phitnas nanma

oru stattistikkal modalinte phitnas oru koottam nireekshanangalkk ethra nannayi yojikkunnuvennu vivarikkunnu. fittinte nanmayude alavukal saadhaaranayaayi nireekshicha moolyangalum chodyathilulla modalinu keezhil prathekshikkunna moolyangalum thammilulla poruthakkedine samgrahikkunnu. atharam nadapadikal stattistikkal hypothesis testingil upayogikkaam, udha.jii. avasheshikkunnavayude saadhaarana nila parisodhikkuka, ore vitharanagalil ninnu rund saambilukal edukkunnundo (kolmogorov-smirnov testt kaanuka), allengil phala aavruthikal oru nirddishta vitharanathe pinthudarunnundo ennu parisodhikkuka (piyarsante chii-square testt kaanuka). vyathiyaanathinte vishakalanathil, vyathiyaanam vibhajikkunna gadakangalilonnu anuyojyamallaatha chathurangalude thukayayirikkaam.
vitharanagalkk anuyojyamaaya.
thannirikkunna vitharanam oru dattaa settinu anuyojyamaano ennu vilayiruthunnathin, inipparayunna parishodhanakalum avayude adisthaana alavukalum upayogikkaam
regression vishakalanam.
regression vishakalanathil, kooduthal vyakthamaayi regression moolyanirnnayathil, inipparayunna vishayangal fittinte nanmayumaayi bandhappettirikkunnu
varnnasabalamaaya daatta.
kattagarikkal daattayude pashchaathalatthil uyarnnuvarunna udaaharanagal inipparayunnavayaanu.
piyarsans chii-square testt.
piyarsante chii-square testt fittinte nanmayude alavu upayogikkunnu, ithu nireekshichathum pratheekshichathumaaya phala aavruthikal (athaayath nireekshanangalude ennam) thammilulla vyathyaasangalude aakethukayaan, oro square pratheekshayaal harikkappedunnu
soothravaakyam _ 1 
evide
prathekshikkunna aavruthi kanakkaakkunnath
soothravaakyam _ 2
evide
fittinte nanma nirnnayikkunnathin thathfalamaayundaakunna moolyathe oru chii-square vitharanavumayi thaarathamyam cheyyaam. chii-square vitharanathinu ("keey" − "sii") digri oof freedam undu, ivide "keey" ennathu shoonyamallaatha cellukalude ennavum "sii" ennathu vitharanathinum plus onninum kanakkakkiya paaraamettarukalude ennavumaanu (lokkeshan, skeyil paaraamettarukal, aakruthi paaraamettarukal enniva ulppede). udaaharanathinu, oru 3-paaraameettar weibul vitharanathinu, "c" = 4.
udaaharanathina purushanmaarudeyum sthreekaludeyum thulya aavruthi.
udaaharanathinu, purushanmaarum sthreekalum thulya aavruthiyilulla oru janasamkhyayil ninnu 100 aalukalude kramarahithamaya sample eduthuvenna sidhaantham parisodhikkaan, nireekshicha purushanmaarudeyum sthreekaludeyum ennathe 50 purushanmaarudeyum 50 sthreekaludeyum saidhaanthika aavruthikalumaayi thaarathamyam cheyyum. saambilil 44 purushanmaarum 56 sthreekalum undaayirunnengil,
soothravaakyam _ 3
shoonya sidhaantham shariyaanenkil (i.iii.saambilil thulyamaaya saadhyathayode purushanmareyum sthreekaleyum thiranjedukkunnu), oru digri swaathanthryathode chii-square vitharanathil ninnu testt sthithivivarakkanakku edukkum. oraalkk rund digri swaathanthryam (purushanmarkkum sthreekalkkum oronnu) pratheekshikkaamenkilum, motham purushanmaarudeyum sthreekaludeyum ennam parimithamaanennu (100) naam kanakkiledukkanam, athinaal oru digri swaathanthryam maathrameyulloo (2−1). mattoru vidhathil paranjaal, purushanmaarude ennam ariyaamenkil sthreekalude ennam nirnnayikkappedunnu, thirichum.
