSi yofnis pirobaSi, -27.8 wami. Sesabamisad, rodesac xdeba urTierTqmedeba, ise, rom damoukidebeli cvladis martivi efeqtebi ar udris erTmaneTs, am damoukidebeli cvladis mTavari efeqti SeZleba zustad ar warmoadgendes cvladis efeqts. aseTi mTavari efeqtebi aris urTierTqmedebis artefaqtebi da ar iZlevian raime mniSvnelobis mqone informacias eqsperimentis Sedegebis Sesaxeb. Sesabamisad, artefaqturi mTavari efeqti aris mTavari efeqti, romelic ar iZleva mniSvnelobis mqone informacias damoukidebeli cvladis efeqtis Sesaxeb, radgan is Tavs iCens mxolod realuri urTierTqmedebis specifikuri paternis gamo. es aris am cvladis martivi efeqtebis saxis xelovnuri Sedegi. aqedan gamomdinare, faqtorul sqemaSi mTavari efeqtebis axsnasTan dakavSirebiT SemoRebulia Tavis dasazRvevi mniSvnelovani SeniSvna:

a. Tu faqtorul sqemaSi xdeba statistikurad mniSvnelovani urTierTqmedeba, maSin rogorc A, aseve B Bfaqtorebis mTavari efeqtebi SeiZleba iyos artefaqturi da SeiZleba ar warmoadgendnen mniSvnelobis mqone Sedegebs am damoukidebeli cvladis efeqtis Sesaxeb.

b. Tu urTierTqmedeba faqtorul sqemaSi aramniSvnelovania, maSin rogorc A, aseve B faqtorebis mTavari efeqtebi warmoadgenen mniSvnelobis mqone Sedegebs am damoukidebeli cvladis efeqtis Sesaxeb.

artefaqturi mTavari efeqti: mTavari efeqti, romelic ar iZleva mniSvnelobis mqone informacias damoukidebeli cvladis efeqtis Sesaxeb faqtorul sqemaSi.

dispersiuli analizSi statistikurad mniSvnelovani urTierTqmedeba ar niSnavs imas, rom mTavari efeqtebi iyos artefaqturi, magram is aris gafrTxileba, rom Semowmdes nebismieri mniSvnelovani mTavari efeqti, raTa gamovlindes, iZleva Tu ara is mniSvnelobis mqone Sedegebs damoukidebeli cvladis efeqtis Sesaxeb.

martivi mTavari efeqtebis axsna, rodesac ar xdeba statistikurad mniSvnelovani urTierTqmedeba

Tu damoukidebel cvladebs Soris ar aris statistikurad mniSvnelovani urTierTqmedeba, maSin erTi damoukidebeli cvladis efeqti ar aris damokidebuli meore damoukidebeli cvladis doneze. amitom, Tu urTierTqmedeba ar xdeba, A faqtoris martivi efeqti B1 donisaTvis B2 donisaTvis A faqtoris martivi efeqtis toli iqneba. nebismieri realuri gansxvaveba am martiv efeqtebs Soris mxolod SerCevis SecdomiT aris gamowvuli. ufro metic, Tu A faqtoris martivi efeqtebi erTmaneTis tolia, isini aseve A faqtoris mTavari efeqtis tolia, da A faqtoris mTavari efeqti am damoukidebeli cvladis efeqtis saukeTeso aRweras iZleva.

msgavsi urTierToba aRiniSneba B faqtoris martivi efeqtebisaTvisac. Tu urTierTqmedeba ar xdeba, maSin B faqtoris martivi efeqti A1 doneze A2 doneze B faqtoris martivi efeqtis toli iqneba. nebismieri realuri gansxvaveba am martiv efeqtebs Soris mxolod SerCevis SecdomiT aris gamowvuli. B faqtoris martivi efeqtebi aseve B faqtoris mTavari efeqtis tolia, da B faqtoris mTavari efeqti am damoukidebeli cvladis efeqtis saukeTeso aRweras iZleva. es mimarTebebi Sejamebulia cxrilis # 11.12 (b) nawilSi.

cxrili # 11.12

urTierTqmedeba 2x2 faqtorul dispersiul analizSi da martivi efeqtebis da mTavari efeqtebis axsna.

