Kuhlolwa kwe-chi-square
Kuhlolwa lokujwayelekile kwembuto lotsi “letibalo letingu-37 tiko yini loko lisondvo lelingachemile lebelingakukhicita?”
χ² = Σ (lokubonwe − lokulindzelekile)² / lokulindzelekile kuyo yonkhe imigodzi lengu-37. Catsanisa nekusabalala kwe-chi-square ngemazinga enkhululeko langu-36 kute utfole i-p-value.
Kusibala
Sibalo lesilindzelekile emgodzinitinsitaUmgodziLesinye setikhala letingu-37 letinetinombolo ku-rotor. Kuphindze kutsiwe: slot, cup.Fundza konkhe → ngamunye ngu-n/37. Emgodzini ngamunye, phindzaphindza umehluko emkhatsini walokubonwe nalokulindzelekile ngawo ngekwawo bese wehlukanisa ngalokulindzelekile; hlanganisa emanani langu-37. Lisondvo lelingachemile liniketa emanani lajikeleta 36 ngesilinganiso (emazinga enkhululekolilabhorethriEmazinga enkhululekoLinani lemanani latimele esibalweni setibalo. Ekuhlolweni kwe-chi-square emigodzini lengu-37 lingu-36, ngobe tinombolo kufanele tihlangane tibe linani lonkhe.Fundza konkhe →), nekuphambuka lokujwayelekiletibaloKuphambuka lokujwayelekileImphandze yesikwele yekugucugucuka (variance); libanga lelivamile lemphumela kusuka enanini lelilindzelekile.Fundza konkhe → lokucishe kube ngu-8.5. Ngetulu kwa-51.0 kubalulekile elizingeni lelingu-5%; ngetulu kwa-58.6 ku-1%. Sihlatiyi sekuchema kwelisondvo le-roulette sibala sibalo kanye ne-p-valuelilabhorethriI-p-valueLitfuba lekubona kuphambuka lokungenani lokukhulu njengaloko lokubonwe nangabe lisondvo belingachemile.Fundza konkhe → lecondzile kusuka ku-regularized incomplete gamma function.
Sibonelo lesibaliwe
Kujikeleta lokungu-1,000. Imigodzi lengemashumi lamatsatfu nesitfupha ishaywa emkhatsini wetikhatsi letingu-20 naletingu-34; umgodzi 8 ushaywe tikhatsi letingu-41. Lokulindzelekile ngu-27.03. Linani lemgodzi 8 lodvwa lingu-(41 − 27.03)²/27.03 = 7.2. Asitsi lamanye emanani langu-36 ahlangana abe ngu-38 (lokujwayelekile). χ² = 45.2 ku-36 df, p ≈ 0.14. Akubalulekile: lisondvo lelingachemile likwenta loku kanye etikhatsini letisikhombisa. Umgodzi 8 ungumsolwa nje, hhayi intfo letfoliwe, futsi imphendvulo kujikeleta lokunye lokuyinkhulungwane.
Lokucatshangwako
Kujikeleta lokutimeletibaloKujikeleta lokutimeleKujikeleta ngakunye kunematfuba lafanako noma ngabe umlandvo unjani. Sisekelo sako konkhe kubala kulelisayithi.Fundza konkhe →, kanye netibalo letilindzelekile lokungenani letingu-5 emgodzini ngamunye, lokusho kutsi n ≥ 185 kute kuhlolwa kusebente nhlobo, futsi lokunyenti kakhulu kute kube lusito. Kuhlanganisa kujikeleta kwemasondvo lahlukene kwephula lokwekucala lokucatshangwako ngekwemcondvo (uhlola inhlanganisela, hhayi lisondvo). Umtselela welusayino lwe-croupier bewungakwephula ngempela, futsi bewungakhulisa i-χ² ngaphandle kwekutsi kube nemgodzi lotsandvwa ngekwesakhiwo.
Lusayino lwe-croupier ku-rouletteKujikeleta lokutimele ku-roulette
Pearson ne-Monte Carlo
Karl Pearson washicilela kuhlolwa nga-1900, futsi sinye setibonelo takhe tekucala letibaliwe bekukujikeleta kwe-roulette e-Monte Carlo lokungu-26,306 lokwabhalwa phansi, lakutfola kutsi bekungalingani kakhulu kutsi kube yinhlanhla futsi wamemetela kutsi “i-roulette yase-Monte Carlo… akusiwo umdlalo wenhlanhla”. Babhali bakamuva baphetsa ngekutsi tintfatseli letabhala kujikeleta tibhalela liphephandzaba tasungula lokunyenti kwako, lokusifundvo ngekwaso mayelana nemvelaphi yedatha.
