Chi-square sɔhwɛ
Gyinapɛn sɔhwɛ a ɛbisa sɛ “so akontaa 37 yi ne deɛ ntwahonan a ɛyɛ pɛ bɛma?”
χ² = Σ (deɛ wohunuiɛ − deɛ wɔhwɛ kwan)² / deɛ wɔhwɛ kwan wɔ ntokuru 37 no nyinaa so. Fa toto chi-square nhyehyɛe a ɛwɔ ahofadie dodoɔ 36 so ho na wobɛnya p-boɔ.
Sɛdeɛ wobɛbu
Akontaa a wɔhwɛ kwan wɔ tokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → biara so ne n/37. Wɔ tokuru biara so no, fa nsonsonoeɛ a ɛda deɛ wohunuiɛ ne deɛ wɔhwɛ kwan ntam no bɔ ne ho mmɔho na fa deɛ wɔhwɛ kwan kyɛ mu; ka nneɛma 37 no bom. Ntwahonan a ɛyɛ pɛ ma boɔ a ɛbɛyɛ 36 wɔ mfinimfini mu (ahofadie dodoɔnhwehwɛmu danAhofadie dodoɔBoɔ a ɛmfa ho dodoɔ a ɛwɔ akontaabu nsunsuansoɔ bi mu. Wɔ chi-square sɔhwɛ a ɛwɔ ntokuru 37 so no, ɛyɛ 36, ɛfiri sɛ ɛsɛ sɛ nkontaabu no nyinaa bom yɛ dodoɔ no nyinaa.Kenkan ne nyinaa → no), a ne gyinapɛn nsakraeɛakontaabuGyinapɛn nsakraeɛNsakraeɛ ntini; ntam kwan a ɛtaa da deɛ ɛfiri mu ba ne boɔ a wɔhwɛ kwan ntam.Kenkan ne nyinaa → yɛ bɛyɛ 8.5. Deɛ ɛboro 51.0 so no wɔ nnyinasoɔ wɔ 5% so; deɛ ɛboro 58.6 so no wɔ 1% so. Roulette ntwahonan animhwɛ nhwehwɛmu afidie no bu akontaa no ne p-boɔnhwehwɛmu danp-boɔHokwan a wobɛhunu nsonsonoeɛ a ɛso te sɛ deɛ wohunuu no anaa ɛboro saa, sɛ ntwahonan no yɛ pɛ a.Kenkan ne nyinaa → pɛpɛɛpɛ firi regularized incomplete gamma function mu.
Nhwɛsoɔ a yɛayɛ
Kyinhyia 1,000. Ntokuru aduasa nsia ba mprɛ 20 kɔsi 34; tokuru 8 ba mprɛ 41. Deɛ wɔhwɛ kwan ne 27.03. Tokuru 8 deɛ nko ara yɛ (41 − 27.03)²/27.03 = 7.2. Susu sɛ 36 a aka no nyinaa bom yɛ 38 (deɛ ɛtaa ba). χ² = 45.2 wɔ df 36 so, p ≈ 0.14. Ɛnni nnyinasoɔ: ntwahonan a ɛyɛ pɛ yɛ saa prɛ baako wɔ nson mu. Tokuru 8 yɛ deɛ ɛsɛ sɛ wohwɛ, ɛnyɛ nhunumu, na mmuaeɛ no ne kyinhyia apem foforɔ.
Susuo a ɛwɔ ase
Kyinhyia a ɛmfa hoakontaabuKyinhyia a ɛmfa hoKyinhyia biara hokwan yɛ pɛ sɛdeɛ deɛ atwam teɛ biara. Ɛno ne akontaabu biara a ɛwɔ wɛbsaet yi so nnyinasoɔ.Kenkan ne nyinaa →, ne akontaa a wɔhwɛ kwan a ɛyɛ 5 anaa ɛboro so wɔ tokuru biara so, na ɛno kyerɛ sɛ n ≥ 185 ansa na sɔhwɛ no ayɛ adwuma koraa, na ɛboro saa kɛseɛ ansa na mfasoɔ aba. Sɛ wode kyinhyia a ɛfiri ntwahonan ahodoɔ so ka bom a, wobu susuo a edi kan no so wɔ ne nkyerɛaseɛ mu (worehwɛ nneɛma a afrafra, ɛnyɛ ntwahonan baako). Dila nsa agyiraehyɛde bɛbu so ampa, na ɛbɛma χ² akɔ soro a tokuru biara nni hɔ a ntwahonan no ankasa boa.
Pearson ne Monte Carlo
Karl Pearson tintimii sɔhwɛ no wɔ 1900, na ne nhwɛsoɔ a edi kan no mu baako yɛ Monte Carlo roulette kyinhyia 26,306 a wɔkyerɛw too hɔ, a ɔhunuu sɛ ɛnyɛ pɛ koraa ara ma ɛrentumi nyɛ akɔntɔnkye, na ɔkaa sɛ “Monte Carlo roulette… nyɛ akɔntɔnkye agorɔ”. Akyire nwomakyerɛfoɔ kaa sɛ nsɛmmɔnefoɔ a wɔkyerɛw kyinhyia no too hɔ maa nsɛmma krataa bi no bɔɔ dodoɔ no ara ho atorɔ, na ɛno ankasa yɛ asuadeɛ a ɛfa baabi a nsɛm firi ho.
