Laboratwari ya Roulette · Laboratwari · Ibarurishamibare · iminota 8

Isuzuma rya Chi-Square

Isuzuma risanzwe ry'ikibazo “ese iyi mibare 37 ni yo uruziga rutabogamye rwatanga?”

Igisubizo kigufi

χ² = Σ (ibyabonetse − ibiteganyijwe)² / ibiteganyijwe ku tuzu 37 twose. Bigereranye n'ikwirakwizwa rya chi-square rifite ibipimo by'ubwisanzure 36 kugira ngo ubone p-value.

igipimo

Σ (O−E)²/E

agaciro ntarengwa kuri 5%

51,0

agaciro ntarengwa kuri 1%

58,6

Kuyibara

Umubare uteganyijwe kuri buri kazuibikoreshoAkazuKamwe mu tuzu 37 twanditseho imibare turi kuri rotor. Nanone: slot, cup.Soma byose → ni n/37. Kuri buri kazu, fata itandukaniro hagati y'ibyabonetse n'ibiteganyijwe urikube ryo ubwaryo, urigabanye ibiteganyijwe; ongeranya ibyo bice 37. Uruziga rutabogamye rutanga agaciro kari hafi ya 36 ku mpuzandengo (ibipimo by'ubwisanzurelaboratwariIbipimo by'ubwisanzureUmubare w'agaciro kigenga mu mubare w'ibarurishamibare. Ku isuzuma rya chi-square ku tuzu 37 ni 36, kuko imibare yabaruwe igomba guteranwa ikangana n'igiteranyo.Soma byose →), gafite ikinyuranyo gisanzweimibareIkinyuranyo gisanzweUmuzi wa kare w'ihindagurika; intera isanzwe y'igisubizo uvuye ku gaciro gateganyijwe.Soma byose → cya hafi 8,5. Hejuru ya 51,0 bifite igisobanuro ku rugero rwa 5%; hejuru ya 58,6 kuri 1%. Isesengura ry'Ukubogama k'Uruziga rwa Roulette ribara icyo gipimo na p-valuelaboratwarip-valueAmahirwe yo kubona itandukaniro rinini nk'iryabonetse cyangwa ririruta, iyo uruziga ruba rutabogamye.Soma byose → nyayo hakoreshejwe regularized incomplete gamma function.

amazunguruka nibiteganyijwe kuri buri kazuσ kuri buri kazuakazu kuri +2σakazu kuri +3σ

370103,11619

1.000275,13742

3.7001009,9120130

10.00027016,2303319

37.0001.00031,21.0621.094

σ ≈ √(n·p·(1−p)) aho p = 1/37. Mu mazunguruka 1.000, akazu kaguyemo inshuro 37 nta kidasanzwe gafite; akaguyemo 42 gakwiye icyitegererezo cya kabiri.

Urugero rubazwe

Amazunguruka 1.000. Utuzu mirongo itatu na dutandatu tuguyemo hagati y'inshuro 20 na 34; akazu 8 kaguyemo 41. Ibiteganyijwe ni 27,03. Igice cy'akazu 8 cyonyine ni (41 − 27,03)²/27,03 = 7,2. Tuvuge ko ibindi bice 36 byose hamwe ari 38 (bisanzwe). χ² = 45,2 kuri df 36, p ≈ 0,14. Nta gisobanuro gifite: uruziga rutabogamye rukora ibi rimwe mu nshuro zirindwi. Akazu 8 ni umukandida, si ikintu wavumbuye, kandi igisubizo ni andi mazunguruka igihumbi.

Ibyo isuzuma rifata nk'ukuri

Amazunguruka yigengaimibareAmazunguruka yigengaBuri zunguruka rifite amahirwe amwe uko amateka yaba ari kose. Ni ryo shingiro rya buri mubare ubarwa kuri uru rubuga.Soma byose →, n'imibare iteganyijwe nibura 5 kuri buri kazu, bivuga n ≥ 185 kugira ngo isuzuma ribe ryemewe na mba, n'amazunguruka menshi cyane kurushaho kugira ngo rigire akamaro. Guhuriza hamwe amazunguruka y'inziga zitandukanye binyuranya n'icya mbere mu buryo bw'igitekerezo (uba usuzuma uruvange, si uruziga). Ingaruka y'umukono wa kurupiye yabinyuranya mu by'ukuri, kandi yakongera χ² nta kazu na kamwe gatoneshwa n'ibikoresho.

Umukono wa Kurupiye wa Roulette Amazunguruka ya Roulette Yigenga

Pearson na Monte Carlo

Karl Pearson yatangaje iri suzuma mu 1900, kandi kimwe mu ngero ze za mbere yabaze cyari amazunguruka 26.306 ya roulette yo muri Monte Carlo yanditswe, asanga atangana na gato ku buryo bidashobora kuba amahirwe, maze avuga ko “roulette ya Monte Carlo… si umukino w'amahirwe”. Abanditsi baje nyuma banzuye ko abanyamakuru banditse ayo mazunguruka ku kinyamakuru bahimbye menshi muri yo, ibyo bikaba isomo ryihariye ku byerekeye inkomoko y'amakuru.

