Sivi Chi-Square
Ko e sivi angamaheni ki he fehuʻi “ko e ngaahi lau ʻe 37 ko ʻeni ko e meʻa ia ʻe ʻomi ʻe ha veʻeteka faitotonu?”
χ² = Σ (meʻa naʻe sio ki ai − meʻa ʻamanekina)² / meʻa ʻamanekina ʻi he luo kotoa ʻe 37. Fakahoa ia ki he tufaki chi-square ʻi he tuʻunga tauʻatāina ʻe 36 ke maʻu ha mahuʻinga p.
Founga hono fakakaukauʻi
Ko e lau ʻamanekina ki he luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → taki taha ko e n/37. Ki he luo taki taha, fakaliunga ua ʻa e faikehekehe ʻi he vahaʻa ʻo e meʻa naʻe sio ki ai mo e meʻa ʻamanekina pea vahe ʻaki ʻa e meʻa ʻamanekina; tānaki ʻa e konga ʻe 37. Ko ha veʻeteka faitotonu ʻoku ne ʻomi ha ngaahi mahuʻinga ʻoku meimei 36 ʻi he ʻavalisi (ko e tuʻunga tauʻatāinalēpiTuʻunga tauʻatāinaKo e lahi ʻo e ngaahi mahuʻinga tauʻatāina ʻi ha fika fakasitetisitika. Ki ha sivi chi-square ʻi he luo ʻe 37 ko e 36 ia, koeʻuhi kuo pau ke tānaki ʻa e ngaahi lau ki he fakakātoa.Lau kotoa →), ʻo meimei 8.5 hono mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa →. ʻI ʻolunga ʻi he 51.0 ʻoku mahuʻinga ia ʻi he tuʻunga ʻo e 5%; ʻi ʻolunga ʻi he 58.6 ʻi he 1%. ʻOku fakakaukauʻi ʻe he Meʻa Vakaiʻi ʻo e Hehema ʻo e Veʻeteka ʻa e fika sitetisitika mo e mahuʻinga plēpiMahuʻinga pKo e ngalingali ke sio ki ha mavahe ʻoku lahi tatau pe lahi ange ʻi he meʻa naʻe sio ki ai kapau naʻe faitotonu ʻa e veʻeteka.Lau kotoa → tonu mei he fankisini kama taʻekakato kuo fakamaau (regularized incomplete gamma function).
Ko ha fakatātā kuo ngāueʻi
Vilo ʻe 1,000. Ko e luo ʻe tolungofulu mā ono ʻoku tō ki ai ʻi he vahaʻa ʻo e 20 mo e 34; ko e luo 8 ʻoku 41. Ko e meʻa ʻamanekina ko e 27.03. Ko e konga ʻo e luo 8 pē ko e (41 − 27.03)²/27.03 = 7.2. Pehē ʻoku 38 ʻa e fakakātoa ʻo e toenga ʻo e konga ʻe 36 (angamaheni). χ² = 45.2 ʻi he df ʻe 36, p ≈ 0.14. ʻOku ʻikai mahuʻinga: ʻoku fai eni ʻe ha veʻeteka faitotonu ʻo tuʻo taha ʻi he fitu. Ko e luo 8 ko ha meʻa ke vakaiʻi, ʻo ʻikai ko ha meʻa kuo ʻilo, pea ko e tali ko ha vilo ʻe afe kehe.
Ngaahi fakakaukau ʻoku tali
Ngaahi vilo tauʻatāinamatematikaNgaahi vilo tauʻatāinaʻOku tatau pē ʻa e ngalingali ʻi he vilo takitaha neongo pe ko e hā naʻe hoko kimuʻa. Ko e tefito ia ʻo e fakatatau kotoa pē ʻi he uepisaiti ni.Lau kotoa →, mo e ngaahi lau ʻamanekina ʻo e 5 pe lahi ange ki he luo taki taha, ʻa ia ʻoku ʻuhinga ia ki he n ≥ 185 ke lava pē ke tonu ʻa e sivi, pea lahi ange ʻaupito ke ʻaonga. Ko hono fakataha ʻa e ngaahi vilo mei he ngaahi veʻeteka kehekehe ʻoku ne maumauʻi ʻa e ʻuluaki fakakaukau ʻi hono ʻuhinga (ʻoku ke siviʻi ha meʻa fakataha, ʻo ʻikai ha veʻeteka). Ko ha ola ʻo e fakaʻilonga ʻo e tīla ʻe maumauʻi moʻoni ai ia, pea ʻe fakalahi ai ʻa e χ² neongo ʻoku ʻikai ha luo ʻoku tō lahi ange ki ai koeʻuhí ko ha meʻa fakaesino.
Fakaʻilonga ʻo e Tīla LulētiNgaahi Vilo Tauʻatāina ʻi he Lulēti
Pearson mo Monte Carlo
Naʻe pulusi ʻe Karl Pearson ʻa e sivi ʻi he 1900, pea ko e taha ʻo ʻene ʻuluaki ngaahi fakatātā kuo ngāueʻi ko e vilo lulēti ʻe 26,306 naʻe tohi ʻi Monte Carlo, ʻa ia naʻa ne ʻilo ʻoku fuʻu taʻetatau ʻaupito ke hoko noa pē pea ne fakahaaʻi ko e “lulēti ʻi Monte Carlo… ʻoku ʻikai ko ha vaʻinga ʻo e hoko noa pē”. Naʻe fakaʻosi ʻe ha kau faʻu tohi ki mui ko e kau faiongoongo naʻa nau tohi ʻa e ngaahi vilo maʻa ha nusipepa naʻa nau faʻu loi ha tokolahi ʻo kinautolu, ʻa ia ko ha lēsoni ia ki he tupuʻanga ʻo e ngaahi fakamatala.