1 digri swaathanthryathinaayulla chii-square vitharanathinte koodiyaalochana kaanikkunnath janasamkhyayil purushanmaarum sthreekalum thulya samkhyayilaanenkil formula 4 nekkaal kooduthal vyathyasam nireekshikkaanulla sanjitha saadhyatha ekadesham 0.13 aanennaan. eee saadhyatha sthithivivarakkanakku praadhaanyathinulla parambaraagathamaayi amgeekaricha maanadandathekkaal kooduthalaanu (0.001-05 enna saadhyatha), athinaal janasamkhyayile purushanmaarude ennam sthreekalude ennathinu thulyamaanenna shoonya sidhaantham saadhaaranayaayi nammal nirasikkilla (athaayath.iii. 50/50 purusha/sthree anupaathathil njangal prathekshikkunna paridhikkullil njangalude sample pariganikkum.) 
sample srishticha samvidaanam kramarahithamanu enna anumaanam shradhikkuka, athe saadhyathayulla swatantra kramarahithamaya thiranjeduppinte ardhathil, ivide purushanmarkkum sthreekalkkum 0.5. udaaharanathinu, thiranjeduttha 44 purushanmaaril oororutharum oru purusha suhruthine konduvarikayum 56 sthreekalil oororutharum oru sthree suhruthine konduvarikayum cheythaal, oro formula 5 nte ghadakam 4 vardhikkum, athesamayam oro formula 6 nte ghadakam 2 vardhikkum. sthithivivarakkanakkinte moolyam 2.88 aayi erattiyaakum. eee adisthaana samvidaanam ariyumbol, nammal theerchayaayum jodikal ennanam. pothuve, prathirodhaparamaayi kramarahithamallengil, samvidaanam ariyilla. parisodhanaa sthithivivarakkanakku ruffer cheyyenda vitharanam, athanusarichu, chii-squareil ninnu valare vyathyasthamayirikkum.
binomial cases.
pareekshanangal vijayamo paraajayamo aaya rund phalangalil onninu kaaranamakunna swatantra pareekshanangalude oru sreniyaanu binomial pareekshanam. p" kondu soochippikkunna vijayasadhyathayulla oro "n" pareekshanangalum undu. oro "i" num (ivide "i" = 1,2,) "np" i "′1 aanenkil...keey"), pinne
soothravaakyam _ 7
ithinu ekadesham oru chii-square vitharanamundu, "keey" − 1 digri oof freedam. k" −1 digri oof freedam undu enna vastutha restruction formula _ 8-nte anantharafalamaanu. "k" nireekshicha koshangalude ennam undennu namukkariyam, ennirunnaalum, eathenkilum "k" −1 arinjukazhinjaal, bakkiyullava advitheeyamaayi nirnnayikkappedunnu. adisthaanaparamaayi, oraalkk parayaan kazhiyum, swathanthramaayi nirnnayikkappedunna koshangalude ennam "k" −1 maathrameyulloo, athinaal "k" −1 digri oof freedam.
"jii"-testt.
"piyarsante chii-square testtukal munbu shupaarsha cheytha saahacharyangalil kooduthalaayi upayogikkunna sthithivivarakkanakku praadhaanyamulla saadhyatha-anupatha parisodhanakalaanu "jii"-testtukal.
jii" yude pothuvaaya soothravaakyam ithaanu
formula _ 10 umm formula _ 6 umm chii-square testtinu thulyamaanengil, formula _ 12 swaabhaavika logarithathe soochippikkunnu, koodaathe shoonyamallaatha ellah cellukalilum thuka edukkunnu. koodaathe, nireekshicha motham ennam motham pratheekshicha ennathinu thulyamaayirikkanam formula _ 13, ivide formula _ 14 ennathu nireekshanangalude aake ennamaanu.
"roobert aarr. 1981ll prasidheekaricha statistiks paatapusthakatthinte pathipp muthal "jii"-testtukalenkilum shupaarsha cheythittundu. sokkal, eph. jaims rolph.