Isuzuma n'uruziga

1900

Pearson atangaza isuzuma rya chi-square ry'ukuntu amakuru ahura n'icyitegererezo, akoresheje amazunguruka ya Monte Carlo nk'urugero.

imyaka ya 1900

Amakuru y'amazunguruka arashidikanywaho; abayanditse basa n'abahimbye impererekane.

imyaka ya 1920

Fisher ashyira ku murongo ibipimo by'ubwisanzure; akamenyero ka 5% gafata.

imyaka ya 1940–50

Abahanga mu ibarurishamibare bakoresha amazunguruka ya roulette nk'amakuru yo mu bitabo by'amasomo mu masuzuma y'ukungana.

imyaka ya 1990

Umuryango wa García-Pelayo ukoresha ubu buryo ku makuru nyayo yanditswe kandi utsindira i Madrid.

uyu munsi

Kazino zikora iryo suzuma ku nziga zazo nk'igice cy'isana risanzwe.

Isuzuma rya Pearson ryo mu 1900 ryasanze amazunguruka ya Monte Carlo atangana na gato; abanditsi b'ikinyamakuru bari barahimbye menshi muri yo.

Roulette ya Monte Carlo

Isuzuma nyaryo: inziga zikora zonyine i Las Vegas

Abakinnyi bakunze gukeka ko uruziga rukora rwonyine ruyobya agapiraibikoreshoAgapiraAgapira gato koherezwa mu nzira kerekeza mu cyerekezo kinyuranye n'icya rotor. Udupira tw'iki gihe dukozwe muri ivorine cyangwa Teflon, mm 18–21.Soma byose → kure y'amatega manini. Isesengura ryo mu 2017 ryasuzumye icyo gikeko ku nziga za Interblock zidafite kurupiye, zifite zeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → ebyiri, i Las Vegas, hategwa ku muheto w'imibare itanu yegeranye, ubwoko bw'itega umuntu upima uruziga akora. Mu mazunguruka 299 uwo muheto watsinze inshuro 29 mu gihe hateganyijwe 39,3, ibura uruziga rutabogamye rutanga hafi 4% by'igihe. Chi-square ku tuzu 38 twose yari 45,29 ku bipimo by'ubwisanzure 37: p = 16,5%. Icyitegererezo cya kabiri cy'amazunguruka 1.204 ku nziga eshatu cyatanze χ² = 34,79, p = 57%, kandi nta muheto n'umwe w'ingano iyo ari yo yose wageragejwe wagize igisobanuro. Ibyitegererezo byombi hamwe, amazunguruka 1.503, byatanze χ² = 41,75, p = 27%. Umwanzuro wabaye ko nta kimenyetso cyo kuyobya agapira. Icyitegererezo cya mbere cyonyine cyasaga n'igiteye amakenga; icya kabiri ni cyo cyabikemuye.

icyitegererezoamazungurukaχ²dfp

icya mbere29945,293716,5%

icya kabiri, inziga eshatu1.20434,793757%

byombi1.50341,753727%

Imibare ituruka kuri iryo sesengura ryo mu 2017; buri p-value ikomoka kuri χ² yayo. Uruziga rufite zeru ebyiri rufite utuzu 38, bityo ibipimo by'ubwisanzure 37.

Hejuru ya chi-square

Ku kazu kamwe gakekwa, isuzuma rya binomial rifite imbaraga kurushaho. Ku muheto ukekwa, z-test y'igice cy'uruzigauruzigaIgice cy'uruzigaUmuheto w'utuzu dukurikirana ku ruziga, bitandukanye n'itsinda ku mbonerahamwe y'amatega.Soma byose → iri ku ipaji ya Isesengura ry'Ibice by'Uruziga. Chi-square ni isuzuma rusange: rikubwira ko hari ikitagenda neza ritavuga icyo ari cyo. Ribanze, hanyuma urebe.

Isesengura ry'Ibice by'Uruziga

Formula

χ² = Σᵢ (Oᵢ − Eᵢ)² / Eᵢ

Eᵢ = n / 37 · df = 36

agaciro ntarengwa: 51,0 (5%) · 58,6 (1%)

Ibibazo

Kuki ibipimo by'ubwisanzure ari 36 aho kuba 37?

Imibare 37 igomba kungana na n iyo iteranyijwe, bityo 36 gusa ni yo ishobora guhinduka mu bwisanzure.

Uruziga rubogamye cyane rwagaragaza χ² ingana iki?

Uruziga rufite akazu kamwe ka 1/25 mu mazunguruka 10.000 rwatanga igice cy'ako kazu cyonyine kiri hafi ya 60; χ² hafi 100, p hafi zeru rwose.

Ese nshobora kurikora ku mazunguruka 200?

Mu buryo bwa tekiniki yego, biteganyijwe 5,4 kuri buri kazu. Nta cyo rizatahura keretse uruziga rufite akazu kafunzwe na kole.

Akanya k'urwenya

Teranya ibitunguranye bikubwe ubwabyo. Bigereranye na 51,0.

Inkomoko

Pearson, K. “On the criterion that a given system of deviations from the probable…” Philosophical Magazine 50(302), 1900.
Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gushira igishoro k'umukinnyi w'urusimbi (gambler’s ruin), igice cya XIV.
Wizard of Odds. “Organic Roulette Experiment.” Werurwe 2017; byavuguruwe ku wa 3 Kanama 2026.

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