Whakamātautau Chi-square
Te whakamātautau paerewa mō te pātai “koinei ngā tatau e 37 ka whakaputaina e tētahi wīra tōkeke?”
χ² = Σ (kitea − tūmanakohia)² / tūmanakohia puta noa i ngā kōhao katoa e 37. Whakatairitea ki te tohatoha chi-square i runga i ngā taumata herekore 36 kia whiwhi ai i tētahi uara-p.
Te tātai
Ko te tatau e tūmanakohia ana mō ia kōhaotaputapuKōhaoTētahi o ngā wehenga e 37 kua tauia i te rōta. Arā anō: slot, cup.Pānuitia katoatia →, he n/37. Mō ia kōhao, pūrua te rerekētanga i waenga i te mea i kitea me te mea e tūmanakohia ana, ka wehe ai ki te mea e tūmanakohia ana; tāpiria ngā wāhanga e 37. Ka hoatu e tētahi wīra tōkeke ngā uara huri noa i te 36 i te toharite (ngā taumata herekoretaiwhangaTaumata herekoreTe maha o ngā uara motuhake i tētahi tatauranga. Mō te whakamātautau chi-square i ngā kōhao e 37, e 36, nā te mea me tāpiri ngā tatau ki te tapeke.Pānuitia katoatia →), me te hipanga paerewapāngarauHipanga paerewaTe pūtake rua o te tītaringa; te tawhiti noa o te hua i te uara tūmanako.Pānuitia katoatia → i te āhua o te 8.5. Ki runga ake i te 51.0, he hira i te taumata 5%; ki runga ake i te 58.6, i te 1%. Ka tātaihia e te Wheel Bias Analyzer te tauanga me te uara-ptaiwhangaUara-pTe tūponotanga ka kitea he rerekētanga ōrite te nui, nui ake rānei i te mea kua kitea, mēnā he tōkeke te wīra.Pānuitia katoatia → tika mai i te pānga gamma koretake kua whakaritea.
He tauira kua mahia
1,000 hurihanga. E toru tekau mā ono ngā kōhao kei waenga i te 20 me te 34 ngā pā; e 41 tā te kōhao 8. Ko te mea e tūmanakohia ana, he 27.03. Ko te wāhanga o te kōhao 8 anake, he (41 − 27.03)²/27.03 = 7.2. Me kī ka tae te tapeke o ērā atu wāhanga e 36 ki te 38 (he mea noa). χ² = 45.2 i runga i te 36 df, p ≈ 0.14. Kāore e hira: ka pēnei tētahi wīra tōkeke kotahi i ia whitu. He kaitono te kōhao 8, ehara i te kitenga, ā, ko te whakautu, he kotahi mano hurihanga anō.
Ngā whakapae
Ngā hurihanga motuhakepāngarauNgā hurihanga motuhakeHe ōrite ngā tūponotanga o ia hurihanga, ahakoa te hītori. Koia te tūāpapa o ia tātaitanga i tēnei pae.Pānuitia katoatia →, me ngā tatau e tūmanakohia ana kia 5 neke atu mō ia kōhao, arā, n ≥ 185 kia whai mana noa ai te whakamātautau, ā, he nui kē atu kia whai hua ai. Mā te whakahiato i ngā hurihanga o ngā wīra maha ka takahia te wairua o te whakapae tuatahi (kei te whakamātau koe i tētahi ranunga, ehara i tētahi wīra). Mā tētahi pānga waitohu kaitiritiri ka tino takahia, ā, ka whakanui ake i te χ² ahakoa kāore he kōhao e manakohia ā-tinana ana.
Pearson me Monte Carlo
I whakaputaina e Karl Pearson te whakamātautau i te 1900, ā, ko tētahi o ana tauira tuatahi, ko ngā hurihanga rūreti 26,306 i tuhia i Monte Carlo; i kitea e ia he tino kore ōrite rawa kia kīia he tūpono noa, ā, i kī ia “Monte Carlo roulette… is not a game of chance” (ehara te rūreti o Monte Carlo i te kēmu tūpono). I muri mai i whakatau ētahi kaituhi, nā ngā kairīpoata i tuhi i ngā hurihanga mō tētahi niupepa te nuinga i hanga noa, he akoranga anō tēnā mō te pūtake o ngā raraunga.
