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Tavi XII. cdis pirTa Sida erTfaqtoriani sqema da dispersiuli analizi
cdis pirTa Sida erTfaqtoriani sqemis magaliTi
cdis pirTa Sida erTfaqtoriani sqemis dispersiuli analizi monacemTa dayofa da kvadratebis jamebis gamoTvlaTavisuflebis xarisxebis gamoTvlagadaxrebis kvadratebis saSualos da F statistikis gamoTvla
statistikuri hipoTezis Semowmeba Frealuris meSveobiTCarevis efeqtis siZlieris gazomvacdis pirTa Sida dispersiuli analizis daSvebebi
dispersiuli analizis Sedegebis prezentacia
kvlevis sqemis arCeva: cdis pirebs Soris Tu cdis pirebs Sidacdis pirebis saWiro raodenobadamoukidebeli cvladis efeqturobamravaljeradi Carevis efeqtebi
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me-9 TavSi warmodgenili iyo cdis pirTa Sida sqemebi da t kriteriumi damokidebuli qulebisTvis. am TavSi grZeldeba cdis pirTa Sida sqemebis ganxilva da warmodgenilia maTi dispersiuli analizi.
cdis pirTa Sida sqema: kvlevis sqema, rodesac cdis pirTa erTi jgufi ganicdis damoukidebeli cvladis zemoqmedebas, rac izomeba am cvladis yoveli donis Sesabamisad.
cdis pirTa Sida erTfaqtorian sqemaSi cdis pirTa erTi jgufi ganicdis damoukidebeli cvladis zemoqmedebas, rac izomeba am cvladis yoveli donis Sesabamisad. radgan cdis pirTa Sida sqemaSi cdis pirebi ganmeorebiT izomebian, am sqemas aseve uwodeben ganmeorebiTi gazomvis sqemas an “Careva cdis pirebze” sqemas, rac imaze migviTiTebs, rom TiToeuli cdis piri damoukidebeli cvladis yvela donis mixedviT mowmdeba. cxrilSi # 12.1 sqematuradaa warmodgenili cdis pirTa Sida erTfaqtoriani sqemis monacemebi damoukidebeli cvladis oTxi doniT da xuTi cdis piris monawileobiT. damoukidebeli cvladi gansazRvrulia, rogorc A faqtori A1, A2, A3
da A4 doneebiT. A faqtoris doneebis raodenoba aRniSnulia a-Ti; cxrilisaTvis # 12.1 a = 4. cdis piris monacemi (qula) aRniSnulia Xij-T, sadac indeqsi i migviTiTebs cdis piris aRmniSvnel ricxvs (mag., X1j, X2j, . . . X5j) da indeqsi j migviTiTebs ricxvs, romelic aRniSnavs damoukidebeli cvladis dones. amdenad, X34 aRniSnavs me-3 cdis piris qulas A faqtoris me-4 doneze. rodesac ar aris saWiro konkretuli cdis piris identificireba, gamovtovebT ij indeqsebs da ubralod X-s viyenebT. damoukidebeli cvladis TiToeuli donis saSualoebi aRiniSneba , , da an zogadad . qulebis raodenoba damoukidebeli cvladis donisaTvis aRiniSneba nA. miaqcieT yuradReba, rom nA aseve aris cdis pirTa raodenoba cdis pirTa Soris sqemaSic. qulebis sruli raodenoba eqsperimentSi aRniSnulia N-iT. cxrilisaTvis # 12.1, nA
= 5 da N = 20. cdis piris saSualo A faqtoris yvela doneze aRiniSneba . es saSualo gamosaxavs cdis piris tipur Sesrulebas damoukidebeli cvladis yvela doneze.
cdis pirTa Sida erTfaqtoriani sqemis magaliTi
cxrili # 12.1 qulebis sqematuri gamosaxuleba cdis pirTa Sida erTfaqtorian sqemaSi damoukidebeli cvladis oTxi doniTa da xuTi cdis piriT.
cdis piri A faqtori________________________________________________A1 A2 A3 A4
cdis piris saSualo
S1
S2
S3
S4
S5
X11
X21
X31
X41
X51
X12
X22
X32
X42
X52
X13
X23
X33
X43
X53
X14
X24
X34
X44
X54
A faqtoris saSualoebi
SexedeT suraTs # 12.1. miuxedavad imisa, rom aq mxolod nawilobriv Sevsebuli wreebia warmodgenili, suraTze isini TiTqos kideebs qmnian, romelTa Sorisac samkuTxedia moTavsebuli. am kideebs subieqturi konturebi
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ewodeba, radganac isini TavisTavad stimulSi ar aris mocemuli. SesaZlebelia Tu ara subieqturi konturebis gamoyeneba aRqmis iluziis gamosawvevad? davuSvaT, gadavwyviteT am sakiTxis gamorkveva poncos (Ponzo) iluziis ramdenime formis gamoyenebiT, rogorc es maierma gaakeTa (Meyer, 1986). suraTze # 12.2a naCvenebia poncos standartuli iluzia. es suraTi iluziaa, radganac ori horizontaluri xazi fizikurad erTi da imave sigrZisaa, Tumca isini tolad ar gamoiyureba. zeda xazi ufro grZeli Cans, vidre qveda. suraTze # 12.2b warmodgenilia am iluziis versia subieqturi konturebiT. versia suraTze # 12.3g gvawvdis saorientacio informacias, magram mTliani wertilebi ar iZleva subieqtur konturebs. dabolos, suraTze # 12.2d mocemulia sakontrolo piroba, sadac iluzia ar unda iyos. davuSvaT, cdis pirs sTxoven, ise Secvalos qveda horizontaluri xazis sigrZe, rom is zeda xazis tolad aRiqmebodes, Semdeg ki davuSvaT, rom zeda xazis sigrZe 14 santimetria (sm). Tu iluzia ar Cndeba, maSin qveda xazi aseve 14 sm unda gaxdes. xolo Tu iluzia Cndeba, maSin zeda xazi ufro grZeli unda aRmoCndes, vidre es sinamdvileSia (anu is 14 sm-ze grZeli unda aRmoCndes) da qveda xazi ise unda Seicvalos, rom aRqmuli sigrZis Sesabamisi iyos. gamotovebulia suraTi 12.1cdis pirTa Sida erTfaqtoriani eqsperimenti iluziis tipis (A faqtori) oTxi doniTa da xuTi cdis piriT gamoiyeneba imisaTvis, raTa Semowmdes iluziis pirobis efeqti iluziis aRqmul sidideze. yoveli cdis piri aTvalierebs oTxive stimuls, romlebic naCvenebia suraTze # 12.2 da cvlis qveda horizontalur xazs ise, rom is sigrZeSi zeda xazis tolad gamoiyurebodes. santimetrebSi gamosaxuli qveda xazis Secvlili sigrZe aris damokidebuli cvladi. davuSvaT, miiReT monacemebi, romlebic mocemulia cxrilSi # 12.2. imoqmeda Tu ara aRqmuli iluziis sidideze iluziis pirobam?
cxrili # 12.2 im xuTi cdis pirisagan miRebuli xazebis aRqmuli toli sigrZeebi (santimetrebSi), romelTac poncos iluziis oTxi versia naxes.
cdis piri iluziis piroba (A) ________________________________________________standartuli subieqturi mTliani sakontrolo konturebi wertilebi (A1 ) (A2 ) (A3) (A4)
cdis piris saSualo
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iseve, rogorc cdis pirTa Soris sqemebSi, cxrilSi # 12.2 moyvanili monacemebis analizi aRweriTi statistikebis gamoTvliT iwyeba. amdenad, pirobebis saSualoebi da standartuli gadaxrebi naCvenebia cxrilis yoveli svetis boloSi. Tu damoukidebeli cvladi gavlenas axdens iluziis aRqmaze, maSin pirobebis saSualoebi gansxvavebuli unda iyos. magram, rogorc Cven viciT, pirobebis saSualoebs Soris miRebuli nebismieri sxvaoba yovelTvis unda SevadaroT Secdomis cvalebadobas. ramdenad aris SesaZlebeli, rom saSualoebis gansxvaveba mxolod SerCevis Secdomis gamo momxdariyo?
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saSualoebis ubralo mxedvelobiTi Semowmeba ar gvaZlevs am kiTxvaze pasuxis gacemis SesaZleblobas. rogorc es cdis pirTa Soris sqemisaTvis gavakeTeT, am gadawyvetilebis miRebis problemas statistikuri kriteriumis gamoyenebiT vwyvetT. es aris cdis pirTa Sida erTfaqtoriani dispersiuli analizi.
cdis pirTa Sida erTfaqtoriani sqemis dispersiuli analizi
cdis pirTa Sida erTfaqtoriani dispersiuli analizi gamoiyeneba erTfaqtoriani mravaldoniani cdis pirTa Sida sqemebis gaanalizebisaTvis. Tu damoukidebeli cvladis mxolod ori done icvleba, cdis pirTa Soris erTfaqtoriani dispersiuli analizi SeiZleba tdamokidebulis magivrad gamoviyenoT. es analizi eqsperimentSi qulebis srul cvalebadobas sam wyarod yofs:
1. A faqtoris efeqtiT gamowveuli cvalebadoba; 2. cdis pirTa Soris individualuri gansxvavebebis, S faqtoris efeqtiT
gamowveuli cvalebadoba;3. pirobebisa da cdis pirebis urTierTqmedebiT (AxS) gamowveuli
cvalebadoba.
es sami dayofa gamoiyeneba sami kvadratebis saSualos misaRebad:
1. MSA, romelic A faqtoris efeqtTan da Secdomis cvalebadobasTan erTad icvleba;
2. MSS, romelic cdis pirebs Soris gansxvavebebTan erTad icvleba;3. MSAxS, romelic pirobebis cdis pirebTan urTierTqmedebasTan erTad
icvleba da eqsperimentSi Secdomis cvalebadobis zomas iZleva.
F statistika, romelic statistikuri hipoTezis Semowmebisas gamoiyeneba, aris
F =
monacemis dayofa da kvadratebis jamebis miReba
am seqciaSi ganvixilavT monacemebis dayofas da kvadratebis jamebis miRebas cdis pirTa Sida sqemebisaTvis. ramdenadac aq gamoyenebuli midgoma Zalian hgavs imas, romelic gamoiyeneba cdis pirTa Soris sqemebSi, dayofis wardgena mokle iqneba. imis gasagebad, Tu rogor unda daiyos cvalebadobis wyaroebi cdis pirTa Sida sqemebSi, cdis pirTa Sida sqema warmovidginoT, rogorc orfaqtoriani sqema, sadac damoukidebeli cvladi erTi faqtoria (A faqtori), da cdis pirebi ki - meore faqtori (S faqtori, sadac S warmoadgens cdis pirs). radganac TiToeuli cdis piri damoukidebeli cvladis yovel doneze mowmdeba, cdis pirTa Sida erTfaqtoriani sqema SeiZleba ganvixiloT, rogorc AxS faqtoruli sqema A faqtoris a doneebiT da S faqtoris nA doneebiT. ase rom, miviRebT a x nA
pirobebs anu ujredebs, da TiToeuli ujredi warmoadgens, konkretul cdis pirTan kombinirebul damoukidebeli cvladis erT dones. cxrilSi # 12.2 A faqtoris oTxi done da xuTi cdis piria; amdenad, eqsperimenti SeiZleba ganvixiloT, rogorc 4 (iluziis pirobis doneebi) x 5 (cdis pirebis raodenoba) faqtoruli sqema, sadac sul 20 gansxvavebuli Careva/cdis piri (AxS) pirobaa. magram TiToeuli AxS pirobisaTvis mxolod erTi qula miiReba.
