Izimiso Zokusatshalaliswa Kwesampula
I-Pendahuluan
Ukusatshalaliswa kwamasampula kuwumqondo oyisisekelo kuzibalo ogxile ezicini zokusabalalisa amasampula atholwe kubantu. Isimiso sokusatshalaliswa kwamasampula sibalulekile ekucabangeni kwezibalo ngoba sisivumela ukuthi silinganise futhi sibikezele amapharamitha abantu ngokusekelwe kudatha yesampula.
Ezweni langempela, ukuqoqa idatha kubantu bonke ngokuvamile akunakwenzeka noma akunakwenzeka. Ngakho-ke, abacwaningi bathatha amasampula kubantu abaningi futhi basebenzisa izimiso zokusatshalaliswa kwamasampula ukuze bafinyelele iziphetho ezifanele ngabantu.
Lesi sihloko sizoxoxa ngezimiso zokusatshalaliswa kwamasampula, kanye neminye imiqondo ebalulekile ehlobene nokusatshalaliswa kwamasampula, njengokusatshalaliswa kwamasampula kwesilinganiso, i-central limit theorem, kanye nokusatshalaliswa kwamasampula kwezilinganiso.
Izimiso Eziyisisekelo Zokusatshalaliswa Kwesampula
Inani labantu vs. Isampula
Isibalo sabantu yiqoqo labo bonke abantu noma izakhi eziyizihloko zocwaningo noma ucwaningo lwezibalo. Ngokuphambene nalokho, isampula iyiqembu elincane labantu elikhethelwe ukubonwa nokuhlaziywa. Le ndlela isetshenziswa ngoba ukulinganisa noma ukubuka sonke isibalo sabantu kunzima noma akunakwenzeka.
Amapharamitha kanye nezibalo
Ipharamitha iyinani lezinombolo elichaza isici sabantu, njengesilinganiso, ukuhlukahluka, noma isilinganiso. Ngakolunye uhlangothi, isibalo siyinani lezinombolo elithathwe kusampula futhi lisetshenziselwa ukulinganisa ipharamitha yabantu. Isibonelo, uma sifuna ukwazi ukuphakama okumaphakathi kwabantu, singathatha isampula kubantu, sibale ukuphakama okumaphakathi kwesampula (izibalo), bese sisebenzisa lokhu ukulinganisa isilinganiso sabantu (ipharamitha).
Ukusatshalaliswa Kwesampula
Ukusatshalaliswa kwesampula kubhekisela ekusatshalalisweni kwamathuba ezibalo zesampula. Ake sithi sithatha amasampula amaningana kubantu abafanayo bese sibala isilinganiso sesampula ngasinye, ukusatshalaliswa kwalezi zindlela zesampula kuwukusatshalaliswa kwesampula kwesilinganiso.
Ukusatshalaliswa kwamasampula kunikeza umbono jikelele wokuthi izibalo zesampula ziziphatha kanjani ngaphansi kokuphindaphinda okuhlukene kwamasampula. Lokhu kubalulekile ekuqondeni ukuguquguquka okungokwemvelo kwezibalo zesampula kanye nokwenza izilinganiso ezinembile kakhulu zamapharamitha abantu.
Ithiyori Yomkhawulo Ophakathi (Ithiyori Yomkhawulo Ophakathi)
Omunye wemibono ebaluleke kakhulu ehlobene nokusatshalaliswa kwamasampula yi-Central Limit Theorem (CLT). Le theorem ithi, kungakhathaliseki ukuthi ukusatshalaliswa kwabantu kunjani, ukusatshalaliswa kwamasampula kwesilinganiso sesampula kuzolinganisa ukusatshalaliswa okuvamile (ukusatshalaliswa kwe-Gaussian) uma usayizi wesampula mkhulu ngokwanele, ngokuvamile u-n ≥ 30.
Ukuqonda i-Central Limit Theorem
Ngokwesiko, i-Central Limit Theorem ithi uma sithatha isampula enkulu ngokwanele kubantu abanesilinganiso esingu-µ kanye nokwehluka okungu-σ², khona-ke ukusatshalaliswa kwesampula kwalezo zindlela zesampula kuzolinganisa ukusatshalaliswa okuvamile okunesilinganiso esingu-µ kanye nephutha elijwayelekile (SE) lika-σ/√n, lapho u-n engusayizi wesampula.
