Igeragezwa rya Chi-Square
Igeragezwa risanzwe ry'ikibazo “ivyo bitigiri 37 ni vyo uruziga rutabogamye rwotanga?”
χ² = Σ (ivyabonetse − ivyitezwe)² / ivyitezwe ku tuzu 37 twose. Bigereranye n'ugutandukana kwa chi-square ku rugero rw'ubwigenge 36 kugira ngo uronke p-value.
Ingene riharurwa
Igitigiri citezwe kuri buri kazuibikoreshoAkazuKimwe mu bibanza 37 bifise inomero kuri rotor. Kandi bita: slot, cup.Soma vyose → ni n/37. Kuri buri kazu, kuba ugutandukana kw'ivyabonetse n'ivyitezwe ku kwako hanyuma ugabure ku vyitezwe; teranya ivyo bice 37. Uruziga rutabogamye rutanga ibitigiri biri hafi ya 36 ku mpuzandengo (urwo ni urugero rw'ubwigengeubushakashatsiUrugero rw'ubwigengeIgitigiri c'agaciro kigenga mu giharuro. Ku igeragezwa rya chi-square ku tuzu 37 ni 36, kuko ibiharuro bitegerezwa gutera hamwe igiteranyo.Soma vyose →), n'itandukaniro risanzweimibareItandukaniro risanzweUmuzi kare w'ihindagurika ry'ivyavuyemwo; intera isanzwe iri hagati y'ivyavuyemwo n'agaciro kitezwe.Soma vyose → rya nka 8,5. Hejuru ya 51,0 bihambaye ku rugero rwa 5%; hejuru ya 58,6 ku 1%. Igikoresho Gisuzuma Ukubogama kw'Uruziga rwa Ruleti giharura ico giharuro na p-valueubushakashatsip-valueUgushoboka kwo kubona itandukaniro rinini nk'iryabonetse canke rirengeye, iyo uruziga rutoba rubogamye.Soma vyose → nyayo ukoresheje igikorwa ca gamma kituzuye gitunganijwe (regularized incomplete gamma).
Akarorero gaharuwe
Ukuzunguruka 1.000. Utuzu mirongo itatu na dutandatu dufatwa hagati y'incuro 20 na 34; akazu 8 kafashwe 41. Ivyitezwe ni 27,03. Igice c'akazu 8 conyene ni (41 − 27,03)²/27,03 = 7,2. Tuvuge ko ibindi bice 36 biteranijwe ari 38 (bisanzwe). χ² = 45,2 kuri df 36, p ≈ 0,14. Ntibihambaye: uruziga rutabogamye rukora ivyo incuro imwe mu ndwi. Akazu 8 ni ako gukekwa, si ikintu cabonetse, kandi inyishu ni ukundi kuzunguruka igihumbi.
Ivyiyumviro bishingirwako
Ukuzunguruka kwigengaimibareUkuzunguruka kwigengaUkuzunguruka kwose kugira ugushoboka kumwe n'ivyabaye kera vyose. Ni co gishingiro c'ibiharuro vyose vyo kuri uru rubuga.Soma vyose →, n'ibitigiri vyitezwe nibura 5 kuri buri kazu, bisigura n ≥ 185 kugira ngo igeragezwa ribe ari iry'ukuri, kandi kurenza cane kugira ngo rigire akamaro. Kuvanga ukuzunguruka kw'inziga zitandukanye birenga ku civyumviro ca mbere mu nsiguro yaco (uba ugerageza uruvangitirane, si uruziga rumwe). Ingaruka y'akaranga ka croupier yoca irenga kuri co vy'ukuri, kandi yokongereza χ² naho nta kazu na kamwe gashigikiwe n'ibikoresho.
Akaranga ka Croupier muri RuletiUkuzunguruka kwa Ruleti Kutisunga Ukundi
Pearson na Monte Carlo
Karl Pearson yasohoye iri geragezwa mu 1900, kandi kimwe mu turorero twiwe twa mbere twaharuwe cari ukuzunguruka 26.306 kwa ruleti kwanditswe i Monte Carlo, ivyo yasanze bitangana na gato ku buryo bidashobora kuba impanuka, aca avuga ko “ruleti ya Monte Carlo… si umukino w'impanuka”. Abanditsi baje inyuma basanze abanyamakuru banditse ukwo kuzunguruka ku kinyamakuru barahimbye igice kinini cakwo, ivyo bikaba ari icigwa ubwaco ku nkomoko y'amakuru.