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cdis pirTa Sida erTfaqtoriani dispersiuli analizis ganxilva, rogorc orfaqtoriani dispersiuli analizisa, A da S faqtorebisaTvis "mTavari efeqtebis" saSualoebs gvaZlevs. cxrilSi # 12.2 miaqcieT yuradReba, rom saSualoebi mocemulia TiToeuli cdis pirisaTvis, iseve, rogorc damoukidebeli cvladis TiToeuli donisaTvis. TiToeuli cdis piris saSualo aris erTi cdis piris qulebis saSualo iluziis yvela pirobisaTvis. es saSualoebi asaxavs iluziis aRqmis individualur gansxvavebebs eqsperimentSi monawile cdis pirebs Soris. miuxedavad imisa, rom cdis pirebis saSualoebi dispersiuli analizis relevanturia, es saSualoebi, Cveulebriv, ar aris xolme warmodgenili im eqsperimentebis aRweriT statistikaSi, romlebSic cdis pirTa Sida sqema gamoiyeneba. cdis pirTa Sida erTfaqtoriani dispersiuli analizis ganxilva, rogorc orfaqtoriani analizisa, ar cvlis eqsperimentis arss: icvleba mxolod erTi damoukidebeli cvladi da xdeba misi efeqtebis analizi. Tumca, analizis orfaqtorian sqemad warmodgena gvexmareba, gavigoT AxS urTierTqmedebis Secdomis nawilad SemoReba F statistikisaTvis. F statistikis misaRebad cdis pirTa Sida dispersiul analizSi iReben srul raodenobas, romliTac qula gansxvavdeba sruli saSualosagan da am gansxvavebas sam komponentad yofen:
= + + . (12.1)
dispersiuli analizis ZiriTadi midgomis mixedviT, dayofili qulebis komponentebi ayvanilia kvadratSi da jamdeba yvela cdis piris da Carevis yvela pirobis mixedviT, raTa kvadratebis jami miviRoT:
SSsruli = SSA + SSS + SSAxS (12.2)
es kvadratebis jamebi migviTiTebs, rom eqsperimentSi qulebis sruli cvalebadoba (aRniSnuli SSsruli) aris im cvalebadobis Sedegi, romelic xdeba A faqtoris (aRniSnuli SSA), S faqtoris (aRniSnuli SSS) da A da S faqtorebis urTierTqmedebis gamo. cxrilSi # 12.2 mocemuli qulebisaTvis es procesi Semdeg ricxviT mniSvnelobebs gvaZlevs:
SSsruli = 22.926,SSA = 21.830,SSS = 0.314,SSAxS = 0.782.
am mniSvnelobebis misaRebad gamyenebulia gamoTvliTi formulebi am Tavis damatebidan. ganvixiloT 12.2 tolobaSi mocemul TiToeuli kvadratebis jami.
SSsruliSSsruli warmoadgens eqsperimentSi qulebis srul cvalebadobas. rogorc 12.2 tolobaSia aRniSnuli, am cvalebadobis nawili damoukidebeli cvladis efeqtis, nawili - cdis pirebs Soris individualuri gansxvavebebis, xolo nawili ki - pirobebis da cdis pirTa urTierTqmedebis Sedegia.
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sruli cvalebadoba cdis piris qulaSi
cvalebadoba A faqtoris gamo plius Secdoma A da S faqtorebis urTierTqme-debis gamo
cvalebadoba cdis pirTa Soris indi-vidualuri gansxvavebe-bis gamo (S faqtori)
cvalebadoba A da S faqtorebis urTierTqme-debis gamo
SSA
SSA icvleba damoukidebeli cvladis efeqts da pirobebsa da cdis pirTa urTierTqmedebasTan erTad. rogorc cdis pirTa Soris erTfaqtorian sqemaSi, damoukidebeli cvladis efeqti zrdis SSA -is mniSvnelobas. garda amisa, SSA
reagirebs pirobebisa da cdis pirTa nebismier urTierTqmedebaze. cdis pirTa Sida sqemaSi pirobebisa da cdis pirTa urTierTqmedeba ganixileba Secdomis cvalebadobad.
SSS SSS icvleba eqsperimentSi cdis pirTa Soris individualur gansxvavebebTan erTad. cdis pirTa Soris am gansxvavebebs aRvniSnavT S faqtoriT. cxrilSi # 12.2 miaqcieT yuradReba, rom me-4 cdis pirs aqvs tendencia, iluziis yvelaze meti raodenoba dainaxos damoukidebeli cvladis yvela doneze ( = 15.70 sm), maSin, rodesac me-2 cdis piri yvelaze nakleb iluzias aRiqvams ( = 15.35 sm). rac ufro metad gansxvavdeba eqsperimentSi cdis piris saSualoebi erTmaneTisagan, miT ufro didi xdeba SSS.
SSAxS pirobebis urTierTqmedeba cdis pirebTan qulis darCenili cvalebadobaa da gavlenas axdens SSAxS-ze. pirobebisa da cdis pirebis es urTierTqmedeba SeiZleba vnaxoT suraTze # 12.3, romelic cxrilis # 12.2 hipoTetur monacemebs gamoxatavs. abscisaze iluziis oTxi tipia warmodgenili. suraTze moTavsebuli funqciebi gamoxataven xuTi cdis pirisagan TiToeulis miRebul oTx qulas. xazis toli aRqmuli sigrZe yvelaze didia yvela cdis pirisaTvis standartuli iluziis pirobaSi. amdenad, aSkaraa iluziis pirobis efeqti xazis aRqmul sigrZeze. Tumca, radganac xuTi funqcia paraleluri ar aris, xdeba pirobebisa da cdis pirebis urTierTqmedebac. xazis aRqmul sigrZes Soris sxvaobebi iluziis pirobebs Soris ar aris erTi da igive yvela cdis pirisaTvis. magaliTad, pirveli cdis piris SemTxvevaSi qulebis sxvaoba standartul pirobasa da subieqturi konturis pirobas Soris aris 16.6 - 15.8 = 0.8 sm, xolo meore cdis piris SemTxvevaSi sxvaoba aris 16.9 - 15.6 = 1.3 sm. ase rom, iluziis pirobis efeqti xazis aRqmul sigrZeze cdis pirebzea damokidebuli. SSAxS
zomavs pirobebisa da cdis pirebis urTierTqmedebis xarisxs cdis pirTa Sida eqsperimentSi. magram, radganac Carevis TiToeul pirobaSi erTi cdis pirisagan mxolod erT qulas viRebT, pirobebisa da cdis pirebis urTierTqmedebas ver gamovacalkevebT nebismieri Secdomisagan, romelic SeiZleba gavlenas axdendes qulaze. Sesabamisad, SSAxS ganixileba, rogorc Secdomis cvalebadobis sazomi cdis pirTa Sida erTfaqtorian sqemaSi da warmoadgens Secdomis nawilis safuZvels F statistikisaTvis am analizSi.
pirobebisa da cdis pirTa urTierTqmedeba (AxS): situacia cdis pirTa Sida erTfaqtorian sqemaSi, rodesac damoukidebeli cvladis efeqti damokidebulia cdis pirze.
Tavisuflebis xarisxebis gamoTvla
F statistikisaTvis saWiro gadaxrebis kvadratebis saSualos misaRebad TiToeuli SS iyofa mis Sesabamis Tavisuflebis xarisxze. Tavisuflebis xarisxebis gamoTvlis procesi Zalian hgavs cdis pirTa Soris sqemaSi gamoyenebul gamoTvlas.
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Tavisuflebis sruli xarisxi
dfsruli = N - 1,
sadac N aris qulebis mTeli raodenoba eqsperimentSi. magaliTad, N = 20; amitom dfsruli = 20 - 1 = 19.
Tavisuflebis xarisxi SSA-sTvis
dfA = a - 1,
sadac a aris A damoukidebeli cvladis doneebis raodenoba. Cvens magaliTSi A faqtoris oTxi donisaTvis a = 4; aqedan gamomdinare, dfA = 4 - 1 = 3.
Tavisuflebis xarisxi SSS-sTvis
dfS = nA - 1
Cvens magaliTSi xuTi cdis piria; Sesabamisad, nA = 5 da dfS = 5 - 1 = 4.
Tavisuflebis xarisxi SSAxS-isTvis
dfAxS = (a - 1)( nA - 1)
Cvens magaliTSi a = 4 da nA = 5; Sesabamisad,
dfAxS = (4 - 1)( 5 - 1) = 12.
Tavisuflebis xarisxis aditiuroba
Tavisuflebis xarisxebi aditiuria, ase rom
dfsruli = dfA + dfS + dfAxS
es mimarTeba Cvens magaliTSic sruldeba, radgan
dfsruli = 19, dfA = 3, dfS = 4, da dfAxS = 12.
gadaxrebis kvadratebis saSualoebisa da F statistikis gamoTvla
kvadratebis sami saSualo miiReba SS-idan 12.2 tolobaSi TiToeuli SS-is mis df-ze gayofiT:
MSA = ,
MSS = ,
MSAxS = .
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MSsruli ar gamoiTvleba, radganac is ar gamoiyeneba dispersiul analizSi. cxrilis # 12.2 qulebisaTvis
SSA = 21.830,SSS = 0.314,SSAxS = 0.782.
am kvadratebis saSualoebisaTvis Tavisuflebis xarisxebia
dfA = 3,dfS = 4,dfAxS = 12.
aqedan gamomdinare,
MSA = = 7.277,
MSS = = 0.078,
MSAxS = = 0.065.
F statistika cdis pirTa Sida erTfaqtorian dispersiul analizSi aris
F = .
ase rom, cxrilis # 12.1 qulebisaTvis
Frealuri = = 111.95.
es Frealuri aris am analizSi gamosaTvleli erTaderTi F; S faqtorisaTvis F ar gamoiTvleba. cxrilis # 12.2 qulebis dispersiuli analizis ricxviTi Sejameba warmodgenilia cxrilSi # 12.3. gamoTvliTi formulebi am analizisaTvis mocemulia Tavis damatebaSi. cxrili # 12.4 ajamebs cdis pirTa Sida erTfaqtorian dispersiul analizSi cvalebadobis wyaroebs - SS, df, MS da F.
cxrili # 12.3 dispersiuli analizis cxrili xazebis hipoTeturi Tanabari aRqmuli sigrZis qulebisaTvis cxrilidan # 12.2.
wyaro SS df MS Filuziis tipi (A)cdis pirebi (S)AxSsul
21.8300.3140.78222.926
341219
7.2770.0780.065
111.95*
* p < .01
cxrili # 12.4 formulebis Sejameba cdis pirTa Sida erTfaqtoriani dispersiuli analizisaTvis.