Pearson tintim chi-square goodness-of-fit sɔhwɛ no, a ɔde Monte Carlo kyinhyia yɛ nhwɛsoɔ.
Wɔbisa kyinhyia nsɛm no ho nsɛm; ɛte sɛ deɛ wɔn a wɔkyerɛw too hɔ no bɔɔ ntoatoasoɔ bi ho atorɔ.
Fisher hyehyɛ ahofadie dodoɔ ma ɛtim; 5% amammerɛ no gye ntini.
Akontaabufoɔ de roulette kyinhyia yɛ adesua nwoma nsɛm ma pɛyɛ sɔhwɛ.
García-Pelayo abusua no de ɔkwan no di dwuma wɔ nsɛm ankasa a wɔkyerɛw too hɔ so na wɔdi nkonim wɔ Madrid.
Kasino ahodoɔ yɛ sɔhwɛ korɔ no ara wɔ wɔn ankasa ntwahonan so sɛ siesie a wɔyɛ daa.
Sɔhwɛ ankasa: ntwahonan a ɛyɛ n’ankasa adwuma wɔ Las Vegas
Agorɔfoɔ taa susu sɛ ntwahonan a ɛyɛ n’ankasa adwuma kyerɛ bɔɔlnneɛma a wɔde diBɔɔlBɔɔl ketewa a wɔto no ma ɛtu mmirika wɔ ne kwan mu tia rotor no. Ɛnnɛ bɔɔl yɛ ivorine anaa Teflon, 18–21 mm.Kenkan ne nyinaa → no kwan ma ɛtwe ne ho firi bɛt akɛseɛ ho. Nhwehwɛmu bi a wɔyɛɛ wɔ 2017 mu sɔɔ saa adwene yi hwɛɛ wɔ Interblock ntwahonan a dila nni ho a hweentwahonanHweeTokuru ahabammono baako a sika pɛ bɛt, dumienu kuo bɛt anaa santen tee bɛt biara nkata so; kasino mfasoɔ fibea. Wɔfrɛ no nso hwee baako, 0.Kenkan ne nyinaa → mmienu wɔ so wɔ Las Vegas, na ɛtoo bɛt wɔ nɔma enum a ɛbɛn wɔn ho ɔfa so, bɛt a ntwahonan bere susufoɔ taa to. Wɔ kyinhyia 299 mu no, ɔfa no dii nkonim mprɛ 29 bere a wɔhwɛ kwan sɛ ɛbɛyɛ 39.3, na ntwahonan a ɛyɛ pɛ ma saa nkoguo yi bɛyɛ 4% wɔ bere mu. Chi-square wɔ ntokuru 38 no nyinaa so yɛ 45.29 wɔ ahofadie dodoɔ 37 so: p = 16.5%. Nhwɛsoɔ a ɛtɔ so mmienu a ɛyɛ kyinhyia 1,204 wɔ ntwahonan mmiɛnsa so maa χ² = 34.79, p = 57%, na ɔfa biara a wɔsɔɔ hwɛeɛ, ne kɛseɛ biara, anni nnyinasoɔ. Nhwɛsoɔ mmienu no nyinaa bom, kyinhyia 1,503, maa χ² = 41.75, p = 27%. Atemmuo no ne sɛ adanseɛ biara nni hɔ sɛ ɛkyerɛ bɔɔl no kwan. Nhwɛsoɔ a edi kan no nko ara de, na ɛyɛ adwenemmɔne; deɛ ɛtɔ so mmienu no na ɛsii asɛm no pi.
Sɛ yɛtra chi-square so a
Sɛ tokuru baako pɛ na wosusu ho a, binomial sɔhwɛ wɔ tumi kɛseɛ. Sɛ ɔfa bi na wosusu ho a, ɔfantwahonanƆfaNtokuru a ɛtoa so wɔ ntwahonan no so, a ɛnyɛ kuo a ɛwɔ bɛt nhyehyɛe no so.Kenkan ne nyinaa → z-sɔhwɛ a ɛwɔ ntwahonan afa ho nhwehwɛmu krataafa no so. Chi-square yɛ sɔhwɛ a ɛhwɛ biribiara: ɛka kyerɛ wo sɛ biribi nteɛ a ɛnka deɛ ɛyɛ. Di kan fa yɛ adwuma, na afei hwɛ.
Akontaabu kwan
Nsɛmmisa
Ɛsɛ sɛ akontaa 37 no nyinaa bom yɛ n, enti 36 pɛ na wɔde wɔn ho wɔ hɔ sɛ wɔbɛsesa.
Ntwahonan a ne tokuru baako ba wɔ 1/25 wɔ kyinhyia 10,000 mu no, ne tokuru no nko ara bɛma bɛyɛ 60; χ² bɛyɛ 100, na p kame ayɛ hwee.
Wɔ mmara kwan so de, aane, a wɔhwɛ kwan sɛ ɛbɛyɛ 5.4 wɔ tokuru biara so. Ɛrenhu hwee gye sɛ ntwahonan a wɔde ɛfam ato ne tokuru bi ano.
Serew kakra
Ka nwonwa a wɔabɔ ho mmɔho no bom. Fa toto 51.0 ho.
Nsɛm fibea
- 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.”