Test ki-kare

Kouma kalkil li

Kont atandi par kazekipmanKazEnn bann 37 konpartiman avek nimero lor rotor. Osi: slot, cup.Lir tou → se n/37. Pou sak kaz, met diferans ant observe ek atandi o kare ek divize par atandi; additionn 37 term-la. Enn rou zis donn valer otour 36 an mwayenn (sa se degre libertelaboratwarDegre liberteNonb valer independan dan enn statistik. Pou enn test ki-kare lor 37 kaz li 36, akoz bann kont bizin fer total-la.Lir tou →), avek enn ekar-tipmatematikEkar-tipRasinn kare varyans; distans tipik ant enn rezilta ek valer atandi.Lir tou → apepre 8.5. Lao 51.0 sinifikatif o nivo 5%; lao 58.6 a 1%. Analizer defo rou kalkil statistik-la ek valer plaboratwarValer pProbabilite trouv enn ekar omwin osi gran ki seki finn observe si rou-la ti zis.Lir tou → egzak avek fonksion gamma enkonple regilarize.

Enn egzanp kalkile

1,000 tour. Trant-sis kaz sorti ant 20 ek 34 fwa; kaz 8 sorti 41 fwa. Atandi se 27.03. Term kaz 8 tousel se (41 − 27.03)²/27.03 = 7.2. Dir ki lezot 36 term fer 38 ansam (tipik). χ² = 45.2 ar 36 df, p ≈ 0.14. Pa sinifikatif: enn rou zis fer sa enn fwa lor set. Kaz 8 se enn kandida, pa enn dekouvert, ek repons-la se ankor mil tour.

Lipotez

Tour independanmatematikTour independanSak tour ena mem probabilite, nenport seki finn pase avan. Baz tou kalkil lor sit-la.Lir tou →, ek kont atandi omwin 5 par kaz, vedir n ≥ 185 pou ki test-la valab dimwin, ek boukou plis pou ki li itil. Melanz tour depi plizir rou kas premie lipotez-la dan lespri (ou pe teste enn melanz, pa enn rou). Enn lefe “sinyatir krupie” ti pou kas li an realite, ek ti pou gonfle χ² san ki okenn kaz pe gagn favorize fizikman.

Sinyatir krupie rouletTour independan dan roulet

Pearson ek Monte Carlo

Karl Pearson ti pibliy test-la an 1900, ek enn so premie egzanp kalkile ti 26,306 tour roulet Monte Carlo ki ti note; li ti trouv zot tro pa iniform pou ete azar ek li ti deklare ki “Monte Carlo roulette… is not a game of chance” (roulet Monte Carlo pa enn zwe azar). Pli tar, lezot oter ti konklir ki bann zournalis ki ti note tour-la pou enn zournal ti invant boukou ladan, ek sa li mem enn leson lor lorizinn done.

Roulet Monte Carlo

Enn vre test: rou otomatik Las Vegas

Souvan zwer sispekte ki enn rou otomatik dirize boul-laekipmanBoulTi boul ki lanse dan simen-la dan sans kontrer rotor. Zordi bann boul an ivorine ouswa Teflon, 18–21 mm.Lir tou → lwin ar bann gro pari. Enn analiz 2017 ti met sa sispision-la a leprev lor bann rou doub zerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou → san krupie Interblock Las Vegas, avek pari lor enn lark sink nimero vwazin, kalite pari ki enn kronometrer rou fer. Lor 299 tour, lark-la ti gagne 29 fwa kont 39.3 atandi, enn mank ki enn rou zis prodir apepre 4% letan. Ki-kare lor tou 38 kaz ti 45.29 ar 37 degre liberte: p = 16.5%. Enn dezyem lesantiyon 1,204 tour lor trwa rou ti donn χ² = 34.79, p = 57%, ek okenn lark, ninport ki gro ki zot ti esaye, pa ti sinifikatif. Lede lesantiyon ansam, 1,503 tour, ti donn χ² = 41.75, p = 27%. Verdik: okenn prev ki rou-la dirize boul-la. Premie lesantiyon tousel ti paret sispe; se dezyem-la ki ti regle kestion-la.

Lao ki-kare

Pou enn sel kaz sispe, enn test binomial pli for. Pou enn lark sispe, test z sekterrouSekterEnn ark kaz ki swiv lor rou-la, pa enn group lor tapi pari.Lir tou → lor paz analiz sekter. Ki-kare se test zeneral: li dir ou ki kiksoz pa korek san dir ou kisannla. Servi li an premie, apre get pli pre.

Analiz sekter

Formil

Kestion