paaristhithikamaaya thettu

vyakthikalude swabhaavathekkurichulla nigamanangal aaa vyakthikal ulppedunna grooppinekkurichulla nigamanagalil ninnu oohikkumbol sambhavikkunna sthithivivarakkanakku daattayude vyaakhyaanathile aupachaarikamaaya oru thettaanu paaristhithika pizhav (paaristhithika "anumaanam" pizhav allengil janasamkhyaa pizhav). "paaristhithika bhrant" ennathu chilappol vibhajanathinte bhranthiye vivarikkan upayogikkunna oru padamaanu, ithu oru sthithivivarakkanakku bhrant allah. kevalashaasthrathinte aashayaparamaaya kazhchappadil, naalu pothuvaaya paaristhithika veezhchakal ivayaanu 
parasparabandham/bandham bhaagangalude bandhavum mothatthilulla bandhavum sambandhicha ashayakkuzhappam, 
savisheshathakal bhaagangalude savisheshathakalum mothatthinte savisheshathakalum thammilulla ashayakkuzhappam, 
extropolation/ekstenshan. bhaagikamaayi ariyappedaathathum koodaathe/allengil bhaaviyile mothathilullathum thaarathamyena bhagikamaaya vivarangalil ninnu manassilakkunna bhaagikamaayi ariyappedaathathum thettaaya anumanangalil ninnulla ashayakkuzhappam.
vyakthigatha bhagangalumaayi bandhamillaattha gunangal, "anthareeksham", "maanasikavastha", "vaibukal" enniva thammilulla ashayakkuzhappam, virudhamaayi gunangal, hysittikal allengil avibhaajya yoonittukalude identittikal.
sthithivivarakkanakku veekshanakonil ninnu nokkumbol, aupachaarika nigamanangal undaakkunnathin sariyaaya sthithivivarakkanakku modalukal vyakthamaakkunnathiloodeya vyakthigatha thalatthilulla daattayil nireekshikkaatha bandhangal undakkaan motham daatta upayogikkunnathiloodeyum eee ashayangal ekeekrithamaakkaan kazhiyum.
udaaharanagal.
sharashariyum madhyavum.
oru vyakthiyude saadhyathakal pariganikkumbol oru janasamkhyaa sharaasharikk lalithamaaya vyaakhyaanamundennu anumaanikkunnath paaristhithika viddithathinte oru udaaharanamaanu.
udaaharanathinu, oru grouppinte sharashari score poojyathekkaal valuthaanenkil, aaa groupile oru kramarahita vyakthikk negatteevu skorinekkaal positteev score undakanulla saadhyatha kooduthalaanennu ithu ardhamaakkunnilla (positteev skorukalekkaal negatteevu skorukal ullidatholam kaalam oru vyakthikk negatteevu score undakanulla saadhyatha kooduthalaanu). athupole, oru prathyeka koottam aalukalkk saadhaarana janasamkhyayekkaal kuranja sharashari ikyu undennu alakkukayaanengil, kramarahithamayi thiranjedukkappetta oru amgathinu saadhaarana janasamkhyayude sharashari ikyuyekkaal kuranja ikyu undakanulla saadhyatha kooduthalaanennu nigamanam cheiyunnathu thettaanu; kramarahithamayi thiranjedukkappetta oru amgathinu saadhaarana janasamkhyayile kramarahithamayi thiranjedukkappetta amgathekkaal kuranja ikyu undakanulla saadhyatha kooduthalaanennathum nirbandhamalla. ganithashaasthraparamaayi, oru vitharanathinu positteev sharashari undayirikkaam, ennaal negatteevu median undayirikkaam enna vasthuthayil ninnaan ithu varunnath. eee vasthu vitharanathinte vakrathayumaayi bandhappettirikkunnu.
thaazhepparayunna samkhyaaparamaaya udaaharanam pariganikkuka
vyakthigathavum samagravumaaya parasparabandhangal.
pradhaanamaayum catholica pradeshangale apekshichu protestant pradeshangal kooduthal aathmahathyaanirakkullavanna emily durkheem muthalulla gaveshanangal soochippikkunnu. friedman parayunnathanusarichu, durkheyiminte kandethalukal oru vyakthiyude mathathe ayaalude allengil avalude aathmahathya apakadavumaayi bandhippikkunnu enna ashayam paaristhithika viddithathinte oru udaaharanamaanu. oru group thalatthilulla bandham vyakthiyude thalatthilulla bandhathe yaanthrikamaayi chithreekarikkunnilla.