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wyaro SS dfa MS FA faqtori
S faqtori
AxS
sul
SSA
SSS
SSAxS
SSsruli
a - 1
nA - 1
(a - 1)( nA - 1)
N - 1 ar gamoiTvleba
aa = A faqtoris doneebis raodenoba; nA = qulebis raodenoba Carevis pirobaSi anu, Sesabamisad, cdis pirebis raodenoba; N - qulebis sruli raodenoba.
SeamowmeT Tqveni codna # 12.1
1. gansazRvreT: AxS urTierTqmedeba, dfA, dfAxS, dfS, dfsruli, A faqtori, S faqtori, MSA, MSAxS, MSS, MSsruli, nA, cdis pirTa Sida erTfaqtoriani sqema, ganmeorebiTi gazomvebis sqema, SSA, SSAxS, SSS, SSsruli, pirobebisa da cdis pirebis urTierTqmedeba.
2. gansazRvreT qulebis cvalebadobis wyaroebi cdis pirTa Sida erTfaqtorian sqemaSi. 3. daasruleT Semdegi gantolebebi cdis pirTa Sida erTfaqtoriani dispersiuli analizisaTvis:
a. SSsruli =b. dfA =g. dfS =d. dfAxS =e. MSA =v. MSS =z. MSAxS =T. F =
4. ra aris SSsrulis mniSvneloba, Tu SSA = 74.00, SSS = 29.00 da SSAxS = 96.00?5. ra aris SSA-is mniSvneloba, Tu SSsruli = 426.00, SSS = 92.00 da SSAxS = 301.00?6. ra aris SSS -is mniSvneloba, Tu SSsruli = 96.00, SSA = 15.00 da SSAxS = 56.00?7. ra aris SSAxS -is mniSvneloba, Tu SSsruli = 173.00, SSA = 41.00 da SSS = 36.00?8. erTma fsiqologma gamoiyena cdis pirTa Sida erTfaqtoriani dispersiuli analizi A
faqtoris xuTi doniT da 13 cdis piriT. ra aris dfA, dfS, dfAxS da dfsrulis mniSvnelobebi?9. ra aris dfsrulis mniSvneloba cdis pirTa Sida erTfaqtorian dispersiul analizSi, Tu dfA = 2 da
dfS = 19?10. ipoveT gadaxrebis kvadratebis saSualoebis ricxviTi mniSvnelobebi Semdegi SS-isa da
df-isaTvis: SSA = 22.00, SSS = 18.00, SSAxS = 36.00, dfA = 2, dfS = 9 da dfAxS = 18. 11. cxrilebi # 1 da 2 warmoadgens arasrul Sejamebis cxrilebs cdis pirTa Sida
erTfaqtoriani dispersiuli analizisaTvis. TiToeul cxrilSi SeavseT gamotovebuli mniSvnelobebi cxrilSi # 12.4 SS-sa da df-s Soris mocemuli mimarTebis gamoyenebiT. Semdeg upasuxeT am kiTxvebs yoveli cxrilisaTvis.
a. damoukidebeli cvladis ramdeni done icvleba?b. ramdeni qulaa miRebuli TiToeul pirobaSi?g. ramdeni cdis piri iRebda monawileobas kvlevaSi?
cxrili # 1
wyaro SS df MS FA faqtoriS faqtoriAxSsul
48.0027.0072.00-------
49--------------
---------------------
-------
cxrili # 2
wyaro SS df MS FA faqtoriS faqtori
6.0036.00
-------12
-------3.00
-------
9
AxSsul
-------78.00
24-------
-------
statistikuri hipoTezis Semowmeba Frealuris meSveobiT
Frealuri = MSA/MSAxS gamoiyeneba imis gadasawyvetad, mniSvnelovnad gansxvavdeba Tu ara Carevis pirobebis saSualoebi. rogorc SSAxS-is ganxilvisas vnaxeT, F-is mniSvneli, MSAxS, am analizSi Secdomis cvalebadobas warmoadgens. F-is mricxveli, MSA, icvleba damoukidebeli cvladis sistematur efeqtTan erTad da pirobebisa da cdis pirebis urTierTqmedebasTan erTad. Tu damoukidebel cvlads ar aqvs efeqti da pirobebis saSualoebis cvalebadoba mxolod pirobebisa da cdis pirebis urTierTqmedebis gamo xdeba, maSin MSA-is mniSvneloba daaxloebiT igive unda iyos, rac MSAxS-is mniSvneloba da Frealuri unda iyos daaxloebiT 1.00. xolo, Tu A faqtors aqvs efeqti da pirobebis saSualoebi gansxvavdeba rogorc am efeqtis, aseve pirobebisa da cdis pirebis urTierTqmedebis gamo, maSin MSA-s ufro didi mniSvneloba unda hqondes, vidre MSAxS-s, da Frealuri 1.00-ze meti xdeba. F Sefardeba MSS-is monawileobiT, romelic individualur gansxvavebebis kvadratis saSualos aRniSnavs, ar gamoiTvleba. miuxedavad imisa, rom MSS
icvleba eqsperimentSi cdis pirebs Soris gansxvavebebis xarisxTan erTad, am analizSi ar gamoiTvleba MS, romelic iZleva individebs Soris mosalodneli Secdomis cvalebadobis Sefasebas. aqedan gamomdinare, MSS-is mniSvneloba xSirad ar aris warmodgenili saboloo cxrilSi. sami kvadratebis saSualo da maTze gavlenis mqone cvalebadobis wyaroebi SeiZleba Semdegnairad Sejamdes:
kvadratebis saSualo masze gavlenas axdens:
MSA A faqtoriT gamowveuli sistematuri cvalebadoba
pirobebisa da cdis pirebis urTierTqmedeba (anu Secdomis cvalebadoba)
MSS S faqtoriT gamowveuli sistematuri cvalebadoba
MSAxS pirobebisa da cdis pirebis urTierTqmedeba (anu Secdomis cvalebadoba)
statistikuri Semowmeba F-is gamoyenebiT ukve nacnob proceduras warmoadgens:
yalibdeba nulovani hipoTeza, H0, da alternatiuli hipoTeza, H1;
im daSvebiT, rom H0 sworia, gamoiTvleba F-is SerCevis ganawileba. es ganawileba mocemulia cxrilSi # A-3;
xdeba mniSvnelovnobis donis SerCeva; F-is kritikuli done, romelic aRiniSneba FkritikuliT, gamoiTvleba F–is
SerCeviTi ganawilebidan, romelic mocemulia cxrilSi # A-3; F–is SerCeviT ganawilebaSi gamoiyofa uaryofis are; SerCevis monacemebidan gamoiTvleba F statistika, romelic
aRiniSneba, rogorc Frealuri;
10
gadawyvetileba imis Taobaze, uarvyoT Tu ara H0, miiReba imaze dayrdnobiT, xvdeba Tu ara Frealuri uaryofis areSi.
statistikuri hipoTezebinulovani hipoTeza. nulovani hipoTeza cdis pirTa Sida sqemisaTvis A faqtoris oTxi doniT ase gamoixateba:
H0: A1 = A2 = A3 = A3
es nulovani hipoTeza asaxavs situacias, romelic Cndeba, Tu damoukidebel cvlads ar aqvs efeqti. Tu H0 marTldeba, maSin pirobebis saSualoebs Soris miRebuli sxvaobebi ubralod Secdomis cvalebadobis gamoa. rogorc cdis pirTa Soris sqemaSi, nulovan hipoTezaSi gansazRvruli populaciis saSualoebis raodenoba yovelTvis Seesabameba damoukidebeli cvladis doneebis raodenobas.
alternatiuli hipoTeza. alternatiuli hipoTezaa: H1: A-ebi ar aris toli.
hipoTezaSi monawile populaciis saSualoebis raodenobis miuxedavad. alternatiuli hipoTeza asaxavs situacias, romelic Cndeba, Tu damoukidebel cvlads aqvs efeqti.
F statistikaze damyarebuli gadawyvetilebebis miRebacdis pirTa Sida erTfaqtorian sqemaSi statistikuri gadawyvetilebebis miRebis procesi cdis pirTa Soris erTfaqtorian dispersiul analizSi gamoyenebuli procesis identuria. –s mniSvneloba, romelic gansazRvravs uaryofis ares FrealurisaTvis, analizis Catarebamde SeirCeva. Semdeg cxrilSi # A-3a an b moiZebneba Fkritikulis mniSvneloba Sesabamisi mricxveli da mniSvneli df-iT. Tu Frealuri udris an metia Fkritikulze, maSin Frealuri xvdeba uaryofis areSi. nulovani hipoTeza uaryofilia da miRebulia alternatiuli hipoTeza. arsebobs sul mcire erTi statistikurad mniSvnelovani sxvaoba pirobebis saSualoebs Soris. Tu Frealuri naklebia, vidre Fkritikuli, maSin Frealuri ar xvdeba uaryofis areSi; nulovani hipoTeza ar aris uaryofili da alternatiuli hipoTeza ar miiReba. pirobebis saSualoebi mniSvnelovnad ar gansxvavdeba; saSualoebs Soris miRebuli sxvaobebi Secdomis cvalebadobis gamo xdeba. vaskvniT, rom damoukidebel cvlads ar hqonda efeqti. Frealurze damyarebuli gadawyvetilebebi da Semdgomi daskvnebi Sejamebulia cxrilSi # 12.5.
cxrili # 12.5 gadawyvetilebebis da daskvnebis Sejameba statitikuri hipoTezebis SemowmebaSi cdis pirTa Sida erTfaqtoriani sqemisaTvis dispersiuli analizis gamoyenebiT. mocemulia mniSvnelovnobis done .05.
Tu Frealuri xvdeba uaryofis areSi = .05-isaTvis, maSin:
Tu Frealuri ar xvdeba uaryofis areSi = .05-isaTvis, maSin:
Frealuris albaToba naklebia, an tolia .05-is, anu p .05. H0 uaryofilia.H1 miRebulia. SerCevis yvela saSualo ar aris erTi da imave populaciidan. pirobebis saSuloebs Soris sul mcire
Frealuris albaToba metia .05-ze, anu p>.05.
H0 ar aris uaryofili.H1 ar aris miRebuli.