Ka whakaputaina e Pearson te whakamātautau chi-square mō te hāngai, me ngā hurihanga o Monte Carlo hei tauira.
Ka pātaitia ngā raraunga hurihanga; te āhua nei i hanga noa ngā kaituhi i ētahi raupapa.
Ka whakaōkawa a Fisher i ngā taumata herekore; ka mau te tikanga 5%.
Ka whakamahia e ngā kaitatauranga ngā hurihanga rūreti hei raraunga pukapuka ako mō ngā whakamātautau ōritenga.
Ka whakamahia e te whānau García-Pelayo te tikanga me ngā raraunga tūturu kua tuhia, ā, ka toa i Madrid.
Ka whakahaerehia e ngā whare petipeti taua whakamātautau anō i ō rātou ake wīra hei tiaki noa.
He whakamātautau tūturu: ngā wīra aunoa i Las Vegas
He maha ngā wā ka whakapae ngā kaitākaro kei te ārahi tētahi wīra aunoa i te pōrotaputapuPōroTe pōro iti ka panga ki te ara, ki te ahunga kōaro ki te rōta. Ko ngā pōro o nāianei he ivorine, he Teflon rānei, 18–21 mm.Pānuitia katoatia → kia mawehe i ngā peti nui. I whakamātauria taua whakapae e tētahi tātaritanga i te 2017 i ngā wīra korewīraKoreTe kōhao kākāriki kotahi kāore e kapia e tētahi peti utu ōrite, tatini, tīwae rānei; te pūtake o te painga o te whare. Arā anō: kore kotahi, 0.Pānuitia katoatia →-rua a Interblock kāore he kaitiritiri, i Las Vegas, mā te peti i tētahi pewa o ngā tau noho tata e rima, te momo peti a tētahi kaiine wā wīra. I roto i ngā hurihanga 299, e 29 ngā toa a te pewa, ki te 39.3 e tūmanakohia ana, he hapa ka whakaputaina e tētahi wīra tōkeke i te āhua o te 4% o te wā. Ko te chi-square puta noa i ngā kōhao katoa e 38, he 45.29 i runga i ngā taumata herekore 37: p = 16.5%. Ko tētahi tauira tuarua o ngā hurihanga 1,204 i ngā wīra e toru, i hoatu χ² = 34.79, p = 57%, ā, kāore tētahi pewa o ngā rahi katoa i whakamātauria i hira. Ko ngā tauira e rua tahi, ngā hurihanga 1,503, i hoatu χ² = 41.75, p = 27%. Ko te whakataunga, kāore he taunakitanga o te ārahi. Ko te tauira tuatahi anake, he āhua whakapae; nā te tuarua i whakatau.
I tua atu i te chi-square
Mō tētahi kōhao kotahi e whakapaetia ana, he kaha ake te whakamātautau huarua. Mō tētahi pewa e whakapaetia ana, ko te whakamātautau-z wāhangawīraWāhangaHe pewa kōhao honohono i te wīra, he rerekē i tētahi rōpū i te mahere peti.Pānuitia katoatia → kei te whārangi tātari wāhanga. Ko te chi-square te whakamātautau whānui: ka kōrero mai kei te hē tētahi mea, engari kāore e kī ko te aha. Whakamahia tuatahi, kātahi ka titiro.
Tātai
Ngā pātai
Me tae te tapeke o ngā tatau e 37 ki te n, nō reira e 36 anake e wātea ana ki te rerekē.
Ko tētahi wīra kotahi te kōhao i te 1/25 i ngā hurihanga 10,000, ka hoatu he wāhanga kōhao i te āhua o te 60 anake; χ² i te āhua o te 100, p tata ki te kore.
Āe, i runga i te ture, me te 5.4 e tūmanakohia ana mō ia kōhao. Kāore e kitea tētahi mea, hāunga tētahi wīra kua whakapiria tētahi kōhao kia kati.
He katakata iti
Tāpiria ngā ohorere kua pūruatia. Whakatairitea ki te 51.0.
Ngā Puna
- 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.”