Pearson asohora igeragezwa rya chi-square ry'ukwisanisha, akoresheje ukuzunguruka kwa Monte Carlo nk'akarorero.
Amakuru y'ukuzunguruka arakemangwa; abayanditse bisa n'abahimbye imirongo y'ivyavuyemwo.
Fisher ashinga neza urugero rw'ubwigenge; akamenyero ka 5% karashinga imizi.
Abahinga mu biharuro bakoresha ukuzunguruka kwa ruleti nk'amakuru yo mu bitabu vyo kwigiramwo amageragezwa y'ukungana.
Umuryango wa García-Pelayo ukoresha ubwo buryo ku makuru nyakuri yanditswe ugatsinda i Madrid.
Amakazino akora iryo geragezwa nyene ku nziga zayo nk'ugusana gusanzwe.
Igeragezwa nyakuri: inziga zikora zonyene i Las Vegas
Abakinyi kenshi bakeka ko uruziga rukora rwonyene rwerekeza umupiraibikoreshoUmupiraUmupira mutoyi uterwa mu nzira uhushanye na rotor. Imipira y'ubu ikozwe muri ivorine canke Teflon, 18–21 mm.Soma vyose → kure y'amatego manini. Isuzuma ryo mu 2017 ryarageragereje ico ciyumviro ku nziga za Interblock zifise zeruuruzigaZeruAkazu kamwe k'icatsi kibisi kadapfukwa n'itego rya rimwe kuri rimwe, ry'umurwi canke ry'inkingi; ni yo soko y'inyungu ya kazino. Kandi bita: zeru imwe, 0.Soma vyose → zibiri zidafise croupier i Las Vegas, rutega ku gice c'inomero zitanu zibanyi, ubwo bwoko bw'itego umuntu apima uruziga yokora. Mu kuzunguruka 299, ico gice catsinze incuro 29 aho hari hitezwe 39,3, ibura uruziga rutabogamye rutanga nko mu 4% vy'igihe. Chi-square ku tuzu 38 twose yari 45,29 ku rugero rw'ubwigenge 37: p = 16,5%. Icitegererezo ca kabiri c'ukuzunguruka 1.204 ku nziga zitatu catanze χ² = 34,79, p = 57%, kandi nta gice na kimwe c'urugero urwo ari rwo rwose cageragejwe cari gihambaye. Ibitegererezo vyombi hamwe, ukuzunguruka 1.503, vyatanze χ² = 41,75, p = 27%. Ingingo yafashwe ni uko nta cemezo c'ukwerekeza umupira. Icitegererezo ca mbere conyene casa n'igiteye amakenga; ica kabiri ni co catanze inyishu.
Hejuru ya chi-square
Ku kazu kamwe gakekwa, igeragezwa rya binomial rifise inguvu kurushiriza. Ku gice gikekwa, igeragezwa rya z ry'igice c'uruzigauruzigaIgice c'uruzigaUrukurikirane rw'utuzu dufatanye ku ruziga, rutandukanye n'umugwi w'inomero ku kibaho c'amatego.Soma vyose → riri ku rupapuro “Isuzuma ry'Igice c'Uruziga”. Chi-square ni igeragezwa rusangi: rikubwira ko hari ikitagenda neza ritavuze ico ari co. Banza urikoreshe, hanyuma uraba.
Ingingo y'imibare
Ibibazo
Ibitigiri 37 bitegerezwa guteranirwa hamwe bigatanga n, ku buryo 36 gusa ari vyo bishobora guhinduka uko bishaka.
Uruziga rufise akazu kamwe kuri 1/25 mu kuzunguruka 10.000 rwotanga igice c'ako kazu conyene kiri hafi ya 60; χ² iri hafi ya 100, p ihwanye na zeru.
Mu buryo bw'amategeko y'ibiharuro ego, ivyitezwe ari 5,4 kuri buri kazu. Nta co rizomenya kiretse uruziga rufise akazu kafunzwe burundu.
Agakuru ko gutwenga
Teranya ivyagutangaje vyakubwe ku kwavyo. Bigereranye na 51,0.
Aho Twakuye
- 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.”