SerCevis saSualoebs Soris ar aris
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erTi sxvaoba statistikurad mniSvnelovania .05 doneze.gadawyvetilia, rom SerCevis Secdomis garda kidev raRac sxva ganapirobebs sxvaobas SerCevis saSualoebs Soris. yvela pirobis dacviT Catarebul eqsperimentSi sxvaoba damoukidebel cvlads miewereba. Tu damoukidebel cvlads sami an meti done aqvs, saWiroa mravlobiTi Sedarebis kriteriumebi.
mniSvnelovani sxvaobebi .05 doneze.
gadawyvetilia, rom SerCevis Secdoma SerCevis saSualoebs Soris sxvaobis yvelaze metad savaraudo axsnaa. ar arsebobs imis safuZveli, rom damoukidebel cvlads efeqti hqonda. mravlobiTi Sedarebis kriteriumebi ar aris saWiro.
gadawyvetilebis procesis ilustraciisaTvis gamoviyenebT cxrilSi # 12.3 Sejamebul analizs cxrilis # 12.2 sanimuSo qulebisaTvis. am analizSi Frealurs
aqvs 3 (mricxveli) da 12 (mniSvneli) df. amdenad, rodesac = .05, Fkritikuli = 3.49 (miRebulia cxrilidan A-3a.) Frealuri = 111.95 metia Fkritikulze da xvdeba uaryofis areSi. uarvyofT
H0: A1 = A2 = A3 = A3
da viRebT
H1: A-ebi ar aris toli,
es gadawyvetileba migviTiTebs, rom arsebobs sul mcire erTi statistikurad mniSvnelovani sxvaoba cxrilis # 12.2 oTx saSualos Soris, magram is ar aRniSnavs konkretulad, Tu romeli saSualoebi gansxvavdeba erTmaneTisagan. imis dasadgenad, Tu romeli wyvilTaSorisi Sedarebebi gansxvavdeba mniSvnelovnad, gamoiyeneba mravlobiTi Sedarebis kriteriumebi.
mravlobiTi Sedarebis kriteriumebi cdis pirTa Sida dispersiuli analizisaTvismravlobiTi Sedarebis kriteriumebTan dakavSirebuli problemebi da sakiTxebi cdis pirTa Sida dispersiuli analizisaTvis igivea, rac ganvixileT me-10 TavSi cdis pirTa Soris dispersiuli analizisaTvis. saboloo SedarebisaTvis SeiZleba gamoyenebul iqnes tukis HSD kriteriumi kritikuli sxvaobiT
CD = q .
Tu am kriteriums Cvens eqsperiments mivusadagebT: MSAxS = 0.065 (miRebulia cxrilidan # 12.3) nA – 5. q .05 doneze damoukidebeli cvladis oTxi donisaTvis da 12 df – MSAxS-
saTvis aris 4.20 (miRebulia cxrilidan # A-4).
am mniSvnelobebis CasmiT viRebT:
CD = 4.20
= 4.20 = 0.48 sm.
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TiToeuli wyvilTaSorisi SedarebisaTvis pirobebis saSualoebs Soris sxvaoba, romelic absoluturi mniSvnelobiT 0.48 sm-ze metia, statistikurad mniSvnelovania .05 doneze. eqvsi wyvilTaSorisi Sedareba, TiToeuli Sedarebis absoluturi mniSvnelobebi, statistikuri hipoTeza da gadawyvetileba TiToeuli hipoTezisaTvis naCvenebia cxrilSi # 12.6 (sadac A1 = standartuli iluzia, A2 = subieqturi konturebis iluzia, A2 = mTliani wertilebis iluzia, A4 = sakontrolo piroba).TiToeuli sxvaobis absoluturi mniSvneloba CD – 0.48 sm-ze metia; amdenad, TiToeuli Sedareba statistikurad mniSvnelovania .05 doneze. standartuli iluzia iluziis mniSvnelovnad nakleb Sedegs qmnis, mTliani wertilebi – mniSvnelovnad kidev ufro nakleb iluzias da sakontrolo piroba ki – yvelaze nakleb iluzias.
Carevis efeqtis siZlieris gazomva
eta kvadrati efeqtis siZlieris sazomad SeiZleba gamoviyenoT cdis pirTa Sida erTfaqtorian sqemaSi. gamoyenebuli formula mciredaa Secvlili cdis pirTa Soris sqemasTan SedarebiT:
2 =
miaqcieT yuradReba, rom am formulis mixedviT individualuri gansxvavebebiT gamowveuli cvalebadoba, romelic mocemulia SSS-iT, ar aris CarTuli eqsperimentis srul cvalebadobaSi.
cxrili # 12.6tukis HSD CD-s gamoyeneba wyvilTaSorisi SedarebebisaTvis sanimuSo eqsperimentSi.
Sedareba Sedarebis absoluturi mniSvneloba
statistikuri hipoTezebi
gadawyvetileba
-Tan (16.92 – 15.90)
-Tan (16.92 – 15.02)
-Tan (16.92 – 14.10)
-Tan (15.90 – 15.02)
-Tan (15.90 – 14.10)
-Tan (15.02 – 14.10)
1.02
1.90
2.82
0.88
1.80
0.92
H0: A1 = A2
H1: A1 A2
H0: A1 = A3
H1: A1 A3
H0: A1 = A4
H1: A1 A4
H0: A2 = A3
H1: A2 A3
H0: A2 = A3
H1: A2 A3
H0: A3 = A4
H1: A3 A4
uaryofiliamiRebulia
uaryofiliamiRebulia
uaryofiliamiRebulia
uaryofiliamiRebulia
uaryofiliamiRebulia
uaryofiliamiRebulia
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Cveni magaliTisaTvis, SSA = 21.830 da SSAxS = 0.782. ase rom,
2 = = .97.
xazis sigrZis gazomvis cvalebadobis 97 procenti xdeba iluziis pirobis gamo, mas Semdeg, rac individualuri gansxvavebebis gamo cvalebadoba gauqmebulia. es damoukidebeli cvladis Zalian Zlieri efeqtia.
cdis pirTa Sida dispersiuli analizis daSvebebi
daSvebebi, romlebsac emyareba cdis pirTa Sida erTfaqtoriani analizis gamoyeneba, Semdegia:
1. TiToeuli cdis piri mowmdeba damoukidebeli cvladis yovel doneze; 2. monacemebi SerCevaSi SemTxveviTad aris aRebuli populaciidan; 3. monacemTa populaciebi Carevis sxvadasxva pirobisaTvis
normaluradaa ganawilebuli;4. populaciaSi monacemTa dispersiebi Carevis sxvadasxva pirobisaTvis
erTnairia;5. cdis piris individualuri gansxvavebebis wili misi qulebisaTvis erTi da
igive rCeba Carevis yvela pirobaSi.
pirveli daSveba aucilebelia cdis pirTa Sida dispersiul analizSi monacemebis saTanado statistikuri kriteriumis arsebobisaTvis; am daSvebis ugulvebelyofa dauSvebelia. meore, mesame da meoTxe daSvebebi cdis pirTa Soris dispersiul analizSi arsebuli daSvebebis identuria. xandaxan eqsperimentebSi maTi darRveva xdeba, magram dispersiuli analizi inarCunebs garkveul mdgradobas aseTi darRvevebis mimarT. mexuTe daSvebis mixedviT, adamianis qceva, Carevis efeqtisagan damoukideblad, stabiluria damoukidebeli cvladis yvela doneze. mosalodnelia, rom es daSveba dairRveva bihevioristuli mecnierebis kvlevis mraval SemTxvevaSi. aseTi darRvevis gavlena isaa, rom mniSvnelovnobis donis mixedviT dadgenili mniSvnelobis zeviT izrdeba I gvaris Secdomis daSvebis albaToba.Secdomis am gazrdil SesaZleblobasTan gamklavebis ramdenime midgoma arsebobs. gaiser-grinhausis (Geisser-Greenhouse) koreqcia cvlis Fkritikulis
misaRebad gamoyenebul df-s ise, rom Frealuris gamosaTvlelad gamoiyeneba ufro didi Fkritikuli. am koreqciiT, Fkritikuli miiReba mricxvelad 1 df-is da mniSvnelad (nA - 1) df -is gamoyenebiT, Cveulebriv gamoyenebuli a – 1, (a - 1)( nA - 1) df-is nacvlad. gaiser-grinhausis koreqciis Cvens magaliTze misadagebiT, Fkritikuli (1.4) = 7.71. Frealuri (3.12) = 111.95 mainc ufro didia, vidre Fkritikuli da H0 uaryofilia – miRebulia igive gadawyvetileba, rac 3 da 12 df-iani Fkritikulis gamoyenebiT. es da sxva midgomebi, romlebic amcirebs Secdomis SesaZleblobas, Tu darRveulia me-5 daSveba, ganxilulia kepelis naSromSi (Keppel, 1991).alternatiuli midgomaa, gamoviyenoT araparametruli uilkoqsonis niSniani rangebis kriteriumi an fridmanis dispersiuli analizi cdis pirTa Sida dispersiuli analizis magivrad. uilkoqsonis kriteriumi warmodgenilia me-15 TavSi.
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SeamowmeT Tqveni codna XII.2
1. gansazRvreT TiToeul MS-ze gavlenis mqone faqtorebi cdis pirTa Sida erTfaqtorian dispersiul analizSi.
2. axseniT, Tu ratom izrdeba MSA-s mniSvneloba, Tu A faqtors aqvs efeqti cdis pirTa Sida erTfaqtorian eqsperimentSi.
3. dawereT statistikuri hipoTezebi cdis pirTa Sida erTfaqtoriani dispersiuli analizisaTvis damoukidebeli cvladis xuTi doniT.
4. gansazRvreT daSvebebi, romlebic safuZvlad udevs cdis pirTa Sida erTfaqtoriani dispersiuli analizis gamoyenebas.
magaliTi # 12.1 cdis pirTa Sida erTfaqtoriani sqemis analizi damoukidebeli cvladis oTxi doniT
amocana: mravali davalebis Sesruleba moiTxovs adamianebisagan, fxizlad iyvnen drois xangrZlivi periodis ganmavlobaSi. amis magaliTia sahaero moZraobis kontroliori, romelic radaris ekrans akvirdeba, raTa TviTmfrinavebs Soris saWiro distancia SenarCundes. ase, fsiqologebma Seiswavles sifxizleze moqmedi mravali faqtori. magaliTad, pfendlerma da uidelma (Pfendler & Widdel, 1986) Caatares eqsperimenti, sadac cdis pirebi 2,5 saaTis ganmavlobaSi akvirdebodnen ekrans masze gamosaxuli skaliT. rac ufro meti dro gadioda, cdis pirebs ufro didi dro sWirdebodaT ekranze cvlilebebis dasadgenad. dauSviT, rom Catarda analogiuri kvleva, sadac cdis pirebs 4 saaTis ganmavlobaSi ramdenime skala unda ekontrolebinaT. cdis piris davaleba iyo, mieTiTebina, rodis Seicvleboda monacemi skalaze. damokidebuli cvladi zomavda im drois xangrZlivobas, romelic cdis pirs cvlilebis SesamCnevad sWirdeboda. cvlilebis SemCnevis dro (wamebSi) 13 cdis pirisaTvis oTxsaaTiani periodidan TiToeuli saaTisaTvis mocemulia cxrilSi # 12.7. mniSvnelovnad gaizarda Tu ara SemCnevis dro?