athupole, vyakthigatha thalatthil, sambathu republican vottinulla pravanathayumaayi kriyaathmakamaayi bandhappettirikkunnavellum, sambannamaaya samsthaanangal janaadhipathyaparamaayi vottu cheiyunna pravanatha kaanikkunnuvenn njangal nireekshikkunnu. udaaharanathinu, 2004ll republican sthaanaarthi jorjju dablyu. ettavum daridramaaya pathinanju samsthaanangalil bush vijayichu, ettavum sambannamaaya 11 samsthaanangalil 9 ennathilum janaadhipathya sthaanaarthi joonn kerry vijayichu. ennittum 200,000 dollaril kooduthal vaarshika varumaanamulla 62 sathamaanam watermar bushinu vottu cheythu, ennaal 15,000 dollaro athil kuravo vaarshika varumaanamulla 36 sathamaanam watermar maathramaan bushinu vottu cheythath.
vyakthigatha sambathu niyanthrichathinusheshavum samsthaanathinte motham sambathu votting mungananakale baadhikkukayaanenkil motham-thala parasparabandham vyakthigatha-thala parasparabandhathil ninnu vyathyasthamayirikkum. votting mungananayile yadhaartha preraka ghadakam svayam manassilakkiya aapekshika sambathaanu; orupakshe ayalkkarekkaal mikachathaayi svayam kaanunnavar republican vottinaayi kooduthal saadhyathayund. eee saahacharyathil, oru vyakthi sambannayaayaal republican vottucheyyaan kooduthal saadhyathayund, ennaal avalude ayalvaasiyude sambathu vardhikkukayaanenkil (sambannamaaya oru raajyathin kaaranamaakunnu) aval oru janaadhipathyavaadiye vottucheyyaan kooduthal saadhyathayund. 
ennirunnaalum, samsthaana thalatthilum vyakthigatha thalatthilumulla sambathine adisthaanamaakkiyulla votting sheelangalile nireekshanaparamaaya vyathyasam mukalil charcha cheythathupole uyarnna sharashariyum uyarnna saadhyathakalum thammilulla pothuvaaya ashayakkuzhappavum vishadeekarikkaam. samsthaanangal kooduthal sambannaraayathinaal avaa sambannamaayirikkilla (athaayath.iii. 200, 000 dollaril kooduthal vaarshika varumaanamulla kooduthal aalukal), marichu avarkk valare kurachu sambannaraaya vyakthikal ullathinaal; sambannamaaya samsthaanangalile vyakthikal sambannaraakaanulla saadhyatha kooduthalaanennu thettayi anumaanikkunnathil ninnaan paaristhithika bhrant undaakunnath.
vividha thalangalil ninnulla vishakalanavum prathyaaghaathangalum samyojippikkunna saamoohika shringalakalude padanangalil paaristhithika pizhavukalude niravadhi udaaharanagal kaanam. sumatrayile karshakarude shringalayekkurichulla oru academic prabandhatthil ithu chithreekarichirikkunnu.
robinsons paradox.
vilyam ezz. 1950-ll ezhuthiya oru prabandham. 1930 leeii sensus prakaram, oro samsthaanathinum columbia jillaykkum usinu purathu janicha janasamkhyayude nirakkum niraksharathayude nirakkum robinson kanakkakki. eee rund kanakkukalum − 0.53 enna negatteevu paraspara bandhavumaayi bandhappettirikkunnave addeham kaanichu; mattoru vidhathil paranjaal, oru samsthaanathe kudiyettakkaarude anupatham kooduthalaanengil, athinte sharashari niraksharatha kurayum (allengil, thulyamaayi, athinte sharashari saksharatha kooduthalaanu). ennirunnaalum, vyakthikale pariganikkumbol, niraksharathayum jananavum thammilulla parasparabandham + 0.12 aayirunnu (kudiyettakkaar thaddesheeya pouranmaarekkaal sharashari kooduthal nirakshararaayirunnu). thaddesheeya janasamkhya kooduthal saksharathayulla samsthaanangalil kudiyettakkaar sthirathaamasamaakkunnathinta falamaayaanu samsthaana janasamkhyayude thalatthilulla prathikoola parasparabandham undaayathenn robinson kaanichu. janasamkhyayude nilavaaram allengil "paaristhithika" daattayude adisthaanathil vyakthikalekurichulla nigamanagalil athicherunnathinethire addeham munnariyipp nalki. 2011ll robinsons nadatthiya paaristhithika bandhangalude kanakkukoottalukal thettaaya samsthaana thalatthilulla daattaye adisthaanamaakkiyullathaane kandethi. mukalil soochippicha − 0.53-nte parasparabandham vaasthavathil − 0.46 aanu. robinsons paper adisthaanaparamaayirunnu, ennaal 'paaristhithika bhrant' enna padam 1958 vare selvin upayogichirunnilla.
