Chi-skwɛ tɛst

Aw fɔ kalkul am

Di kɔnt we yu fɔ ɛkspɛkt fɔ ɛni pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → na n/37. Fɔ ɛni pɔkit, tek di difrɛns bitwin wetin yu si ɛn wetin yu fɔ ɛkspɛkt, skwɛ am, ɛn dibay am wit wetin yu fɔ ɛkspɛkt; dɔn ad di 37 pat dɛn. Fɛr wil de gi valyu we de rawnd 36 pan avrej (di digri fɔ fridɔmlabDigri fɔ fridɔmDi nɔmba fɔ valyu dɛn we nɔ dipen pan wan ɔda insay wan statistik. Fɔ chi-skwɛ tɛst pan 37 pɔkit na 36, bikɔs ɔl di kawnt dɛn fɔ ad ɔp to di tɔtal.Rid ɔl →), wit standad diviyeshɔnmatematiksStandad diviyeshɔnDi skwɛ rut fɔ varians; di nɔmal distans bitwin wan rizɔlt ɛn di valyu we fɔ ɛkspɛkt.Rid ɔl → fɔ lɛk 8.5. Ɔp pas 51.0 na signifikant na di 5% lɛvel; ɔp pas 58.6 na 1%. Di Wil Bayas Analayza de kalkul di statistik ɛn di rayt rayt p-valyulabp-valyuDi prɔbabiliti fɔ si difrɛns we big lɛk di wan we yu si ɔ big pas am, if di wil bin fɛr.Rid ɔl → frɔm di regyularayz inkɔmplit gama fɔnkshɔn.

Wan ɛgzampul we wi dɔn kalkul

1,000 spin. Tati-siks pɔkit kam bitwin 20 ɛn 34 tɛm; pɔkit 8 kam 41 tɛm. Wetin fɔ ɛkspɛkt na 27.03. Di pat fɔ pɔkit 8 in wan na (41 − 27.03)²/27.03 = 7.2. Se di ɔda 36 pat dɛn ad ɔp to 38 (nɔmal). χ² = 45.2 pan 36 df, p ≈ 0.14. I nɔ signifikant: fɛr wil de du dis wan tɛm pan sɛvin. Pɔkit 8 na sɔntin fɔ wach, nɔto sɔntin we yu dɔn fɛn, ɛn di ansa na ɔda wan tawzin spin.

Wetin di tɛst tek am se tru

Spin we nɔ dipen pan ɔda wanmatematiksSpin we nɔ dipen pan wan ɔdaƐni spin gɛt di sem prɔbabiliti, ilɛksɛf wetin dɔn apin bifo. Na dis ɛni kalkulɛshɔn na dis sayt bil pan.Rid ɔl →, ɛn kɔnt we yu fɔ ɛkspɛkt we pan ɔl 5 fɔ ɛni pɔkit. Dat min n ≥ 185 jɔs fɔ mek di tɛm wok, ɛn bɔku mɔ fɔ mek i gɛt yus. Fɔ miks spin frɔm difrɛn wil de brok di fɔs rul fɔ di tɛst in spirit (yu de tɛst miksɔ, nɔto wil). Ifɛkt frɔm di dila in yon sayn go brok am fɔ tru, ɛn i go mek χ² big ilɛk se nɔ pɔkit nɔ gɛt advantej pan di wil.

Di dila in yon we fɔ spinRulɛt spin we nɔ dipen pan ɔda wan

Pearson ɛn Monte Carlo

Karl Pearson bin pɔblish di tɛst na 1900, ɛn wan pan in fɔs ɛgzampul dɛn na 26,306 Monte Carlo rulɛt spin we dɛn bin rayt dɔŋ. I si se dɛn nɔ ikwal pas mɛzhɔ fɔ bi lɔk, ɛn i se “Monte Carlo rulɛt… nɔto gem fɔ chans”. Afta dat, ɔda raytman dɛn si se di jɔnalis dɛn we bin rayt di spin dɛn fɔ nyuspepa bin mek ɔp bɔku pan dɛn. Dat na in yon lɛsin bɔt usay data kɔmɔt.

Monte Carlo rulɛt

Wan rial tɛst: wil dɛn we de wok dɛnsɛf na Las Vegas

Bɔku tɛm, pleya dɛn de tink se wil we de wok insɛf de stia di bɔlikwipmɛntBɔlDi smɔl bɔl we dɛn trowe na di rod agens di rotɔ. Di nyu bɔl dɛn na ivorine ɔ Teflon, 18–21 mm.Rid ɔl → kɔmɔt frɔm big bɛt dɛn. Wan analisis na 2017 bin tɛst dis tink pan Interblock in wil dɛn wit dɔbul zirowilZiroDi wan grin pɔkit we nɔ ivin-mɔni, dɔzin ɔ kɔlɔm bɛt nɔ kɔba; na usay di kasino advantej kɔmɔt. Dɛn kin kɔl am bak: wan ziro, 0.Rid ɔl → na Las Vegas we nɔ gɛt dila, bay fɔ bɛt pan fayv nɔmba we de nia dɛnsɛf pan di wil: di kayn bɛt we pɔsin we de tɛm di wil kin mek. Insay 299 spin, di sɛkta win 29 tɛm, we dɛn bin fɔ ɛkspɛkt 39.3; fɛr wil de mek dis kayn shɔt lɛk 4% pan di tɛm. Di chi-skwɛ fɔ ɔl di 38 pɔkit na bin 45.29 pan 37 digri fɔ fridɔm: p = 16.5%. Sɛkɔn sampul fɔ 1,204 spin pan tri wil gi χ² = 34.79, p = 57%, ɛn nɔ sɛkta, ilɛk aw i big, nɔ bin signifikant. Di tu sampul togɛda, 1,503 spin, gi χ² = 41.75, p = 27%. Di jɔjmɛnt na se nɔ pruf nɔ de se di wil de stia. Di fɔs sampul in wan bin luk sɔspishɔs; na di sɛkɔn wan sɛtul am.

Pas chi-skwɛ

Fɔ wan pɔkit we yu de sɔspɛkt, binomial tɛst gɛt mɔ pawa. Fɔ wan pat pan di wil we yu de sɔspɛkt, yuz di sɛktawilSɛktaPɔkit dɛn we de fala wan ɔda na wan pat fɔ di wil, nɔto grup na di bɛt tebul.Rid ɔl → z-tɛst na di pej fɔ sɛkta analisis. Chi-skwɛ na di tɛst we de luk ɔltin: i de tɛl yu se sɔntin nɔ rayt, bɔt i nɔ de se wetin. Yuz am fɔs, dɔn luk.

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