amoxsna. sqema warmoadgens cdis pirTa Sida erTfaqtorian sqemas damoukidebeli cvladis – drois periodis - oTxi doniT. monacemTa analizis pirveli nabijia cdis qulebis pirTa Sida erTfaqtoriani dispersiuli analizi. Tu Frealuri
statistikurad mniSvnelovania, gamoviyenoT tukis HSD kriteriumi, raTa vipovoT statistikurad mniSvnelovani wyvilTaSorisi sxvaobebi pirobebis saSualoebs Soris.
saWiro statistika:
F = MSA/MSAxS
gamosayenebeli daSvebebi:
1. TiToeuli cdis piri mowmdeba drois yovel periodSi.2. SerCevis qulebi SemTxveviTad aris aRebuli populaciidan.3. SemCnevis droebis populacia gansxvavebuli drois periodebisaTvis
normaluradaa ganawilebuli. 4. SemCnevis droebis populaciis dispersiebi gansxvavebuli drois
periodebisaTvis erTnairia.5. cdis piris individualuri gansxvavebebis wvlili igive rCeba misi
qulebisaTvis drois yvela periodisaTvis.
cxrili # 12.7
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skalaze cvlilebis SesamCnevad saWiro wamebis saSualo raodenoba oTxsaaTiani drois periodisaTvis 13 cdis pirisaTvis.
cdis piri drois periodi (saaTebSi) (A) ________________________________________________ 1 (A1 ) 2 (A2 ) 3 (A3) 4 (A4)
12345678910111213
6.25.98.47.64.15.46.66.14.98.25.75.96.9
6.74.88.77.84.75.36.75.85.18.65.76.46.6
7.46.19.98.75.45.97.26.45.29.36.56.97.1
7.86.910.38.96.67.17.56.76.810.47.27.67.5
sA
6.301.24
6.381.34
7.081.45
7.791.28
statistikuri hipoTezebi: H0: A1 = A2 = A3 = A4
H1: A-ebi ar aris toli,
mniSvnelovnobis done: = .05.
df: dfA = a – 1 = 4 – 1 = 3dfS = nA – 1 = 13 – 1 = 12dfAxS = (a – 1) (nA – 1) = (4 – 1) (13 – 1) = 36dfsruli = N – 1 = 52 – 1 = 51
F-is kritikuli mniSvneloba: Fkritikuli (3.36) = 2.92. df-is mniSvneloba 36, rogorc mniSvneli, ar aris warmodgenili cxrilSi # A-3a. dfSecdomisaTvis
gamoviyeneT kritikuli df-is uaxloesi Semdgomi mniSvneloba cxrilSi – 30.
uaryofis are: Frealuris mniSvnelobebi tolia an meti 2.92-ze.
gamoTvla: Tavis damatebaSi mocemuli formulebis gamoyenebiT gamoviTvaleT dispersiuli analizi, raTa migveRo dispersiuli analizis Semdegi cxrili:
wyaro SS df MS Fdrois periodi (A)cdis pirebi (S)AxSsul
18.98581.1883.727103.900
3123651
6.3286.7660.104
60.85*
* p < .05
gadawyvetileba: Frealuri = 60.85 xvdeba uaryofis areSi; uarvyofT H0: A1 = A2 = A3 = A3 da viRebT H1: A-ebi ar aris toli. H0–is uaryofa gviCvenebs, rom arsebobs sul mcire erTi statistikurad mniSvnelovani sxvaoba Carevis
16
pirobebis saSualoebs Soris. statistikurad mniSvnelovani wyvilTaSorisi sxvaobebis sapovnelad viyenebT tukis HSD kriteriums.
tukis kriteriumi: am kriteriumisaTvis saWiro ricxviTi mniSvnelobebi Semdegia:
q miiReba cxrilidan # A-4. gvaqvs damoukidebeli cvladis oTxi done da 36 df MSAxS-isaTvis. radganac 36 df ar aris mocemuli cxrilSi # A-4, viyenebT 30df-s, df-is uaxloes Semdgom mniSvnelobas cxrilSi. ase rom, q = 3.85 .05 mniSvnelovnobis donisaTvis;
dispersiuli analizidan miRebuli MSAxS aris 0.104; nA, qulebis raodenoba TiToeul Sesadarebel saSualoSi, aris 13.
formulaSi am ricxviTi mniSvnelobebis CasmiT
CD = q = 3.85 = 0.34 wami.
nebismieri sxvaoba, romelic absoluturi mniSvnelobiT 0.34 wamis tolia an metia, statistikurad mniSvnelovania .05 doneze. wyvilTaSorisi Sedarebebi, maTi absoluturi mniSvnelobebi, Semowmebuli statistikuri hipoTezebi da statistikur hipoTezebze damyarebuli gadawyvetilebebi TiToeuli SedarebisaTvis mocemulia cxrilSi # 12.8 (sadac A1 = 1 saaTs, A2 = 2 saaTs, A3
= 3 saaTs da A4 = 4saaTs).
efeqtis siZliere:
2 = = = .84.
cxrili # 12.8tukis HSD CD-s gamoyeneba oTxi drois periodis wyvilTaSoris SedarebaSi.
Sedareba Sedarebis absoluturi mniSvneloba
statistikuri hipoTezebi
gadawyvetileba
-Tan (6.30 – 6.38)
-Tan (6.30 – 7.08)
-Tan (6.30 – 7.79)
-Tan (6.38 – 7.08)
-Tan (6.38 – 7.79)
0.08
0.78
1.49
0.70
1.41
H0: A1 = A2
H1: A1 A2
H0: A1 = A3
H1: A1 A3
H0: A1 = A4
H1: A1 A4
H0: A2 = A3
H1: A2 A3
H0: A2 = A3
H1: A2 A3
H0: A3 = A4
H1: A3 A4
ar aris uaryofiliar aris miRebuli
uaryofiliamiRebulia
uaryofiliamiRebulia
uaryofiliamiRebulia
uaryofiliamiRebulia
17
-Tan (7.08 – 7.79) 0.71
uaryofiliamiRebulia
daskvna: erTaderTi Sedareba, romelic naklebia CD-ze – 0.34 wamze, aris pirvel da meore saaTebs Soris. es sxvaoba aramniSvnelovania. yvela sxva sxvaoba statistikurad mniSvnelovania. ase rom, Sedarebebma gvaCvena, rom SemCnevis droebSi ar aris zrda davalebis Sesrulebis pirvel da meore saaTebs Soris, magram statistikurad mniSvnelovani zrda aRiniSneba me-2 da me-3 saaTebs Soris da me-3 da me-4 saaTebs Soris. efeqtis siZliere, 2
= .84, gviCvenebs, rom drois periodi pasuxs agebs SemCnevis drois cvalebadobis did nawilze mas Semdeg, rac individualuri gansxvavebebis cvalebadoba eqsperimentSi ugulvebelyofilia.
magaliTi # 12.2cdis pirTa Sida erTfaqtoriani dispersiuli analizis gamoyeneba damoukidebeli cvladis ori doniT
amocana: rodesac studenti leqciis dros amTqnarebs, leqtori amas xSirad mowyenis niSnad aRiqvams. magram aris Tu ara mTqnareba namdvilad amis niSani? am hipoTezis gamosakvlevad provinma da hamernikma (Provine & Hamernik, 1986) Caatares eqsperimenti imis Sesamowmeblad, namdvilad zrdis Tu ara mTqnarebis sixSires uintereso masalis swavla. am eqsperimentSi ori sxvadasxva sesiis dros studentebi 30 wuTis ganmavlobaSi uyurebdnen rok-musikis videoklipebs (A1, saintereso stimuli) da 30 wuTis ganmavlobaSi – vertikalur ferad-zolebian ekrans (A2, uintereso stimuli). aRiricxeboda damTqnarebis raodenoba ori sesiis dros. davuSvaT, es eqsperimenti 11 cdis pirze gavimeoreT da aRvricxeT damTqnarebis raodenoba cxrilSi # 12.9. mocemul TiToeul sesiaSi moqmedebs Tu ara videoklipis tipi mTqnarebis raodenobaze?
cxrili # 12.9mTqnarebis miRebuli raodenoba, rogorc nanaxi videoklipis funqcia 11 cdis pirisaTvis.
cdis piri videoklipis tipi (A) _______________________________________ saintereso (A1 ) uintereso (A2)
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sA
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amoxsna. cdis pirTa Sida erTfaqtoriani dispersiuli analizi Sesabamisi statistikuri kriteriumia am monacemebisaTvis. ramdenadac gamoyenebuli iyo mxolod ori Carevis piroba, tdamokidebuli aseve Sesabamisi statistikuri kriteriumi iqneboda. viyenebT .05 mniSvnelovnobis dones.
saWiro statistika: F = MSA/MSAxS
gamosayenebeli daSvebebi:
1. TiToeuli cdis piri mowmdeba videoklipis orive tipis pirobaSi;2. SerCevis monacemebi SemTxveviTad aris aRebuli populaciidan;3. mTqnarebis monacemebis populacia Carevis gansxvavebuli
pirobisaTvis normaluradaa ganawilebuli; 4. mTqnarebis monacemebis dispersiebi populaciaSi Carevis
gansxvavebuli pirobebisaTvis erTnairia;5. cdis piris individualuri gansxvavebebis wvlili igive rCeba misi
qulebisaTvis videoklipis orive tipis pirobaSi.
statistikuri hipoTezebi: H0: A1 = A2
H1: A-ebi ar aris toli,
mniSvnelovnobis done: = .05.
df: dfA = a – 1 = 2 – 1 = 1dfS = nA – 1 = 11 – 1 = 10dfAxS = (a – 1) (nA – 1) = (2 – 1) (11 – 1) = 10dfsruli = N – 1 = 22 – 1 = 21
F-is kritikuli mniSvneloba: Fkritikuli (1,10) = 4.96.
uaryofis are: Frealuris mniSvnelobebi tolia an meti 4.96-ze.
gamoTvla: am Tavis damatebaSi mocemuli formulebis gamoyenebiT, am analizis Sejameba aseTia:
wyaro SS df MS Fvideoklipis tipi (A)cdis pirebi (S)AxSsul
14.728120.36417,272152.364
1101021
14.72812.0361.727
8.53*
* p < .05
gadawyvetileba: Frealuri xvdeba uaryofis areSi; amitom uarvyofT H0-s da viRebT H1-s.
efeqtis siZliere:
2 = = .46.