Pearson ushicilela kuhlolwa kwe-chi-square kwekuhambisana nalokulindzelekile (goodness-of-fit), nekujikeleta kwase-Monte Carlo kusibonelo.
Idatha yekujikeleta iyangabatwa; babhali babonakala basungule luchungechunge.
Fisher uchaza ngekusemtsetfweni emazinga enkhululeko; umkhuba we-5% uyagcila.
Bochwepheshe besitatistiki basebentisa kujikeleta kwe-roulette njengedatha yetincwadzi tekufundza ekuhloleni kulingana.
Umndeni wakaGarcía-Pelayo usebentisa indlela ngedatha yangempela lebhaliwe futsi uyawina eMadrid.
Emakhasino enta kuhlolwa lokufanako emasondvweni awo njengencenye yekunakekelwa lokujwayelekile.
Kuhlolwa kwangempela: emasondvo latisebentelako e-Las Vegas
Badlali bavame kusola kutsi lisondvo lelitisebentelako licondzisa libholatinsitaLibholaLibhola lelincane leliphoswa emzileni lihamba ngakulolunye luhlangotsi kune-rotor. Emabhola alamuhla ayi-ivorine noma i-Teflon, 18–21 mm.Fundza konkhe → khashane nekubheja lokukhulu. Kuhlatiya kwanga-2017 kwahlola loku kusola emasondvweni e-Interblock langenayo i-croupier lanelicandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → lelikabili e-Las Vegas, kubhejwa encenyeni yetinombolo letisihlanu letingebomakhelwane, luhlobo lwekubheja lolwentiwa yi-wheel clocker (umuntfu lobala sikhatsi selisondvo). Ekujikeleteni lokungu-299 leyo ncenye yawina tikhatsi letingu-29 nawucatsanisa naletingu-39.3 letilindzelekile, kushoda lisondvo lelingachemile lelikukhicitako cishe ku-4% wetikhatsi. I-chi-square kuyo yonkhe imigodzi lengu-38 yaba ngu-45.29 ngemazinga enkhululeko langu-37: p = 16.5%. Isampula yesibili yekujikeleta lokungu-1,204 emasondvweni lamatsatfu yaniketa χ² = 34.79, p = 57%, futsi kute incenye yanobe ngubuphi bukhulu leyazanywa leyaba lebalulekile. Tisampula totimbili ndzawonye, kujikeleta lokungu-1,503, taniketa χ² = 41.75, p = 27%. Sincumo saba kutsi kute bufakazi bekucondzisa. Isampula yekucala yodvwa yabukeka isolisa; yesibili yiyo leyakusombulula.
Ngale kwe-chi-square
Emgodzini munye losolwako kuhlolwa kwe-binomial kunemandla lamakhulu. Encenyeni yelisondvo lesolwako, i-z-test yesigabalisondvoSigabaIngcenye lelandzelanako yemigodzi elisondvweni, lehlukile kulicembu letinombolo elithebuleni lekubheja.Fundza konkhe → ekhasini lelitsi Kuhlatiya tigaba. I-chi-square kuhlolwa lokubanti: ikutjela kutsi kukhona lokungalungi ngaphandle kwekusho kutsi yini. Yisebentise kucala, bese uyabuka.
Lifomula
Imibuto
Tibalo letingu-37 kufanele tihlangane tibe ngu-n, ngako letingu-36 kuphela letikhululekile kuguculuka.
Lisondvo lelinemgodzi munye loshaywa ku-1/25 ekujikeleteni lokungu-10,000 belitawuniketa linani lemgodzi lelijikeleta 60 lodvwa; i-χ² lejikeleta 100, p ecinisweni ilicandza.
Ngekwebuchwepheshe yebo, lokulindzelekile kube ngu-5.4 emgodzini ngamunye. Ngeke kutfole lutfo ngaphandle kwekutsi lisondvo libe nemgodzi lonamatsiselwe wavaleka.
Lokuhlekisako
Hlanganisa lokumangalisako lokuphindzaphindzwe ngako ngekwako. Catsanisa na-51.0.
Imitfombo
- 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.”