(a) Tu Frealuri AxB urTierTqmedebisaTvis xvdeba uaryofis areSi, maSin:

1. urTierTqmedebis F Sefardeba statistikurad mniSvnelovania;

2. erTi damoukidebeli cvladis efeqti damokidebulia meore damoukidebeli cvladis doneze;

3. A faqtoris martivi efeqti B1 doneze (anu

1

1

B

A

X

–

1

2

B

A

X

) ar udris A faqtoris martiv efeqts B2 doneze (anu

2

1

B

A

X

–

2

2

B

A

X

). A faqtoris martiv efeqtebs Soris realuri sxvaoba gamowveulia damoukidebeli cvladebis urTierTqmedebiT da ara mxolod SerCevis SecdomiT;

4. B faqtoris martivi efeqti A1 doneze (anu

1

1

B

A

X

–

2

1

B

A

X

) ar udris B faqtoris martiv efeqts A2 doneze (anu

1

2

B

A

X

–

2

2

B

A

X

). B faqtoris martiv efeqtebs Soris realuri sxvaoba gamowveulia damoukidebeli cvladebis urTierTqmedebiT da ara mxolod SerCevis SecdomiT;

5. A faqtoris martivi efeqtebi ar udris A faqtoris mTavar efeqts;

6. B faqtoris martivi efeqtebi ar udris B faqtoris mTavar efeqts;

7. TiToeuli martivi efeqti unda Sedardes tukis CD-s, raTa vipovoT, Tu ujredis romeli saSualoebi gansxvavdeba erTmaneTisagan mniSvnelovnad;

8. rogorc A, aseve B faqtoris mTavari efeqtebi SeiZleba artefaqturi iyos da SeiZleba ar warmoadgendes mniSvnelobis mqone Sedegebs damoukidebeli cvladis efeqtis Sesaxeb.

(b) Tu Frealuri AxB urTierTqmedebisaTvis ar xvdeba uaryofis areSi, maSin:

1. urTierTqmedebis F Sefardeba ar aris statistikurad mniSvnelovani;

2. erTi damoukidebeli cvladis efeqti ar aris damokidebuli meore damoukidebeli cvladis doneze;

3. A da B faqtorebis mTavari efeqtebi warmoadgenen mniSvnelobis mqone Sedegebs eqsperimentis Sedegebis Sesaxeb;

4. A faqtoris martivi efeqti B1 doneze (anu

1

1

B

A

X

–

1

2

B

A

X

) mniSvnelovnad ar gansxvavdeba A faqtoris martivi efeqtisagan B2 doneze (anu

2

1

B

A

X

–

2

2

B

A

X

). A faqtoris martiv efeqtebs Soris realuri gansxvaveba gamowveulia SerCevis SecdomiT;

5. B faqtoris martivi efeqti A1 doneze (anu

1

1

B

A

X

–

2

1

B

A

X

) mniSvnelovnad ar gansxvavdeba B faqtoris martivi efeqtisagan A2 doneze (anu

1

2

B

A

X

–

2

2

B

A

X

). B faqtoris martiv efeqtebs Soris realuri gansxvaveba gamowveulia SerCevis SecdomiT;

6. A faqtoris martivi efeqtebi ar gansxvavdeba A faqtoris mTavari efeqtisagan. A faqtoris mTavari efeqti warmoadgens A faqtoris efeqtis saukeTeso aRweras;

7. B faqtoris martivi efeqtebi ar gansxvavdeba B faqtoris mTavari efeqtisagan. B faqtoris mTavari efeqti warmoadgens B faqtoris efeqtis saukeTeso aRweras;

8. ar aris saWiro martivi efeqtebis gaanalizeba mravlobiTi Sedarebis kriteriumiT.

Sejameba: dispersiuli analizis axsna sanimuSo eqsperimentSi

faqtoruli eqsperimentis Sedegebis gageba moiTxovs TiToeuli mTavari efeqtis da urTierTqmedebis ganxilvas da maT axsnas dispersiul analizSi miRebuli gadawyvetilebebis gaTvaliswinebiT. rodesac xdeba statistikurad mniSvnelovani urTierTqmedeba, rogorc es mocemuli eqsperimentis magaliTSia (ix. cxrili # 11.8), Sedegebis axsna urTierTqmedebiT unda daiwyos.

cdis piris mxedvelobis areSi yofnisa da siaxlis tipis urTierTqmedebis axsna

Frealuris mniSvneloba urTierTqmedebisaTvis cxrilidan # 11.8 = 15.32 metia, vidre Fkritikulis mniSvneloba 4.49 da amdenad xvdeba uaryofis areSi. aqedan gamomdinare, H0 A da B faqtorebis urTierTqmedebisaTvis,

H0: yvela ((AB – ( A – ( B + ( G) = 0

uaryofilia da

H1: yvela ((AB – ( A – ( B + ( G) ar udris 0-s

miRebulia. am urTierTqmedebis interpretaciisaTvis Tavdapirvelad viyenebT tukis HSD kritikul sxvaobas cxrilis # 11.11 martivi efeqtebisaTvis. tukis CD aris 17.0 wami; amitom nebismieri martivi efeqti cxrilSi # 11.11, romelic absoluturi mniSvnelobiT tolia an metia 17.0 wamze, statistikurad mniSvnelovania .05 doneze.