aupachaarikamaaya prashnam.
motham alavukalude (allengil paaristhithika parasparabandham) parasparabandham vyakthigatha alavukalude parasparabandhathinu thulyamalla. vyakthigatha thalatthil "x" "i", "y" "i" enningane rund alavukal kondu soochippikkuka. n" valuppathilulla grouppukalilulla motham alavukalude covarians enna soothravaakyam
rund samyojitha veriyabilukalude covarians ore vyakthikalkullile rund veriyabilukalude koveriyansine mathramalla, vyathyastha vyakthikal thammilulla veriyabilukalude koveriyansukaleyum aasrayichirikkunnu. mattoru vidhathil paranjaal, motham veriyabilukalude parasparabandham vyakthigatha thalatthil prasakthamallaatha cross sekshanal efakttukal kanakkiledukkunnu.
paraspara bandhangalude prashnam swaabhaavikamaayum motham veriyabilukalile regressionukalkku oru prasnamaanan athinaal kaaryakaarana prathyaaghaathangal alakkaan aagrahikkunna oru gaveshakane sambandhichidatholam parasparabandham thettaanu oru pradhana prashnam. phala soothravaakyam _ 2 formula _ 3 swaadheenikkunna oru regression modalil ninnu aarambikkuka.
vyakthigatha samavaakyangal sangrahikkunnathiloodeyaanu motham thalatthilulla regression model labhikkunnatha
regressorukalum pishakukalum mothatthilulla thalatthil parasparabandhithamaakunnathil ninnu onnum thadayunnilla. athinaal, saadhaaranayaayi, motham daattayil oru regression pravarthippikkunnathu vyakthigatha daatta upayogichu oru regression pravarthippikkunnathinni ore model kanakkakkunnilla.
motham model shariyaanenkil maathram
ithinartham, formula _ 3, formula _ 10 enniva niyanthrikkunnath formula _ 11 nirnnayikkunnilla ennaanu.
motham, vyakthigatha nigamanagalkkidayil thiranjedukkuka.
oraalkk motham modalil thaalpparyamundengil motham daattayil regressionukal pravarthippikkunnathil thettonnumilla. udaaharanathinu, oru samsthaana govarnore sambandhichidatholam, police senayude vardhanavinte nayaparamaaya prathyaaghaathangalil oraalkk thaalpparyamundengil samsthaana thalatthil kuttakrithya nirakkil police senaykkidayil pinvaangal nadathunnathu sariyaanu. ennirunnaalum, samsthaana thalatthile paraspara bandhatthil ninnu nagarathalatthile kuttakrithya nirakkil police senayude vardhanavinte aaghaatham oru sitti kaunsil oohichaal paaristhithika vidditham sambhavikkum.
chila nayangalil mothatthilulla prathyaaghaathangal manasilakkaan mothatthilullatho vyakthigathamo aaya regressionukal pravarthippikkaan thiranjedukkunnathu inipparayunna trade-oof aasrayichirikkunnu motham regressionukalkku vyakthigatha thalatthilulla daatta nashtappedunnu, ennaal vyakthigatha regressionukal sakthamaaya modeling anumanangal cherkkunnu. chila gaveshakar abhipraayappedunnathu paaristhithika parasparabandham pothu naya pravartthanangalude falathekkurichu mikacha chithram nalkunnathinaal eee aavashyathinaayi vyakthigatha thalatthilulla parasparabandhathekkaal paaristhithika parasparabandham avar shupaarsha cheiyunnu (lubinsky & humphries, 1996). mattu gaveshakar viyojikkunnu, prathyekichu thalangal thammilulla bandhangal vyakthamaayi maathrkayaakkappedaathpol. paaristhithika vidditham thadayunnathinu, vyakthigatha daattayillaatha gaveshakarkk aadyam vyakthigatha thalatthil enthaanu sambhavikkunnathenn maathrkayaakkaanum thudarnnu vyakthigathavum group thalangalum engane bandhappettirikkunnave maathrkayaakkaanum group thalatthil enthengilum sambhavikkunnath bandhathekkurichulla dhaarana vardhippikkunnundo ennu parisodhikkaanum kazhiyum. udaaharanathinu, samsthaana nayangalude swaadheenam vilayiruthumbol, nayangalude swaadheenangal nayangalekkaal samsthaanangalkkidayil kuravaanennu ariyunnathu sahaayakamaan, uyarnna paaristhithika parasparabandhangal undaayirunnittum (rooss, 1973) naya vyathyaasangal falangalaayi nannayi vivarthanam cheyyappedunnillennu ithu soochippikkunnu.