Imiphumela ye-Central Limit Theorem
I-CLT inemiphumela ebalulekile ekuqondeni kwezibalo ngoba isivumela ukuthi sisebenzise imithetho yokusatshalaliswa okuvamile lapho silinganisa futhi sihlola imicabango, noma ngabe idatha yokuqala ayisakazwanga ngokujwayelekile. Lokhu kunamandla kakhulu emisebenzini yezibalo yansuku zonke ngoba kwenza amasu amaningi ezibalo asekelwe ngokujwayelekile abe yinto evamile ekusetshenzisweni kwawo.
Ukusatshalaliswa Kwesampula Kwesilinganiso
Enye yezindlela eziyinhloko zokusebenzisa i-Central Limit Theorem ukuqonda ukusatshalaliswa kwesampula kwesilinganiso. Uma sithatha isampula engahleliwe kubantu bese sibala isilinganiso sesampula, sifuna ukwazi ukuthi isilinganiso sesampula sihluka kanjani kuye ngesampula.
Isilinganiso kanye nokwehluka
Kumasayizi amakhulu esampula, ukusatshalaliswa kwesampula kwesilinganiso kuzosondela ekusatshalalisweni okuvamile okunesilinganiso esilingana nesilinganiso sabantu (μ) kanye nokwehluka okuncane kuka-σ²/n, lapho u-σ kuwukuphambuka okujwayelekile kwabantu kanye no-n kuwusayizi wesampula.
Iphutha Elijwayelekile
Iphutha elijwayelekile (i-SE) ukuphambuka okujwayelekile kokusatshalaliswa kwesampula kusuka ku-mean. Linikeza isilinganiso sokuthi isilinganiso sesampula kulindeleke ukuthi siphambane kangakanani nesilinganiso sabantu. I-SE ibalwa njengo-σ/√n, okubonisa ukuthi ukwandisa usayizi wesampula kuzonciphisa i-SE futhi kwenze isilinganiso sabantu sibe neqiniso kakhudlwana.
Ukusatshalaliswa Kwezilinganiso Zokuthatha Amasampula
Ukusatshalaliswa kwesampula kwesilinganiso kufana nokusatshalaliswa kwesampula kwesilinganiso, kodwa sigxila kusilinganiso kunesilinganiso. Isibonelo, ake sithi sifuna ukulinganisa isilinganiso sabantu abanesici esithile, njengesilinganiso sabantu ababhemayo kubantu.
Isilinganiso kanye nokwehluka kwezilinganiso
Uma u-p kuyisilinganiso sabantu esinophawu oluthile, khona-ke ukusatshalaliswa kwesampula kwesilinganiso u-p (p-hat) kuzolinganisa ukusatshalaliswa okuvamile okunesilinganiso u-p kanye nokwehluka (pq/n), lapho u-q = 1 – u-p kanye no-n kuyisayizi yesampula.
Iphutha Elijwayelekile Lokulingana
Iphutha elijwayelekile lesilinganiso libalwa njengo-√[p(1-p)/n]. Lokhu kunikeza isilinganiso sokuthi isilinganiso sesampula (p-hat) sikude kangakanani nesilinganiso sangempela sabantu (p).
Isiphetho
Izimiso zokusabalalisa amasampula ziyisisekelo sezakhi eziningi zezibalo zokuphetha. Ukuqonda le mibono kuvumela abacwaningi ukuthi benze izilinganiso ezivumelekile futhi benze ukuhlolwa kwe-hypothesis ngokusekelwe kumasampula anqunyelwe. Nge-Central Limit Theorem, singasebenzisa izimiso zokusabalalisa okuvamile ezimweni ezahlukahlukene futhi senze izilinganiso ezinembile ngisho nalapho idatha yokuqala ingasatshalaliswa ngokujwayelekile.
Ngokuhlaziya ukusatshalaliswa kwesampula kwesilinganiso kanye nesilinganiso, singathola ukuqonda okujulile kokuguquguquka kwezibalo zesampula futhi senze izibikezelo ezingcono mayelana nenani labantu. Lezi zimiso, nakuba zibonakala zingacacile, zinezindlela eziningi ezisebenzayo emikhakheni ehlukahlukene yocwaningo, kusukela kwisayensi yezenhlalo kuya kwisayensi yemvelo kanye nebhizinisi. Umgomo omkhulu ukwenza izinqumo ezingcono ngokusekelwe kudatha etholakalayo, noma ngabe leyo datha iyingxenye encane nje yeqiniso elikhulu.