Tu davubrundebiT cxrils # 11.11, jer ganvixilavT A faqtoris – cdis piris mxedvelobis areSi yofnis martiv efeqtebs. A faqtoris martivi efeqti B1 doneze, sxvaoba +6.2 wami, naklebia CD-ze, romelic 17.0 wamia; es martivi efeqti aramniSvnelovania. cdis piris mxedvelobis areSi yofnas ar aqvs efeqti, rodesac kargi siaxlis Setyobineba xdeba. sxvaoba “Cans” da “ar Cans” ujredebis saSualoebs Soris, rodesac kargi siaxlis Setyobineba xdeba (Sesabamisad, 90.8 da 84.6 wamebi), mxolod SerCevis Secdomis gamoa miRebuli. A faqtoris martivi efeqti B2 doneze, sxvaoba –30.2 wami, absoluturi mniSvnelobiT metia, vidre CD, romelic 17.0 wamia. es martivi efeqti statistikurad mniSvnelovania. cudi siaxlis Setyobineba mniSvnelovnad ufro nela xdeba, rodesac cdis piri mxedvelobis areSi imyofeba (112.4 wami), vidre rodesac cdis piri mxedvelobis areSi ar imyofeba (82.2 wami).

axla SevudgeT B faqtoris – siaxlis tipis – martiv efeqtebs. B faqtoris martivi efeqti A1 doneze, sxvaoba +8.6 wami, absoluturi mniSvnelobiT naklebia CD-ze, romelic 17.0 wamia; es martivi efeqti aramniSvnelovania. rodesac cdis piri ar imyofeba mxedvelobis areSi, kargi da cudi siaxleebis Setyobineba erTnairi siswrafiT xdeba. sxvaoba “kargi siaxlisa” da “cudi siaxlis” ujredebis saSualoebs Soris (Sesabamisad, 90.8 da 82.2. wami) mxolod SerCevis Secdomis gamoa miRebuli. B faqtoris martivi efeqti A2 doneze, sxvaoba –27.8 wami, absoluturi mniSvnelobiT metia CD-ze, romelic 17.0 wamia; amdenad, es martivi efeqti mniSvnelovani sxvaobaa. rodesac cdis piri imyofeba mxedvelobis areSi, cudi siaxlis Setyobineba mniSvnelovnad ufro nela (112.4 wami) xdeba, vidre kargi siaxlis Setyobineba (84.6 wami).

am analizs mivyavarT cdis piris mxedvelobis areSi yofnasa da siaxlis tips Soris urTierTqmedebis Sedegebis Semdgom Sejamebamde:

· cdis piris mxedvelobis areSi yofnis efeqti damokidebulia Sesatyobinebeli siaxlis tipze;

a. kargi siaxlis SemTxvevaSi sxvaoba latentur droSi mxedvelobis areSi myof da armyof cdis pirebs Soris (Sesabamisad, 90.8 da 84.6 wami) ar iyo mniSvnelovani;

b. cudi siaxlis SemTxvevaSi im cdis pirebis latenturi dro, romlebic iyvnen mxedvelobis areSi (112.4 wami) mniSvnelovnad meti iyo im cdis pirebis latentur droze, romlebic ar imyofebodnen mxedvelobis areSi (82.2 wami).

· siaxlis tipis efeqti damokidebulia cdis piris mxedvelobis areSi yofnaze;

a. im cdis pirebisTvis, romlebic ar imyofebodnen mxedvelobis areSi, ar iyo mniSvnelovani sxvaoba kargsa da cud siaxleebs Soris; aseTi cdis pirebi karg da cud siaxleebs ekvivalenturi latenturi drois Semdeg atyobinebdnen (Sesabamisad, 90.8 da 82.2 wami);

b. is cdis pirebi, romlebic imyofebian mxedvelobis areSi, mniSvnelovnad did dros andomeben cudi siaxlis Setyobinebas, vidre kargis Setyobinebas, Sesabamisad, 112.4 da 84.6 wami.

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