Ukuhlolwa kwe-chi-square
Ukuhlolwa okujwayelekile kombuzo othi “ingabe lezi zibalo ezingu-37 yilokho isondo elingachemile elingakukhiqiza?”
χ² = Σ (okubonwe − okulindelekile)² / okulindelekile kuwo wonke amagodi angu-37. Qhathanisa nokusabalala kwe-chi-square ngamazinga enkululeko angu-36 ukuze uthole i-p-value.
Ukukubala
Isibalo esilindelekile egodiniokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → ngalinye ngu-n/37. Egodini ngalinye, phindaphinda umehluko phakathi kokubonwe nokulindelekile ngawo uqobo bese uhlukanisa ngokulindelekile; hlanganisa amanani angu-37. Isondo elingachemile linikeza amanani azungeze u-36 ngokwesilinganiso (amazinga enkululekoilebhuAmazinga enkululekoInani lamanani azimele esitatistikini. Ekuhlolweni kwe-chi-square kumagodi angu-37 lingu-36, ngoba amanani okubala kufanele ahlangane abe yinani lonke.Funda konke →), nokuchezuka okujwayelekileizibaloUkuchezuka okujwayelekileImpande yesikwele yokuguquguquka (variance); ibanga elivamile lomphumela ukusuka enanini elilindelekile.Funda konke → okucishe kube ngu-8.5. Ngaphezu kuka-51.0 kubalulekile ezingeni elingu-5%; ngaphezu kuka-58.6 ku-1%. Umhlaziyi wokuchema kwesondo le-roulette ubala isibalo kanye ne-p-valueilebhuI-p-valueAmathuba okubona ukuchezuka okungenani okukhulu njengalokho okubonwe uma isondo belingenzeleli.Funda konke → eqondile kusuka ku-regularized incomplete gamma function.
Isibonelo esibaliwe
Ukujikeleza okungu-1,000. Amagodi angamashumi amathathu nesithupha ashaywa phakathi kwezikhathi ezingu-20 nezingu-34; igodi u-8 lishaywe izikhathi ezingu-41. Okulindelekile ngu-27.03. Inani legodi u-8 lodwa lingu-(41 − 27.03)²/27.03 = 7.2. Ake sithi amanye amanani angu-36 ahlangana abe ngu-38 (okujwayelekile). χ² = 45.2 ku-36 df, p ≈ 0.14. Akubalulekile: isondo elingachemile likwenza lokhu kanye ezikhathini eziyisikhombisa. Igodi u-8 liwumsolwa nje, hhayi into etholakele, futhi impendulo ngukujikeleza okunye okuyinkulungwane.
Okucatshangwayo
Ukujikeleza okuzimeleizibaloUkujikeleza okuzimeleUkujikeleza ngakunye kunamathuba afanayo noma ngabe kwenzekeni ngaphambili. Isisekelo sazo zonke izibalo kule sayithi.Funda konke →, kanye nezibalo ezilindelekile okungenani ezingu-5 egodini ngalinye, okusho ukuthi n ≥ 185 ukuze ukuhlolwa kusebenze nhlobo, futhi okuningi kakhulu ukuze kube wusizo. Ukuhlanganisa ukujikeleza kwamasondo ahlukene kwephula okokuqala okucatshangwayo ngokomqondo (uhlola inhlanganisela, hhayi isondo). Umthelela wesiginesha ye-croupier bewungakwephula ngempela, futhi bewungakhuphula i-χ² ngaphandle kokuthi kube negodi elithandwa ngokwesakhiwo.
Isiginesha ye-croupier ku-rouletteUkujikeleza okuzimele ku-roulette
U-Pearson ne-Monte Carlo
U-Karl Pearson washicilela ukuhlolwa ngo-1900, futhi esinye sezibonelo zakhe zokuqala ezibaliwe kwakuwukujikeleza kwe-roulette e-Monte Carlo okungu-26,306 okwabhalwa phansi, athola ukuthi kwakungalingani kakhulu ukuthi kube yinhlanhla futhi wamemezela ukuthi “i-roulette yase-Monte Carlo… ayiwona umdlalo wenhlanhla”. Ababhali bakamuva baphetha ngokuthi izintatheli ezabhala ukujikeleza zibhalela iphephandaba zakuqamba okuningi kwakho, okuyisifundo ngokwaso mayelana nemvelaphi yedatha.
