Uvavanyo lwe-chi-square
Uvavanyo oluqhelekileyo lombuzo othi “ingaba la manani angama-37 ngawo ivili elingenamkhethe ebelinokuwavelisa?”
χ² = Σ (okubonwayo − okulindelekileyo)² / okulindelekileyo kuzo zonke izikhewu ezingama-37. Thelekisa nokwabiwa kwe-chi-square kumanqanaba enkululeko angama-36 ukuze ufumane i-p-value.
Ukuyibala
Inani elilindelekileyo kwisikhewuizixhoboIsikhewuEsinye sezikhewu ezingama-37 ezinamanani kwirotha. Kwakhona: slot, cup.Funda yonke → ngasinye ngu-n/37. Kwisikhewu ngasinye, phindaphinda ngokwawo umahluko phakathi kokubonwayo nokulindelekileyo uze wahlule ngokulindelekileyo; dibanisa la manani angama-37. Ivili elingenamkhethe linika amaxabiso amalunga nama-36 ngokomndilili (amanqanaba enkululekoilebhuAmaqondo enkululeko (degrees of freedom)Inani lamaxabiso azimeleyo kwizibalo-manani. Kuvavanyo lwe-chi-square kwizikhewu ezingama-37 ngama-36, kuba izibalo kufuneka zidibane zibe sisixa esipheleleyo.Funda yonke →), nokutenxa okuqhelekileyoizibaloUkutenxa okuqhelekileyo (standard deviation)Ingcambu yesikwere yokwahluka; umgama oqhelekileyo wesiphumo ukusuka kwixabiso elilindelekileyo.Funda yonke → okumalunga ne-8.5. Ngaphezu kwe-51.0 kubalulekile kwinqanaba le-5%; ngaphezu kwe-58.6 kwi-1%. Umhlalutyi wokuthambekela kwevili le-roulette ubala isibalo-manani kunye ne-p-valueilebhup-valueAmathuba okubona ukutenxa okukhulu ubuncinci njengokubonwayo ukuba ivili belinobulungisa.Funda yonke → echanileyo kwi-regularized incomplete gamma function.
Umzekelo osetyenzisiweyo
Imijikelo eyi-1,000. Izikhewu ezingamashumi amathathu anesithandathu ziphuma phakathi kwama-20 nama-34 amaxesha; isikhewu 8 siphume ama-41. Okulindelekileyo ngama-27.03. Inani lesikhewu 8 lodwa ngu-(41 − 27.03)²/27.03 = 7.2. Masithi amanye amanani angama-36 adibana abe ngama-38 (okuqhelekileyo). χ² = 45.2 kwi-df 36, p ≈ 0.14. Akubalulekanga: ivili elingenamkhethe likwenza oku kanye kwasixhenxe. Isikhewu 8 sisikhewu ekufuneka siqwalaselwe, hayi into efunyenweyo, kwaye impendulo yimijikelo elinye iwaka.
Iingcinga ezisisiseko
Imijikelo ezimeleyoizibaloImijikelo ezimeleyoUmjikelo ngamnye unamathuba afanayo nokuba imbali injani na. Isiseko sazo zonke izibalo kule sayithi.Funda yonke →, kunye namanani alindelekileyo ubuncinane ali-5 kwisikhewu ngasinye, nto leyo ethetha u-n ≥ 185 ukuze uvavanyo lusebenze konke konke kwaye kakhulu ngaphezulu ukuze luncede. Ukudibanisa imijikelo evela kumavili ahlukeneyo kwaphula ingcinga yokuqala ngokomoya (uvavanya umxube, hayi ivili). Isiphumo sophawu lomqhubi besinokuyaphula ngokwenene, kwaye besinokunyusa u-χ² ngaphandle kokuba nasiphi na isikhewu sithandwe ngokwasemzimbeni.
UPearson neMonte Carlo
UKarl Pearson wapapasha uvavanyo ngo-1900, kwaye omnye wemizekelo yakhe yokuqala esetyenzisiweyo yayiyimijikelo engama-26,306 ebhaliweyo ye-roulette yaseMonte Carlo, awayifumana ingalinganiyo kakhulu ukuba ibe lithamsanqa waza wabhengeza ukuba “i-roulette yaseMonte Carlo… ayingomdlalo wethamsanqa”. Ababhali bamva bagqiba kwelokuba iintatheli ezazibhala imijikelo yephephandaba zaziyenzile ngokwazo uninzi lwayo, nto leyo isisifundo ngokwayo ngemvelaphi yedatha.