ʻOku pulusi ʻe Pearson ʻa e sivi chi-square ʻo e feʻunga ʻo e mōtolo, ʻo fakatātā ʻaki ʻa e ngaahi vilo ʻi Monte Carlo.
ʻOku fehuʻia ʻa e ngaahi fakamatala ʻo e vilo; ʻoku hā naʻe faʻu loi ʻe he kau tohi ha ngaahi hokohoko.
ʻOku fokotuʻu fakapapau ʻe Fisher ʻa e tuʻunga tauʻatāina; ʻoku tuʻu maʻu ʻa e angamaheni ʻo e 5%.
ʻOku ngāueʻaki ʻe he kau sitetisitika ʻa e ngaahi vilo lulēti ko e ngaahi fakamatala ʻi he tohi ako ki he ngaahi sivi ʻo e tatau.
ʻOku ngāueʻaki ʻe he fāmili García-Pelayo ʻa e founga ʻaki ha ngaahi fakamatala moʻoni naʻe tohi pea nau ikuna ʻi Madrid.
ʻOku fai ʻe he ngaahi kasino ʻa e sivi tatau ʻi heʻenau ngaahi veʻeteka ko e konga ʻo e tauhi angamaheni.
Ko ha sivi moʻoni: ngaahi veʻeteka ʻaatomētiki ʻi Las Vegas
ʻOku faʻa tui ʻa e kau vaʻinga ʻoku fakahinohinoʻi ʻe ha veʻeteka ʻaatomētiki ʻa e pulumeʻangāuePuluKo e kiʻi pulu siʻisiʻi ʻoku tolongi ʻi he hala ʻo fehangahangai mo e konga vilo. Ko e ngaahi pulu ʻo onopooni ʻoku ngaohi ʻaki ʻa e ivorine pe Teflon, 18–21 mm.Lau kotoa → ke mavahe mei he ngaahi peti lalahi. Naʻe siviʻi ʻe ha vakaiʻi ʻi he 2017 ʻa e tui ko ia ʻi he ngaahi veʻeteka noaveʻetekaNoaKo e luo lanu mata pē ʻe taha ʻoku ʻikai kāpui ʻe ha peti totongi tatau, peti tasini pe peti kōlomu; ko e tupuʻanga ia ʻo e tuʻunga lelei ʻo e kasino. ʻOku toe ui: noa ʻe taha, 0.Lau kotoa → ua ʻa Interblock ʻoku ʻikai ha tīla ʻi Las Vegas, ʻo peti ki ha konga ʻo ha fika fekaungāʻapi ʻe nima, ko e faʻahinga peti ʻoku fai ʻe ha tokotaha fua taimi ʻo e veʻeteka. ʻI ha vilo ʻe 299 naʻe ikuna ʻa e konga ʻo tuʻo 29 ʻi he 39.3 naʻe ʻamanekina, ko ha siʻi ʻoku ʻomi ʻe ha veʻeteka faitotonu ʻi he meimei 4% ʻo e taimi. Ko e chi-square ʻi he luo kotoa ʻe 38 ko e 45.29 ʻi he tuʻunga tauʻatāina ʻe 37: p = 16.5%. Ko ha sīpinga hono ua ʻo e vilo ʻe 1,204 ʻi ha veʻeteka ʻe tolu naʻe maʻu ai ʻa e χ² = 34.79, p = 57%, pea naʻe ʻikai mahuʻinga ha konga ʻo ha lahi pē naʻe siviʻi. Ko e ongo sīpinga fakataha, vilo ʻe 1,503, naʻe maʻu ai ʻa e χ² = 41.75, p = 27%. Ko e fakamulituku naʻe ʻikai ha fakamoʻoni ʻo ha fakahinohinoʻi. Ko e ʻuluaki sīpinga pē naʻe hā fakaʻohovale; ko e sīpinga hono ua naʻa ne fakapapauʻi ia.
Tuʻa atu ʻi he chi-square
Ki ha luo pē ʻe taha ʻoku fakaʻohovale, ʻoku mālohi ange ʻa e sivi paionomiale. Ki ha konga ʻoku fakaʻohovale, ko e sivi z ʻo e kongaveʻetekaKongaKo ha konga fakavilo hokohoko ʻo e ngaahi luo ʻi he veʻeteka, ʻoku kehe ia mei ha kulupu ʻi he palani ʻo e tēpile.Lau kotoa → ʻi he peesi ʻo e vakaiʻi ʻo e ngaahi konga. Ko e chi-square ko e sivi fakalūkufua ia: ʻoku ne tala atu ʻoku ʻi ai ha meʻa ʻoku ʻikai tonu kae ʻikai tala pe ko e hā. Ngāueʻaki ia ʻi he ʻuluaki, pea toki vakai.
Fomula
Ngaahi fehuʻi
Ko e lau ʻe 37 kuo pau ke tānaki ʻo n, ko ia ko e 36 pē ʻoku tauʻatāina ke liliu.
Ko ha veʻeteka ʻoku ʻi ai ha luo ʻe taha ʻi he 1/25 ʻi ha vilo ʻe 10,000 ʻe ʻomi ʻe he konga ʻo e luo ko ia pē ha meimei 60; χ² ʻo meimei 100, p ʻoku meimei noa.
ʻIo ʻi he lao, ʻo ʻamanekina ʻa e 5.4 ki he luo taki taha. ʻE ʻikai te ne ʻiloʻi ha meʻa tukukehe ha veʻeteka ʻoku ʻi ai ha luo kuo pipiki tāpuni ʻaki ha kolū.
Meʻa fakaoli
Tānaki ʻa e ngaahi ʻohovale kuo fakaliunga ua. Fakahoa ki he 51.0.
Ngaahi Maʻuʻanga
- 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.”