Bvunzo yeChi-Square
Bvunzo yakajairika yekuti “nhamba idzi 37 ndidzo dzaizoburitswa nevhiri rakarurama here?”
χ² = Σ (zvakaonekwa − zvinotarisirwa)² / zvinotarisirwa pamakomba ese 37. Enzanisai nekugovaniswa kwechi-square pamadhigirii erusununguko 36 kuti muwane p-value.
Kuiverenga
Huwandu hunotarisirwa pagombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → i n/37. Pagomba rimwe nerimwe, sikweyai musiyano uri pakati pezvakaonekwa nezvinotarisirwa mogovanisa nezvinotarisirwa; sanganisai zvikamu 37. Vhiri rakarurama rinopa nhamba dzingangoita 36 paavhareji (iwo madhigirii erusunungukoongororoMadhigirii erusunungukoHuwandu hwemaitiro akazvimirira munhamba yeongororo. Pabvunzo yechi-square pamakomba 37 i36, nokuti nhamba dzinofanira kusanganiswa dzosvika pahuwandu hwese.Verengai zvese →), nestandard deviationmasvomhuStandard deviationMudzi wesikweya wemusiyano; chinhambwe chakajairwa chemhedzisiro kubva pakukosha kunotarisirwa.Verengai zvese → ingangoita 8.5. Pamusoro pe51.0 zvine kukosha padanho re5%; pamusoro pe58.6 pa1%. Muongorori weKutsauka kweVhiri reRoulette anoverenga nhamba iyi nep-valueongororop-valueMukana wekuona kutsauka kwakakura zvakaenzana kana kupfuura kwakaonekwa dai vhiri rakanga rakarurama.Verengai zvese → chaiyo kubva paregularized incomplete gamma function.
Muenzaniso wakaverengwa
Kutenderera 1,000. Makomba makumi matatu nematanhatu anorohwa pakati pe20 ne34; gomba 8 rine 41. Zvinotarisirwa i27.03. Chikamu chegomba 8 chega i(41 − 27.03)²/27.03 = 7.2. Ngatitii zvimwe zvikamu 36 zvinosvika 38 (zvakajairika). χ² = 45.2 pa36 df, p ≈ 0.14. Hazvina kukosha: vhiri rakarurama rinoita izvi kamwe chete muna manomwe. Gomba 8 inyaya yekuongorora, kwete chiwanikwa, uye mhinduro kumwe kutenderera chiuru.
Zvinofungidzirwa
Kutenderera kwakazvimiriramasvomhuKutenderera kwakazvimiriraKutenderera kwega kwega kune mikana imwe chete zvisinei nezvakaitika kare. Ihwo hwaro hwekuverenga kwese pawebhusaiti ino.Verengai zvese →, uye huwandu hunotarisirwa hunosvika 5 pagomba, zvinoreva kuti n ≥ 185 kuti bvunzo ive yakarurama zvachose uye zvakawanda kwazvo kuti ibatsire. Kusanganisa kutenderera kubva pamavhiri akasiyana kunotyora kufungidzira kwekutanga mupfungwa (muri kuedza musanganiswa, kwete vhiri). Siginecha yemutambisi yaizozvityora chaizvo, uye yaizowedzera χ² pasina gomba rinofarirwa nemuviri.
Siginecha yeMutambisi weRouletteKutenderera kweRoulette Kwakazvimirira
Pearson neMonte Carlo
Karl Pearson akaburitsa bvunzo iyi muna 1900, uye mumwe wemienzaniso yake yekutanga kutenderera 26,306 kweRoulette yeMonte Carlo kwakanyorwa, kwaakaona kusina kuenzana zvakanyanya kuti kuve mhanza akazivisa kuti “Roulette yeMonte Carlo… haisi mutambo wemhanza”. Vanyori vakazotevera vakagumisa kuti vatori venhau vakanyora kutenderera kwacho kwepepanhau vakagadzira kwakawanda kwacho, chidzidzo chacho pachacho pamusoro pekwakabva data.
Pearson anoburitsa bvunzo yechi-square goodness-of-fit, nekutenderera kweMonte Carlo semuenzaniso.
Data rekutenderera rinobvunzwa; vanyori vanoratidzika kunge vakagadzira nhevedzano.
Fisher anoronga madhigirii erusununguko; tsika ye5% inotanga kushanda.
Nyanzvi dzenhamba dzinoshandisa kutenderera kweRoulette sedata remumabhuku ebvunzo dzekuenzana.
Mhuri yekwaGarcía-Pelayo inoshandisa nzira iyi nedata chairo rakanyorwa uye inokunda kuMadrid.
Makasino anoita bvunzo imwe chete iyi pamavhiri awo sechikamu chekuchengetedza kwenguva dzose.
Bvunzo chaiyo: mavhiri anozvishandira muLas Vegas
Vatambi vanowanzofungira kuti vhiri rinozvishandira rinotungamira bhoramidziyoBhoraBhora diki rinokandwa mumugero richienda rimwe divi nerotor. Mabhora emazuva ano ndeeivorine kana Teflon, 18–21 mm.Verengai zvese → kure nemabheti makuru. Ongororo ya2017 yakaedza kufungira uku pamavhiri eInterblock asina mutambisi ane zerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → mbiri muLas Vegas, ichibheja pachikamu chenhamba shanu dzakavakidzana, rudzi rwebheti runoitwa nemunhu anoyera nguva yevhiri. Mukutenderera 299 chikamu chacho chakakunda ka29 pane 39.3 zvaitarisirwa, kushaikwa kunoburitswa nevhiri rakarurama ingangoita 4% yenguva. Chi-square pamakomba ese 38 yaive 45.29 pamadhigirii erusununguko 37: p = 16.5%. Sampuru yechipiri yekutenderera 1,204 pamavhiri matatu yakapa χ² = 34.79, p = 57%, uye hapana chikamu chehukuru hupi zvahwo chakaedzwa chaive nekukosha. Masampuru ese ari maviri pamwe chete, kutenderera 1,503, akapa χ² = 41.75, p = 27%. Mhedziso yaive yekuti hapana humbowo hwekutungamira. Sampuru yekutanga yega yaiita seinofungirwa; yechipiri ndiyo yakazvigadzirisa.
Kupfuura chi-square
Kugomba rimwe chete rinofungirwa bvunzo yebinomial ine simba kupfuura. Kuchikamu chinofungirwa, z-test yechikamu chevhirivhiriChikamu chevhiriRutivi rwemakomba akatevedzana pavhiri, rwakasiyana neboka riri patafura yekubhejera.Verengai zvese → iri papeji reOngororo yeZvikamu zveVhiri. Chi-square ibvunzo yezvose: inokuudzai kuti pane chisina kururama isingataure kuti chii. Ishandisei kutanga, mozotarisa.
Fomula
Mibvunzo
Nhamba 37 dzinofanira kusanganiswa dzosvika pa n, saka 36 chete ndidzo dzakasununguka kuchinja.
Vhiri rine gomba rimwe pa1/25 mukutenderera 10,000 raizopa chikamu chegomba chingangoita 60 chega; χ² ingangoita 100, p inenge zero.
Mumutemo hongu, ne5.4 zvinotarisirwa pagomba. Haizooni chinhu kunze kwevhiri rine gomba rakanamirwa rikavharika.
Kuseka zvishoma
Sanganisai zvinoshamisa zvakasikweyiwa. Enzanisai ne51.0.
Zvinyorwa
- 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.”