Mann-Whitney uvavanyo: umzekelo itheyibhile

Ikhrayitheriya ku manani zemathematika - umgaqo engqongqo, ngokungqinelana ne hypothesis ukuba kwinqanaba elithile ukubaluleka yamkelwe okanye ezikhatyiweyo. Alakhe, kufuneka ufumane umsebenzi okhethekileyo. Kufuneka kuxhomekeka kwiziphumo lokugqibela olu lingelo, oko kukuthi, ukususela amaxabiso empirically ezimisele. Yiyo lo msebenzi iya kuba sisixhobo ukuhlola umahluko phakathi iisampulu.

ixabiso ngokwamanani. Overview

ngokubaluleka kwezobalo - elahliweyo lixabiso le amathuba ithuba livela liphantsi kakhulu. Bengabalulekanga njengento embi kakhulu kunye nokusebenza kwayo. Umahluko ibizwa ebonakalayo ngokweenkcukacha kwimeko apho kukho data, amathuba apho ayinamsebenzi ukuba ibango ukuba azikho ezi yantlukwano. Kodwa ke oku akuthethi ukuba lo mahluko kufuneka nakanjani ibe nkulu, ibe ezibalulekileyo.

Inqanaba lovavanyo ngokubaluleka kwezobalo

Eli gama kufuneka kuqondwe ukuba ukwala hypothesis null kwimeko ngenyaniso yawo. Oku kubizwa ngokuba imposiso ye uhlobo lokuqala, okanye isigqibo okungamanga. Kwiimeko ezininzi, le nkqubo isekelwe p-value ( "pi-ixabiso"). Le Amathuba ezongezelekayo ngokondela inqanaba lovavanyo zamanani. Yena, ke, kukho isampuli ngexesha zokwamkelwa hypothesis null. I cebiso kuya kukhatywa ukuba p-value engaphantsi kwe umhlalutyi kwinqanaba ebhengeziweyo. Ukususela kulo mzobo kuxhomekeke ngqo amaxabiso ukubaluleka uvavanyo: i ezincinane oko kukuthi, lo, ngokulandelelana, kwaye isizathu sokuba ukwala hypothesis. Inqanaba Ukubaluleka lidla zibonakaliswe yileta B (alpha). Popular amanani phakathi ziingcali: 0.1%,-1%,-5% ne-10%. Ukuba, umzekelo, wathi amathuba bomdlalo-1 ngo-1000, ngoko ngokuqinisekileyo siya sithetha 0.1% inqanaba ukubaluleka manani of a random variable. iintsingiselo ezahlukeneyo b-amanqanaba babe nobubi zabo kunye bendlela. Ukuba isalathiso ingaphantsi ngoko mkhulu ilinganisa ukuba nokwenzeka kokuba hypothesis enye ebalulekileyo. Nangona oku kungaba ingozi ukuba null hypothesis lobuxoki akabalahlanga. Kunokwenziwa isigqibo lokuba ukhetho eyiyo b-level kuxhomekeke eseleyo 'ukubaluleka kwamandla "okanye, ngokulandelelana, ukulalanisa amathuba a izigqibo okungamanga kunye lobuxoki navumelanayo. Nelithi "ukubaluleka kwezobalo" kwiincwadi Russian igama elithi "ukunyaniseka".

Ukubekwa hypothesis null

Ngo-manani zemathematika, le nkolelo lukhangelwa kane kunye ubungqina ezikhoyo reseach ngesandla. Kwiimeko ezininzi, hypothesis null sithatyathwa hypothesis ukuba unxulumano phakathi kwezinto isifundo ilahlekile okanye loo nto kufuneka ukufunda umahluko nokwabiwa efanayo. Phantsi yezibalo uphando standard ukuzama ayingqinelani hypothesis null, oko kukuthi, ukungqina ukuba akukho uphindelelo iziphumo zovavanyo. Neya kuqhubeka kwaye enye hypothesis ukuba yamkelwe endaweni a zero.