19
daskvna: sxvaoba ori Carevis pirobis saSualos Soris – 3.9 da 5.5 damTqnarebas Soris – statistikurad mniSvnelovania. rodesac saintereso videoklipebs uyurebdnen, cdis pirebi naklebad amTqnarebdnen, vidre uintereso videoklipebis yurebisas. radganac mxolod ori saSualoa CarTuli, mravlobiTi Sedarebis kriteriumi ar aris saWiro. 2 miuTiTebs, rom damokidebuli cvladis dispersiis 46 procentze pasuxs agebs videoklipis tipi, mas Semdeg, rac eqsperimentidan amoRebulia SSS.
dispersiuli analizis Sedegebis prezentacia
iluziis pirobasa da xazis aRqmul sigrZeze (ix. cxrilebi # 12.2 da 12.3) moyvanili magaliTis analizis Sedegebis aRwera, romelic misdevs amerikis fsiqologTa asociaciis publikaciebis saxelmZRvanelos (1994) stils, statiis Sedegebis seqciaSi ase SeiZleba daiweros:
xazis aRqmuli sigrZeebis saSualoebi iluziis standartuli, subieqturi konturebis, mTliani wertilebis da sakontrolo pirobebisaTvis aRmoCnda 16.92 (SD = 0.24), 15.90 (SD = 0.29), 15.02 (SD = 0.26) da 14.10 (SD = 0.25) sm, Sesabamisad. alfas .05 doneze, cdis pirTa Sida erTfaqtorianma dispersiulma analizma gviCvena, rom saSualoebi mniSvnelovnad gansxvavdeba, F (3,12) = 111.95, MSE = 0.065, p < .01. wyvilTaSorisi Sedarebebisas tukis kriteriumma aCvena, rom iluziis TiToeuli piroba mniSvnelovnad gansxvavdeboda iluziis yoveli sxva pirobisagan, p < .05 (CD = 0.48 sm). eta kvadrati qulebisaTvis iyo .97.
am angariSSi informaciis didi nawili cdis pirTa Soris sqemis msgavsia. mokled ganvixiloT es prezentacia.
SerCevis saSualo SerCevis saSualoebis da standartuli gadaxrebis miRebuli mniSvnelobebi warmodgenilia pirvel winadadebaSi. radganac miRebuli iyo mxolod oTxi saSualo, isini warmodgenilia winadadebis da ara cxrilis an suraTis saxiT.
= .05 miuTiTebs kriteriumisaTvis SerCeul mniSvnelovnobis dones.
F (3,12) aRniSnavs kriteriumis statistikis saxels, rogorc F-s. frCxilebSi naCvenebi ricxvebi aRniSnavs Frealuris mricxvelis da mniSvnelos df-ebs (Sesabamisad, 3 da 12).
= 111.95 iZleva Frealuris mniSvnelobas.
p < .01 aRniSnavs, rom:a. Frealuris albaToba, Tu H0 marTldeba,
naklebia an tolia .01-is. es mniSvneloba aris Frealuris albaToba an Frealuris kidev ufro ukiduresi mniSvneloba, Tu H0marTalia.
b. H0: A1 = A2 = A3 = A4 uaryofilia.H1: A-ebi ar aris toli, miRebulia.
g. arsebobs sul mcire erTi statistikurad20
mniSvnelovani sxvaoba pirobebis saSualoebs Soris.
d. SerCevis Secdomis garda kidev sxva mizeziagebs pasuxs pirobebis saSualoebs Soris sxvaobaze.
MSE = 0.065 gvaZlevs MSAxS mniSvnelobas FrealurisaTvis. es MS aris Secdomis nawili F SefardebisaTvis; agreTve, is SeiZleba ganisazRvros, rogorc MSAxS.
CD = 0.48 sm gvaZlevs kritikul sxvaobas wyvilTaSorisi SedarebebisaTvis tukis HSD kriteriumis gamoyenebiT. Semdeg aRiwereba statistikurad mniSvnelovani wyvilTaSorisi Sedarebebi.
2 = .97 gviCvenebs, rom xazis aRqmuli Tanabari sigrZeebis dispersiis 97 procenti am eqsperimentSi iluziis pirobis gamo xdeba, mas Semdeg, rac individualuri gansxvavebebis gamo arsebuli cvalebadoba gauqmebulia.
kvlevis sqemis arCeva: cdis pirebs Soris Tu cdis pirebs Sida
rogor unda gadawyvitos bihevioristma mecnierma, romeli kvlevis sqema gamoiyenos kvlevis hipoTezis Sesafaseblad – cdis pirebs Soris Tu cdis pirebs Sida? sqemis TiToeul tips aqvs upiratesobebi da SezRudvebi. zogadad, am gadawyvetilebis miRebisas sami sakiTxi dgeba xolme: (1) cdis pirTa saWiro raodenoba, (2) damoukidebeli cvladis mosalodneli efeqturoba da (3) Carevis mravaljeradi efeqtebis miRebis albaToba.
cdis pirTa saWiro raodenobacdis pirTa Sida sqemaSi cdis pirs Carevis yovel pirobaSi zomaven; ase rom, aq naklebi cdis pirebia saWiro, vidre cdis pirTa Sida sqemaSi. cxrilSi # 12.2 naCveneb magaliTSi iluziis pirobis oTxi donidan TiToeulisaTvis miRebulia xuTi qula, Sesabamisad, sul 20 qulaa. magram mxolod xuTi cdis piria saWiro am 20 qulis misaRebad. cdis pirTa Soris sqemaSi am 20 qulis misaRebad saWiro iqneboda 20 sxvadasxva cdis piri. ase rom, rodesac cdis pirebis moZieba Znelia an rodesac cdis pirebis moZieba da maTTvis instruqciebis micema bevrad met dros moiTxovs, vidre TviTon eqsperimentuli davalebis Sesruleba, cdis pirTa Sida sqema SeiZleba upiratesi iyos cdis pirTa Soris sqemasTan SedarebiT cdis pirebis gamoyenebis TvalsazrisiT.
damoukidebeli cvladis efeqturobais, Tu ramdenad advilad xdeba eqsperimentSi damoukidebeli cvladis efeqtis dadgena, nawilobriv damokidebulia am cvladis efeqtis siZliereze. cdis pirTa Sida sqema xSirad ufro mgrZnobiarea damoukidebeli cvladis efeqtis aRmoCenis mxriv, vidre cdis pirTa Soris sqema. amdenad, cdis pirTa Sida sqemas SeiZleba upiratesoba mieniWos, rodesac damoukidebeli cvladis mosalodneli efeqti sustia. cdis pirTa Sida sqema metad mgrZnobiarea imis gamo, rom TiToeuli cdis piri iRebs damoukidebeli cvladis yovel dones da xvdeba Carevis yvela pirobaSi. cdis pirTa Sida dispersiuli analizi
21
gamoacalkevebs cvalebadobas cdis pirTa Soris individualuri gansxvavebebis gamo (anu S faqtoris gamo cvalebadobas - MSS), ase rom am ukanasknels ar Seaqvs wvlili F-is Secdomis nawilSi (anu MSAxS). cdis pirTa Soris sqemaSi es cvalebadoba Sedis MSSecdomaSi. ase rom, Secdomis veqtori cdis prTa Sida sqemaSi (anu MSAxS) ufro mcire iqneba, vidre Secdomis veqtori cdis pirTa Soris sqemaSi (anu MSSecdoma). ufro mcire Secdomis veqtori iwvevs Frealuris ufro did mniSvnelobas, ris Sedegadac ufro mosalodnelia, rom H0-s uaryofa miviRoT. ase rom, eqsperimentSi, sadac cdis pirTa Soris didi individualuri gansxvavebebia da damoukidebeli cvladis efeqti ar unda iyos Zlieri, cdis pirTa Sida sqema ufro kargad gamoavlens damoukidebeli cvladis efeqts, vidre cdis pirTa Soris sqema.
Carevis mravaljeradi efeqtebicdis pirTa Sida sqemaSi cdis pirs damoukidebeli cvladis yovel doneze zomaven drois garkveuli periodis ganmavlobaSi. Carevebis es Tanmimdevroba cdis pirTa Sida sqemaSi Carevis mravaljeradi efeqtebis moxdenis SesaZleblobas qmnis; damoukidebeli cvladis donis efeqti SeiZleba damokidebuli iyos mis winamorbed doneebze. Carevis mravaljeradi efeqtebi moicavs rogorc gavarjiSebis, aseve Carevis gadatanis efeqtebs. gavarjiSebis efeqtebi aris Sesrulebis cvlilebebi, romlebic imis gamo xdeba, rom eqsperimentuli davaleba ganmeorebiT sruldeba. am cvlilebebma SeiZleba gamoiwvios an gaumjobesebuli, an gauaresebuli Sesruleba eqsperimentis msvlelobisas. magaliTad, eqsperimentis magaliTSi, sadac izomeba iluziis xarisxi iluziis oTx gansxvavebul pirobaSi, cdis pirebs SeiZleba mobezrdeT eqsperimenti misi msvlelobisas an SeiZleba isini, rac ufro met Sefasebebs akeTeben, miT ufro skrupulozurni xdebian TavianT SefasebebSi. orive SemTxvevaSi cdis piris Sesrulebam SeiZleba Secvalos, moqmedebs Tu ara qcevaze iluziis piroba.Carevis gadatanis efeqtebi aris damoukidebeli cvladis erTi donis specifikuri efeqtebi, romlebic SeiZleba ise iqnen gadatanili, rom gavlena moaxdinon Sesrulebaze, damoukidebeli cvladis Semdgom doneze. magaliTad, amocanaSi, sadac iluziebis aRqma ganixileba, rogorc iluziis pirobis funqcia, Tu cdis pirebi sakontrolo iluzias yovelTvis bolo rigSi xedavdnen, maT SeiZleba aReqvaT iluzia, radgan sakontrolo pirobis win isini xedavdnen iluziis Semqmnel pirobebs. maT aqvT iluziis danaxvis molodini, romelic gadaitaneba sakontrolo pirobaze. Tu isini sakontrolo pirobas pirvel rigSi naxavdnen iluziis danaxvis molodinis gareSe, isini mas ar aRiqvamdnen rogorc iluzias. gavarjiSebis efeqtebi da Carevis gadatanis efeqtebi mniSvnelovania, radgan Tu isini Cndebian da ar arian kontrolirebadi, isini arTuleben eqsperiments. am efeqtebis kontroli Cveulebriv xorcieldeba cdis pirebisaTvis Carevis pirobebis sxvadasxva TanmimdevrobiT miwodebis gziT. ganxiluli sakiTxebidan – cdis pirebis saWiro raodenoba, damoukidebeli cvladis mosalodneli efeqturoba da Carevis mravaljeradi efeqtebis miRebis albaToba – TiToeuli unda miviRoT mxedvelobaSi, rodesac kvlevis sqemas virCevT. cdis pirebis efeqturad gamoyeneba da ufro meti mgrZnobiaroba damoukidebeli cvladis efeqtis dasafiqsireblad cdis pirTa Sida sqemis upiratesobebia. xolo Carevis mravaljeradi efeqtebis miRebis SesaZlebloba am sqemis naklovanebaa. Carevis mravaljeradi efeqtebi ar SeiZleba moxdes cdis pirTa Soris sqemaSi, radganac yoveli cdis piri eqvemdebareba damoukidebeli cvladis mxolod erTi dones. ase rom, rodesac eqsperimentSi mosalodnelia Carevis mravaljeradi efeqtebis miReba da maTi gakontroleba
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ar aris advili Carevebis Tanmimdevrobis gziT, sasurvelia cdis pirTa Soris sqemis gamoyeneba. radganac Carevis mravaljeradi efeqtebi xdeba maSin, rodesac mravali damoukidebeli cvladi gvaqvs da am efeqtebis gakontroleba ar aris advili cdis pirTa Sida sqemaSi, bihevioristi mecnierebi xSirad arCeven cdis pirTa Soris sqemis gamoyenebas. Carevis mravaljeradi efeqti: cdis pirTa Soris sqemaSi Sesrulebis cvlilebebi, romlebic xdeba imis gamo, rom mowmdeba damoukidebeli cvladis yovel doneze. gavarjiSebis efeqti: Carevis mravaljeradi efeqti, romelic xdeba imis gamo, rom cdis pirebi SeiZleba gavarjiSdnen an daiRalnen eqsperimentis davalebis Sesrulebisas. Carevis gadatanis efeqti: Carevis mravaljeradi efeqti, romelic xdeba maSin, rodesac damoukidebeli cvladis erTi donis erTi efeqti gadaitaneba, gavlenas axdens Sesrulebaze damoukidebeli cvladis meore doneze.