U-Pearson ushicilela ukuhlolwa kwe-chi-square kokuhambisana nokulindelekile (goodness-of-fit), nokujikeleza kwase-Monte Carlo kuyisibonelo.
Idatha yokujikeleza iyangabazwa; ababhali babonakala beqambe uchungechunge.
U-Fisher uchaza ngokusemthethweni amazinga enkululeko; umkhuba we-5% uyagxila.
Ochwepheshe besitatistiki basebenzisa ukujikeleza kwe-roulette njengedatha yezincwadi zokufunda ekuhloleni ukulingana.
Umndeni wakwa-García-Pelayo usebenzisa indlela ngedatha yangempela ebhaliwe futhi uwina e-Madrid.
Amakhasino enza ukuhlolwa okufanayo emasondweni awo njengengxenye yokunakekelwa okujwayelekile.
Ukuhlolwa kwangempela: amasondo azenzakalelayo e-Las Vegas
Abadlali bavame ukusola ukuthi isondo elizenzakalelayo liqondisa ibholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → kude nokubheja okukhulu. Ukuhlaziywa kwango-2017 kwahlola lokhu kusola emasondweni e-Interblock angenayo i-croupier aneqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → eliphindiwe e-Las Vegas, kubhejwa engxenyeni yezinombolo ezinhlanu ezingomakhelwane, uhlobo lokubheja olwenziwa yi-wheel clocker (umuntu obala isikhathi sesondo). Ekujikelezeni okungu-299 leyo ngxenye yawina izikhathi ezingu-29 uma kuqhathaniswa nezingu-39.3 ezilindelekile, ukushoda isondo elingachemile elikukhiqizayo cishe ku-4% wezikhathi. I-chi-square kuwo wonke amagodi angu-38 yaba ngu-45.29 ngamazinga enkululeko angu-37: p = 16.5%. Isampula yesibili yokujikeleza okungu-1,204 emasondweni amathathu yanikeza χ² = 34.79, p = 57%, futhi ayikho ingxenye yanoma yibuphi ubukhulu eyazanywa eyaba ebalulekile. Zombili izampula ndawonye, ukujikeleza okungu-1,503, zanikeza χ² = 41.75, p = 27%. Isinqumo saba ukuthi abukho ubufakazi bokuqondisa. Isampula yokuqala iyodwa yabukeka isolisa; eyesibili yiyona eyakuxazulula.
Ngale kwe-chi-square
Egodini elilodwa elisolwayo ukuhlolwa kwe-binomial kunamandla amakhulu. Engxenyeni yesondo esolwayo, i-z-test yesigabaisondoIsigabaIngxenye eqhubekayo yamagodi alandelanayo esondweni, ehlukile eqenjini lezinombolo ethebuleni lokubheja.Funda konke → ekhasini elithi Ukuhlaziywa kwezigaba. I-chi-square ingukuhlolwa okubanzi: ikutshela ukuthi kukhona okungalungile ngaphandle kokusho ukuthi yini. Yisebenzise kuqala, bese uyabheka.
Ifomula
Imibuzo
Izibalo ezingu-37 kufanele zihlangane zibe ngu-n, ngakho ezingu-36 kuphela ezikhululekile ukuguquguquka.
Isondo elinegodi elilodwa elishaywa ku-1/25 ekujikelezeni okungu-10,000 belizonikeza inani legodi elizungeze u-60 lodwa; i-χ² ezungeze u-100, u-p empeleni uyiqanda.
Ngokobuchwepheshe yebo, okulindelekile kube ngu-5.4 egodini ngalinye. Ngeke kuthole lutho ngaphandle kokuthi isondo libe negodi elinamathiselwe lavaleka.
Okokuhlekisa
Hlanganisa okumangazayo okuphindaphindwe ngakho uqobo. Qhathanisa no-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.”