group motham sharashariyum.
paaristhithikamaaya bhrant inipparayunna bhranthiyeyum soochippikkaam oru grouppinte sharashari motham janasamkhyayile sharashariye grouppinte valuppathaal harikkunnathukond kanakkakkunnu. amerikkayil protestantumaarude ennavum aathmahathyaanirakkum oraalkk ariyaamenn karuthuka, ennaal mathatheyum athmahathyayeyum bandhippikkunna vivarangal vyakthigatha thalatthil oraalude pakkalilla. protestantumaarude aathmahathyaanirakkil oraalkk thaalpparyamundengil, motham aathmahathyaanirakkine protestantumaarude ennathaal harikkunnath thettaanu.
aupachaarikamaayi, formula _ 12 grouppinte sharashariye soochippikkuka, namukk saadhaaranayaayi undu
ennirunnaalum, motham saadhyathayude niyamam nalkunnu
formula _ 15 0 num 1 num edayilaanennu namukkariyavunnathinaal, eee samavaakyam formula _ 12 nuu oru paridhi nalkunnu.
simpsons paradox.
simpsons paradox" ennathu sradheyamaaya oru paaristhithika viddithamaanu rund janasamkhyakale grouppukalaayi vibhajikkumbol, aadya janasamkhyayile chila veriyabilukalude sharashari ellah grouppukalilum kooduthalaayirikkaam, ennaal motham janasamkhyayil kuravaayirikkum. aupachaarikamaayi, "z"-nte oro moolyavum mattoru groupine soochippikkukayum "x" chila chikilsakale soochippikkukayum cheyyumbol, athu sambhavikkam
formula _ 18 formula _ 19 neey aashrayikkaathappol, simpsansinte virodhabhaasam krithyamaayi "x" ll "y" enna regressionulla ozhivakkiya variable bayas aanu, avide regressor formula _ 20 oru dummy variable ozhivakkiya variable formula _ 19 athu edukkunna oro moolyathinum grouppukale nirvachikkunna oru kattagarikkal variablaanu. prayogam sradheyamaanu, kaaranam pakshapaatham vipareeta adayaalangalulla paaraamettarukalkk mathiyaya uyarnnathaan.
niyamaparamaaya apekshakal.
apekshakal washington govarnarative thiranjeduppinulla oru kodathi velluviliyil paaristhithika vidditham charcha cheyyappettu, athil thiranjeduppinu sesham niravadhi anadhikritha vottarmaare thiricharinju; avarude vottukal anjjaathamaayirunnu, kaaranam vottu rahasya baalattiloodeyaayirunnu. thiranjeduppil vottu cheytha anadhikritha vottukal avar vottu cheytha parisaratthe votting reethikal pinthudarnnathaayirikkumnum athinaal athinanusarichu krameekaranangal nadathanamennum velluvilikal vaadichu. oro pradeshatheyum vottarmaarude praathinidhyamillaatha saambilaanu niyamavirudhamaaya vottukal nalkiyathennum, ithu thante teaminte mattu bhaagangalil ninnulla isiro pole thanne pradeshathe sharashari vottaril ninnu vyathyasthamaayirikkamennum, eee sameepanam muzhuvan siyaattil marainers teaminteyum baiting sharashari nokki isiro suzukiyude baiting sharashari kandethaan sramikkunnathu poleyaanennum oru vidagdha driksaakshi paranju. velluvilikal nalkunnavarude vaadam paaristhithikamaaya oru thettaanenn jadji nirnnayikkukayum athu nirasikkukayum cheythu.