SeamowmeT Tqveni codna XII.3
1. gansazRvreT: Carevis mravaljeradi efeqtebi, gavarjiSebis efeqti, Carevis gadatanis efeqti. 2. rodesac adamianebis geografiul adgilmdebareobebze fiqroben, adgilis maT mier identifikaciaze xSirad gavlenas axdens Tanadaqvemdebarebis gadaxra. es niSnavs, rom iseTi geografiuli adgilebi, rogoricaa qalaqebi, moTavsebulia ufro did geografiul arealSi, rogoricaa regioni an qveyana. ufro didi geografiuli arealebi (anu Tanadaqvemdebarebuli adgilebi) SeiZleba gavlenas axdendnen imaze, Tu rogor warmovidgenT maTSi moTavsebul adgilebs. magaliTad, kanada amerikis SeerTebuli Statebisagan CrdiloeTiT aris ganlagebuli, Tumca arsebobs zogierTi kanaduri qalaqi, romelic bevrad ufro samxreTiT mdebareobs, vidre zogierTi aSS-s qalaqi. magram adamianebis umetesoba CaTvlida, rom aSS-s qalaqebi ufro samxreTiTaa, ubralod imis gamo, rom SeerTebuli Statebi kanadis samxreTiT mdebareobs. marTlac, fridmanma da braunma (Friedman and Brown, 2000) aRmoaCines, rom adamianebi Tvlidnen, rom vaSingtonSi mdebare sietli (SeerTebuli Statebi) bevrad ufro samxreTiTaa, vidre niufaundlendSi mdebare sent-jonsi (kanada), Tumca orive qalaqi erTsa da imave ganedzea. davuSvaT, Tqven gainteresebT es sakiTxi da sTxoveT cdis pirebs, daesaxelebinaT sami arseboTad erT ganedze ganlagebuli qalaqis ganedebi. es qalaqebia dalasi, texasis Stati (aSS), tihuana (meqsika) da tripoli (libia). yovel cdis pirebs eZleva instruqcia da utardeba ganedis dadgenis mcire savarjiSo, amis Semdeg ki sTxoven, daasaxelos yoveli qalaqis ganedi. miRebuli iyo Semdegi monacemebi:'
cdis piriqalaqi (A)dalasi (A1) tihuana (A2) tripoli (A3)
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ipoveT saSualo da standartuli gadaxra Carevis TiToeuli pirobisaTvis. Semdeg am qulebze CaatareT cdis pirTa Sida erTfaqtoriani dispersiuli analizi imis gansasazRvrad, arsebobs Tu ara Tanadaqvemdebarebis gadaxra ganedebis dasaxelebisas da upasuxeT Semdeg kiTxvebs:a. CamoayalibeT F kritetiumis statistikuri hipoTezebi am qulebisaTvis.b. ra aris Frealuris mniSvneloba?
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g. ra aris Frealuris df-ebi?d. ra aris Fkritikuli .05 doneze?e. ra aris uaryofis are FrealurisaTvis?v. xvdeba Tu ara Frealuri uaryofis areSi?z. ra gadawyvetilebebs miiRebT statistikuri hipoTezebis Sesaxeb? uaryofT Tu ar uaryofT H0-s? miiRebT Tu ar miiRebT H1-s?T. ras daaskvniT, saSualoebi erTi da igive Tu sxvadasxva populaciebidanaa?i. arsebobs Tu ara statistikurad mniSvnelovani sxvaoba sul mcire saSualoebis erT wyvils Soris?k. saWiroa Tu ara am eqsperimentSi mravlobiTi Sedarebis kriteriumebi? daasabuTeT Tqveni pasuxi.l. ra aris tukis CD-s mniSvneloba?m. romeli wyvilTaSorisi sxvaobebia statistikurad mniSvnelovani?n. ra aris 2 am eqsperimentisaTvis?o. aRwereT am eqsperimentis Sedegebi im stilis gamoyenebiT, romelic ilustrirebuli iyo am Tavis seqciaSi "dispersiuli analizis Sedegebis prezentacia".
savarjiSoebi # 3 da 4 warmoadgens cdis pirTa Sida erTfaqtoriani dispersiuli analizis angariSis nimuSebs. TiToeuli savarjiSosaTvis upasuxeT Semdeg kiTxvebs:
a. damoukidebeli cvladis ramdeni done iyo gamoyenebuli eqsperimentSi?b. ramdeni cdis piri iRebda monawileobas eqsperimentSi?g. ra aris Frealuris mniSvneloba?d. ra aris Fkritikulis mniSvneloba .05 mniSvnelovnobis doneze?e. uaryofT Tu ar uaryofT H0-s?v. miiRebT Tu ar miiRebT H1-s?z. arsebobs Tu ara sul mcire erTi statistikurad mniSvnelovani sxvaoba saSualoebs Soris?T. romeli Carevis pirobebi gansxvavdeba mniSvnelovnad, Tuki aseTebi saerTod arseboben?
1. saSualo reaqciis dro martivi stimulis pirobaSi 396 miliwami (mw) iyo, maSin, rodesac rTuli stimulis pirobaSi - 412 mw. alfas .05 doneze cdis pirTa Sida erTfaqtorianma dispersiulma analizma aCvena saSualoebs Soris mniSvnelovani sxvaoba, F (1,18) = 4.76, MSE = 510.924, p < .05.
2. sworad amocnobili saxeebis saSualo raodenoba 13.9 iyo pirvel cdaSi, 14.6 - meore cdaSi da 14.1 - mesame cdaSi. alfas .05 doneze cdis pirTa Sida erTfaqtorianma dispersiulma analizma ar aCvena sxvaoba cdebSi sworad amocnobis raodenobebs Soris, F (2,22) = 2.81, MSE = 0.555, p > .05.
Sejameba
cdis pirTa Sida erTfaqtorian sqemaSi cdis pirTa erTi jgufi ganicdis damoukidebeli cvladis yoveli donis zemoqmedebas.
cdis pirTa Sida erTfaqtoriani dispersiuli analizi gamoiyeneba cdis pirTa Sida erTfaqtoriani mravaldoniani sqemis qulebis gasaanalizeblad.
cdis pirTa Sida erTfaqtoriani dispersiuli analizidan miiReba sami kvadratebis saSualo: MSA, romelic icvleba damoukidebeli cvladis efeqtTan erTad da Carevis pirobebis da cdis pirTa urTierTqmedeba MSS, romelic icvleba cdis pirTa Soris gansxvavebebTan erTad, da MSAxS, romelic icvleba pirobebis cdis pirebTan urTierTqmedebasTan erTad da iZleva eqsperimentSi Secdomis cvalebadobis sazoms.
F statistika, romelic gamoiyeneba cdis pirTa Sida erTfaqtorian dispersiul analizSi, aris F = MSA/ MSAxS.
F statistikis gamoyeneba misdevs statistikuri hipoTezebis Camoyalibebis Cveulebriv nabijebs, rogorebicaa mniSvnelovnobis
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donis dadgena, uaryofis aris dadgena, Frealuris gamoTvla da statistikur hipoTezebTan dakavSirebuli gadawyvetilebebis miReba.
rodesac damoukidebel cvlads sami an meti done aqvs, statistikurad mniSvnelovani F moiTxovs mravlobiTi Sedarebis kriteriumis gamoyenebas, raTa dadgindes statistikurad mniSvnelovani wyvilTaSorisi Sedarebebi.
tukis kriteriumi gamoiyeneba yvela SesaZlebeli wyvilTaSorisi saboloo SedarebisaTvis.
2 SeiZleba gamoyenebuli iqnes, rogorc Carevis efeqtis siZlieris sazomi.
cdis pirTa Soris da cdis pirTa Sida sqemebs Soris arCevanis gakeTeba moiTxovs Semdegi sakiTxebis ganxilvas: cdis pirTa saWiro raodenoba, damoukidebeli cvladis mosalodneli efeqturoba, da Carevis mravaljeradi efeqtebis miRebis SesaZlebloba.
------------------------------------------------------------------------------------------------------------------------------ZiriTadi terminebi da simboloebi
kritikuli sxvaoba (CD)dfA
dfS
dfAxS
dfsruli
eta kvadrati (2)A faqtori S faqtori MSA
MSS MSAxS
Carevis mravaljeradi efeqtebi
nA
gavarjiSebis efeqti ganmeorebiTi gazomvis sqema SSA
SSS
SSAxS
SSsruli
Carevis gadatanis efeqtiCarevis pirobebis da cdis pirebis urTierTqmedebis sqemaCarevis pirobebis da cdis pirebis urTierTqmedeba (AxS) cdis pirTa Sida sqema
__________________________________________________________________Tavis damatebacdis pirTa Soris orfaqtoriani dispersiuli analizis gamoTvla formulebis meSveobiT__________________________________________________________________am damatebaSi mocemulia gamoTvliTi formati cdis pirTa Sida erTfaqtoriani dispersiuli analizisaTvis. eqsperimenti A damoukidebeli cvladis oTxi doniT da xuTi cdis piriT yovel doneze qvemoTaa warmodgenili:
cdis piri A faqtori________________________________________________A1 A2 A3 A4
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S1
S2
S3
S4
S5
X11
X21
X31
X41
X51
X12
X22
X32
X42
X52
X13
X23
X33
X43
X53
X14
X24
X34
X44
X54
sadac Xij = cdis piris qulaTa = qulebis jami damoukidebeli cvladis donisaTvisTS = qulebis jami cdis pirisaTvisG = qulebis saerTo sruli jaminA = qulebis jami damoukidebeli cvladis donezea = damoukidebeli cvladis doneebis raodenobaN = qulebis sruli raodenoba.
am aRniSvnebis gamoyenebiT miiReba oTxi ricxviTi mniSvneloba:
[1] = yvela qulis kvadratebis jami
[2] = damoukidebeli cvladis TiToeuli donis kvadratebis jami, gayofili cdis pirebis raodenobaze.