UPearson upapasha uvavanyo lwe-chi-square goodness-of-fit, nemijikelo yaseMonte Carlo njengomzekelo.
Idatha yemijikelo iyathandatyuzwa; ababhali babonakala benze uluhlu lobuxoki.
UFisher wenza ngokusesikweni amanqanaba enkululeko; isiqhelo se-5% siyazinza.
Iingcali zezibalo-manani zisebenzisa imijikelo ye-roulette njengedatha yeencwadi zokufunda kuvavanyo lokulingana.
Usapho lakwaGarcía-Pelayo lusebenzisa indlela ngedatha yokwenyani ebhaliweyo kwaye luphumelela eMadrid.
Iikhasino ziqhuba uvavanyo olufanayo kumavili azo njengenxalenye yokugcinwa rhoqo.
Uvavanyo lokwenyani: amavili azisebenzelayo eLas Vegas
Abadlali bahlala berhanela ukuba ivili elizisebenzelayo liqhubela ibholaizixhoboIbholaIbhola encinci ephoswa emzileni ngokuchasene nerotha. Iibhola zanamhlanje zenziwe nge-ivorine okanye nge-Teflon, zi-18–21 mm.Funda yonke → kude neebheji ezinkulu. Uhlalutyo lwango-2017 lwakuvavanya oko kukrokra kumavili e-Interblock angenamqhubi aneqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → eliphindiweyo eLas Vegas, kubhejwa kwinxalenye yamanani amahlanu angabamelwane, uhlobo lwebheji eyenziwa ngumntu olinganisa ixesha levili. Kwimijikelo engama-299 inxalenye yaphumelela amaxesha angama-29 ngokuchasene nama-39.3 alindelekileyo, ukusilela ivili elingenamkhethe elikuvelisa malunga ne-4% yexesha. I-chi-square kuzo zonke izikhewu ezingama-38 yayingama-45.29 kumanqanaba enkululeko angama-37: p = 16.5%. Isampulu yesibini yemijikelo eyi-1,204 kumavili amathathu yanika χ² = 34.79, p = 57%, kwaye akukho nxalenye yabo nabuphi na ubukhulu eyazanywayo eyayibalulekile. Zombini iisampulu kunye, imijikelo eyi-1,503, zanika χ² = 41.75, p = 27%. Isigwebo sasikukuba akukho bungqina bokuqhubela. Isampulu yokuqala yodwa yayikhangeleka irhanelisa; eyesibini yiyo eyakucacisayo.
Ngaphaya kwe-chi-square
Kwisikhewu esinye esirhanelwayo uvavanyo lwe-binomial lunamandla ngakumbi. Kwinxalenye erhanelwayo, uvavanyo lwe-z lwecandeloiviliIcandeloIsiqwenga esiqhubekayo sezikhewu evilini, esahlukileyo kwiqela elikwibhodi yokubheja.Funda yonke → kwiphepha elithi Uhlalutyo lwecandelo. I-chi-square luvavanyo olubanzi: ikuxelela ukuba kukho into engalunganga ngaphandle kokuthi yintoni. Yisebenzise kuqala, uze ujonge.
Ifomula
Imibuzo
Amanani angama-37 kufuneka adibane abe ngu-n, ngoko angama-36 kuphela akhululekileyo ukwahluka.
Ivili elinesikhewu esinye esiku-1/25 kwimijikelo eli-10,000 belinokunika inani lesikhewu elimalunga nama-60 lilodwa; χ² malunga ne-100, p iphantse ibe liqanda.
Ngokobuchwephesha ewe, ngokulindelekileyo kwe-5.4 kwisikhewu ngasinye. Ayizukufumana nto ngaphandle kwevili elinesikhewu esinamathiselwe savaleka.
Uncumo
Dibanisa izimangaliso eziphindaphindwe ngokwazo. Thelekisa ne-51.0.
Imithombo
- Pearson, K. “On the criterion that a given system of deviations from the probable…”
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Organic Roulette Experiment.”