iinkcazelo ezingundoqo

Ikhrayitheriya U (Mann-Whitney) e manani zemathematika ivumela ukuhlola umahluko phakathi iisampuli ezimbini. Bona inokunikwa kwinqanaba yimfanelo ulinganiswa nangokobungakanani. Le ndlela kokufanelekileyo ukuba uvandlakanyo somahluko iisampuli ezincinane. Le bemfuno elula yaphakanyiswa ngu Frank Wilcoxon ngo-1945. Kwaye kakade ngo-1947, le ndlela iye yahlaziywa eya kuthi yongezwe zizazinzulu H. B. Mann kunye D. R. Uitni, amagama athe ubizwa unanamhla. uvavanyo Mann-Whitney e bengqondo, imathematika, amanani, kunye nezinye izifundo zesayensi ezininzi yenye izinto ezibalulekileyo isiseko lweMathematika uphando theoretical component.

incazelo

Mann-Whitney - indlela elula kakhulu ngaphandle parameters. umthamo yayo ebalulekileyo. It iphezulu kakhulu kunaleyo amandla Rosenbaum Q-test. Le ndlela ayivavanyi encinane kangakanani na indawo lomnqamlezo-lwamaxabiso phakathi iisampuli, oko kukuthi phakathi imiqolo amaxabiso zichongwe kokukhethiweyo yokuqala neyesibini. Ixabiso lingaphantsi kwenani iingongoma, kokukhona ukuba amaxabiso parameter umahluko esebenzayo. Ukuze isicelo kahle njengekhrayitheriya U (Mann-Whitney), musa ukulibala malunga ethile. isampuli nganye kufuneka ibe ubuncinane 3 ixabiso isici. Kusenokwenzeka ukuba kwimeko omnye amaxabiso ezimbini, kodwa ke ixesha lesibini wona kufuneka ubuncinane ezintlanu. Kule iisampulu zovavanyo kufuneka ubuncinane benani kwezalathisi coincident. Onke amanani kufuneka ezahlukeneyo kwimeko efanelekileyo.

ukusetyenziswa

Indlela yokusebenzisa ngokuchanekileyo uvavanyo Mann-Whitney? Table, nto leyo senziwa le ndlela iqulathe ixabiso ethile ebalulekileyo. Okokuqala kufuneka ukwenza iqela elilodwa iisampuli afane ezimbini, ezithi ke ngoko ubekwe. Oko kukuthi, izinto zicwangciswe ngokungqinelana iqondo bendyebo msebenzi isikhundla ephantsi yabelwa kwixabiso elincinane. Ngenxa yoko, nathi ufumane inani elipheleleyo lamabakala:

N = N1 + N2,

apho le milinganiselo N1 no-N2 - inani leeyunithi eziqulethwe iisampulu yokuqala neyesibini ngokulandelelanayo. Ngaphezu koko, a amaxabiso nenombolo eyodwa ubekwe yahlulwe iindidi ezimbini. Units, ngokulandelelanayo, iisampulu yokuqala neyesibini. Ngoku kwi ukujika isixa sezikhundla lamaxabiso imiqolo yokuqala neyesibini. Bubungakanani kakhulu kubo (TX), ongqamana iisampula kunye neeyunithi nx. Ukusebenzisa indlela Wilcoxon ngakumbi, ixabiso layo ibalwa yi le nkqubo ilandelayo. Kuyimfuneko ukuba itafile ukuqinisekisa inqanaba ekhethiweyo ukubaluleka kwiimpawu abalulekileyo ithathwa ngokukhethekileyo N1 no-N2. Icandelo ngenxa kunokuba ngaphantsi kwe okanye elingana nexabiso ukusuka etafileni. Kulo mzekelo, kukho umahluko omkhulu ukuba waqondisisa kakuhle amanqanaba usikhokele kwisampulu wafunda. Ukuba ixabiso eliphuma mkhulu etafileni, ngoko ke hypothesis null yamkelwe. Xa ubalo lwenziwa Mann-Whitney uvavanyo, kufanele kuqatshelwe ukuba hypothesis null kuyinyaniso, eyona nto iphambili iya kuba okulindelekileyo, ngokunjalo kwiintsali. Qaphela ukuba ininzi kakhulu kwiisampuli data indlela igqalwa distribution phantse eqhelekileyo. Ukubaluleka lweeyantlukwano iphezulu, ixabiso iba ncinci uvavanyo Mann-Whitney.