[3] = TiToeuli cdis piris qulebis kvadratebis jami, gayofili A
faqtoris doneebis raodenobaze.
[4] = saerTo sruli jamis kvadrati, gayofili qulebis srul raodenobaze.
am ricxviTi mniSvnelobebis gamoyenebiT miiReba Semdegi dispersiuli analizi:
wyaro SS dfa MS FA faqtori
cdis pirebi (S)
AxS
sul
[2] – [4]
[3] – [4]
[1] – [2] – [3] + [4]
[1] – [4]
a - 1
nA - 1
(a - 1)( nA - 1)
N - 1 ar gamoiTvleba
am gamoTvlebis ilustraciisaTvis gamoviyenoT cxrilSi # 12.2 moyvanili monacemebi, romelTa dispersiuli analizi Sejamebulia cxrilSi # 12.3.
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cdis piriA faqtori cdis piris
jamebiA1 A2 A3 A4
1 16.6 15.8 14.7 14.4 = 61.502 16.9 15.6 15.1 13.8 = 61.403 17.1 16.1 14.8 13.9 = 61.904 17.2 16.3 15.2 14.1 = 62.805 16.8 15.7 15.3 14.3 = 62.10
= 84.60 79.50 75.10 70.50 = 309.70
nA = 5, a = 4 da N = 20.ricxviTi mniSvnelobebia:
[1] = [(16.6)2 + ... + (16.8)2 + (15.8)2 + ... + (15.7)2 + (14.7)2 + ... (15.3)2 + (14.4)2 + ... +
(14.3)2] = 4818.630[2] = = 4817.534
[3] = = 4796.018
[4] = = 4795.704
Semdeg
SSA = [2] – [4] = 4817.534 – 4795.704 = 21.830dfA = a – 1 = 4 – 1 = 3MSA = = 7.277
SSS = [3] – [4] = 4796.018 – 4795.704 = 0.314dfS = nA – 1 = 5 – 1 = 4MSS = = 0.078
SSAxS = [1] – [2] – [3] + [4] = 4818.630 - 4817.534 - 4796.018 + 4795.704 = 0.782dfAxS = (a – 1)(nA – 1) = (4 - 1)(5 – 1) = 12MSAxS = = 0.065
SSsruli = [1] – [4] = 4817.534 – 4795.704 = 22.926dfsruli = N – 1 = 20 – 1 = 19Frealuri = = = 111.95
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dispersiuli analizis Sejamebaa:
wyaro SS df MS FA faqtoricdis pirebi AxSsul
21.8300.3140.78222.926
341219
7.2770.0780.065
111.95*
* p < .01
am gamoTvliTi midgomis Sedegad miRebuli mniSvnelobebi identuria im mniSvnelobebisa, romelic warmodgenilia cxrilSi # 12.3 dispersiuli analizis ganmartebiTi formulebidan.
__________________________________________________________________kiTxvebi________________________________________________________
1. davuSvaT, gainteresebT, moqmedebs Tu ara sityviT (mxiaruli, neitraluri an sevdiani) gamoxatuli xasiaTis tipi imaze, Tu ramdenad kargad xdeba mocemuli siidan sityvis damaxsovreba. SeadgenT eqvsi samxiarulo sityvisagan (magaliTad, mxiaruli, gaciskrovnebuli), eqvsi neitraluri sityvisagan (magaliTad, gamoyvana, gadacema) da eqvsi sevdiani sityvisagan (magaliTad, daRvremili, martosuli) Semdgar sias. Semdeg rva cdis piridan TiToeuli Seiswavlis sias, sanam orjer sruli sizustiT ar gaimeorebs mas. erTi kviris Semdeg TiToeuli cdis piri cdilobs siis gaxsenebas. sworad aRdgenili erTeulebis raodenobebi, rogorc sityvis tipis funqcia, ase gamoiyureba:
cdis pirisityvis tipibednieri neitraluri mowyenili
12345678
56453625
43531323
34212431
a. sityvis pirobis TiToeuli tipisaTvis ipoveT saSualo da standartuli gadaxra. Semdeg gaaanalizeT qulebi cdis pirTa Sida erTfaqtoriani analizis meSveobiT, raTa upasuxoT Semdeg kiTxvebs: moqmedebs Tu ara sityvis tipi aRdgenaze? gamoiyeneT .05 mniSvnelovnobis done. Tu saWiroa, gamoiyeneT tukis HSD kriteriumi mravlobiTi SedarebisaTvis.
b. ra aris damoukidebeli cvladis - sityvis tipis - efeqtis siZliere?g. aRwereT Sedegebi im stilis gamoyenebiT, romelic
ilustrirebuli iyo am Tavis seqciaSi "dispersiuli analizis Sedegebis prezentacia".
2. sanimuSo magaliTSi 10.3 warmoadgenili iyo cdis pirTa Sida sqemis mixedviT agebuli morinagas (Morinaga) SeuTavseblobis iluziis kvleva [ix. suraTi # 10.3, paneli (a)]. davuSvaT, eqsperimentators surs, icodes, Secvlis Tu ara cdis pirebis mier iluziis aRqmas maTi instruqtireba am iluziis Sesaxeb. Tavdapirvelad eqsperimentatorma sTxova 12 cdis pirs,
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SeeTavsebinaT (erT xazze ganelagebinaT) kuTxeebis wveroebi da gazoma Secdomis raodenoba yoveli adamianisTvis. mas Semdeg, rac cdis pirebma SeaTavses wveroebi, maT Seatyobines iluziis Sesaxeb da kidev erTxel sTxoves kuTxeebis SeTavseba. miRebuli iqna Secdomis ori gazomva (milimetrebSi) yoveli cdis pirisaTvis:
cdis piriinstruqciis piroba (A) _______________________________________ instruqciamde (A1 ) instruqciis Semdeg (A2)
123456789101112
1.32.12.51.93.02.51.82.43.13.42.52.9
1.42.02.72.03.42.81.62.53.33.42.32.8
a. instruqciis TiToeuli pirobisaTvis ipoveT saSualo da standartuli gadaxra. Semdeg gaaanalizeT qulebi cdis pirTa Sida erTfaqtoriani analizis meSveobiT, raTa upasuxoT Semdeg kiTxvebs: iqonia Tu ara instruqciam gavlena aRqmuli iluziis raodenobaze? gamoiyeneT .05 mniSvnelovnobis done.
b. SeadareT Frealuri me-9 Tavis "kiTxvebidan" meoTxeSi moyvanil tdamokidebuls. sworia Tu ara = tdamokidebuli?
g. dispersiuli analizisa da tdamokidebuli kriteriumis gamoyenebisSedegad erTsa da imave daskvnebs gaakeTebT damoukidebeli cvladis efeqtis Sesaxeb, Tu gansxvavebulebs?
d. aRwereT am eqsperimentis Sedegebi im stilis gamoyenebiT, romelicilustrirebuli iyo am Tavis seqciaSi "dispersiuli analizis Sedegebis prezentacia".
3. davuSvaT, gegmavT, CaataroT cdis pirTa Sida erTfaqtoriani eqsperimenti damoukidebeli cvladis xuTi doniTa da 12 cdis piriT.
a. dawereT dispersiuli analiziT Semowmebuli statistikuri hipoTezebi im qulebisaTvis, romlebsac Tqven miiRebdiT.
b. ipoveT df am sqemis dispersiuli analizisaTvis. g. ra aris Fkritikulis mniSvneloba .05 mniSvnelovnobis doneze am
sqemis dispersiuli analizisaTvis? d. davuSvaT, rom Frealuris mniSvneloba ufro didi iyo, vidre
Fkritikulis mniSvneloba. ra gadawyvetilebebs miiRebdiT H0-Tan da H1-Tan dakavSirebiT?
e. davuSvaT, rom am eqsperimentisaTvis Tqven uaryaviT H0 damiiReT H1. ra daskvnas gaakeTebdiT am gadawyvetilebebidan Carevis saSualoebis Sesaxeb?
4. qvemoT moyvanilia dispersiuli analizis arasruli Sejamebis cxrilebi. SS-s, df-sa da MS-s Soris arsebuli mimarTebebis gamoyenebiT TiToeul cxrilSi
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SeitaneT gamotovebuli mniSvnelobebi. Semdeg TiToeuli cxrilisaTvis upasuxeT Semdeg kiTxvebs:
a. ramdeni done hqonda damoukidebel cvlads?b. damoukidebeli cvladis TiToeul doneze ramdeni qula iyo
miRebuli?g. ramdeni cdis piri iRebda monawileobas kvlevaSi?d. aris Tu ara Frealuris mniSvneloba statistikurad
mniSvnelovani .05 doneze?e. ra gadawyvetilebebs miiRebT H0-isa da H1-isaTvis yovel
analizSi?
cxrili # 1
wyaro SS df MS FA faqtoriS faqtoriAxSsul
____138.00253.00____
____234671
11.006.00____
____
cxrili # 2
wyaro SS df MS FA faqtoriS faqtoriAxSsul
60.00133.00____573.00
____1995____
____7.00____
____
5. ramdenime eqsperimentatorma gamoikvlia Cvilis interesi ucnobi saxeebis mimarT nacnob saxeebTan SedarebiT. 14 Cvilidan TiToeuli aTvalierebda nacnobi saxeebis (magaliTad, dedis da mamis fotoebi), ucnobi saxeebis (magaliTad, CvilisTvis ucnobi mamakacebisa da qalebis fotoebi) da saxis zomis carieli ovalebis fotoebs. eqsperimentatorebi afiqsirebdnen dros, romlis ganmavlobaSic TiToeuli Cvili akvirdeboda saxes. cxrilSi # 1 warmodgenilia stimulis piroba da drois saSualo xangrZlivoba, romelic ixarjeboda stimulze TiToeul pirobaSi. cxrilSi # 2 warmodgenilia am monacemebis dispersiuli analizi.
cxrili # 1dakvirvebis saSualo dro (wamebSi), rogorc stimulis pirobis funqcia.
stimulis pirobanacnobi saxe (A1) ucnobi saxe (A2) carieli ovali (A3)34.2 26.8 18.5
cxrili # 2dispersiuli analizis Sejameba cxrilSi # 1 warmodgenili dakvirvebis saSualo droebisaTvis.
wyaro SS df MS Fstimulis piroba (A)cdis pirebi (S)AxSsul
1727.322047.371404.525179.21
2132641
863.66157.4954.02
15.99*
30
* p < .01
tukis HSD-m mogvca CD = 6.9 wuTi mniSvnelovnobis .05 doneze. a. ra aris stimulis pirobis efeqti dakvirvebis droze?b. aRwereT am eqsperimentis Sedegebi im stilis gamoyenebiT, romelic
ilustrirebuli iyo am Tavis seqciaSi "dispersiuli analizis Sedegebis prezentacia".
31