Gwajin chi-square

Yadda ake lissafa shi

Ƙidayar da ake tsammani a kowane ramikayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → ita ce n/37. Ga kowane rami, ku ninka bambanci tsakanin abin da aka gani da abin da ake tsammani da kansa, ku raba da abin da ake tsammani; sannan ku haɗa ɓangarorin 37. Dabaran mai adalci yana ba da ƙima kusan 36 a matsakaici (adadin matakan ʼyancigwajiDegrees of freedomYawan ƙimomi masu zaman kansu a cikin wata ƙididdiga. A gwajin chi-square a kan ramuka 37, 36 ne, saboda dole ne ƙirge-ƙirgen su haɗu su ba da jimillar.Karanta gaba ɗaya →), tare da standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → (ma'aunin bambanci daga matsakaici) na kusan 8.5. Sama da 51.0 yana da muhimmanci a matakin 5%; sama da 58.6 a 1%. Mai nazarin karkatar dabaran roulette yana lissafa ƙimar da ainihin p-valuegwajip-valueYiwuwar ganin bambanci da ya kai girman wanda aka gani ko ya fi shi, idan dabaran yana da adalci.Karanta gaba ɗaya → daga regularized incomplete gamma function.

Misalin lissafi

Juye-juye 1,000. Ramuka talatin da shida suna samun tsakanin 20 da 34; rami na 8 yana da 41. Abin da ake tsammani shi ne 27.03. Ɓangaren rami na 8 kaɗai shi ne (41 − 27.03)²/27.03 = 7.2. Bari mu ce sauran ɓangarori 36 sun kai 38 (abin da aka saba). χ² = 45.2 a kan df 36, p ≈ 0.14. Ba mai muhimmanci ba ne: dabaran mai adalci yana yin haka sau ɗaya cikin bakwai. Rami na 8 abin zargi ne kawai, ba abin da aka gano ba, kuma amsar ita ce ƙarin juye-juye dubu.

Zato

Juye-juye da ba sa dogara da junalissafiJuye-juye masu zaman kansuKowane juyi yana da yiwuwa iri ɗaya komai abin da ya faru a baya. Tushen kowane lissafi a wannan shafin.Karanta gaba ɗaya →, da ƙidayar da ake tsammani aƙalla 5 a kowane rami, wanda ke nufin n ≥ 185 don gwajin ya zama mai inganci kwata-kwata, kuma fiye da haka sosai don ya zama mai amfani. Haɗa juye-juye daga dabaran daban-daban yana karya zato na farko a ma'ana (kuna gwada haɗaɗɗiya, ba dabaran ɗaya ba). Tasirin sa hannun croupier zai karya shi a zahiri, kuma zai ƙara χ² ba tare da wani rami ya zama ana fifita shi a zahiri ba.

Alamar hannun croupier a rouletteJuye-juyen roulette masu zaman kansu

Pearson da Monte Carlo

Karl Pearson ya wallafa gwajin a 1900, kuma ɗaya daga cikin misalansa na farko shi ne juye-juyen roulette 26,306 da aka rubuta a Monte Carlo, waɗanda ya ga ba su da daidaito sosai har ba za su zama kwatsam ba, ya kuma bayyana cewa “roulette na Monte Carlo… ba wasan sa'a ba ne”. Daga baya marubuta sun kammala cewa ʼyan jaridar da suka rubuta juye-juyen don wata jarida sun ƙirƙiri da yawa daga cikinsu, wanda shi kansa darasi ne game da asalin bayanai.

Roulette na Monte Carlo

Gwaji na gaske: dabaran masu aiki da kansu a Las Vegas

ʼYan wasa sukan zargi cewa dabaran mai aiki da kansa yana karkatar da ƙwallonkayan aikiƘwalloƘaramin ƙwallon da ake jefawa a hanyarsa a akasin juyawar rotor. Ƙwallayen zamani na ivorine ko Teflon ne, 18–21 mm.Karanta gaba ɗaya → daga inda aka sa manyan cace-cace. Wani bincike na 2017 ya gwada wannan zato a kan dabaran Interblock masu sifilidabaranSifiliRamin kore guda ɗaya da babu cacar ɗaya zuwa ɗaya, ta dozin ko ta ginshiƙi da ke rufe shi; tushen fifikon gidan caca. Ana kuma kiransa: sifili ɗaya, 0.Karanta gaba ɗaya → biyu da ke aiki ba tare da croupier ba a Las Vegas, ta hanyar yin caca a kan baka na lambobi biyar maƙwabta, irin cacar da mai auna lokacin dabaran yake yi. A juye-juye 299 bakan ya ci sau 29 maimakon 39.3 da ake tsammani, gibin da dabaran mai adalci yake bayarwa kusan a 4% na lokaci. Chi-square a kan dukkan ramuka 38 ya kai 45.29 a kan matakan ʼyanci 37: p = 16.5%. Samfuri na biyu na juye-juye 1,204 a kan dabaran uku ya ba da χ² = 34.79, p = 57%, kuma babu bakan kowane girma da aka gwada da ya zama mai muhimmanci. Samfuran biyu tare, juye-juye 1,503, sun ba da χ² = 41.75, p = 27%. Hukuncin shi ne babu hujjar cewa ana karkatar da ƙwallon. Samfuri na farko shi kaɗai ya yi kamar abin zargi; na biyu ne ya warware lamarin.

Bayan chi-square

Ga rami guda da ake zargi, binomial test ya fi ƙarfi. Ga baka da ake zargi, z-test na sashedabaranSasheRamuka da ke bin juna a jere a kan dabaran kamar baka, sabanin ƙungiyar lambobi a kan teburin caca.Karanta gaba ɗaya → da ke shafin Nazarin sassan dabaran. Chi-square gwaji ne na gaba ɗaya: yana gaya muku akwai matsala ba tare da faɗin mece ce ba. Ku fara amfani da shi, sannan ku duba.

Nazarin sassan dabaran

Ƙa'idar lissafi

Tambayoyi