Ukuhlolwa kukaMann-Whitney kuzibalo
Izibalo ziyigatsha lezibalo eliphathelene nokuqoqwa, ukuhlaziywa, ukuchazwa, kanye nokwethulwa kwedatha. Izibalo zisetshenziswa emikhakheni eyahlukene ukwenza izinqumo eziqhutshwa idatha. Enye indlela evame ukusetshenziswa kwizibalo ukuhlolwa kweMann-Whitney (okwaziwa nangokuthi ukuhlolwa kweMann-Whitney U noma ukuhlolwa kwe-Wilcoxon rank-sum). Lena indlela engeyona ipharamitha esetshenziselwa ukunquma ukuthi kukhona yini umehluko omkhulu phakathi kwamaqembu amabili angabhangqiwe.
Isingeniso ku-Mann-Whitney Test
Ukuhlolwa kweMann-Whitney kwethulwa nguHenry Mann noDonald Whitney ngo-1947 njengendlela ehlukile engeyona ipharamitha esikhundleni se-t-test. Le ndlela ayidingi ukucabanga ngokujwayelekile. Ngakho-ke, iwusizo kakhulu lapho idatha ingalandeli ukusatshalaliswa okuvamile noma lapho usayizi wesampula umncane kakhulu ukuqinisekisa ukucabanga ngokujwayelekile.
Izimiso Eziyisisekelo Zokuhlolwa KweMann-Whitney
Ukuhlolwa kweMann-Whitney kusetshenziselwa ukuqhathanisa ama-median amaqembu amabili. Isimiso esiyisisekelo yilesi:
1. Ukuqaphelwa Kwezinga: Yonke idatha evela kumaqembu womabili ihlanganiswa futhi ibekwe ezilinganisweni kusukela kwezincane kuya kwezinkulu. Uma kunamanani afanayo, ukuqaphelwa ngakunye kubekwa ezilinganisweni ngokwesilinganiso sezinga lakho elifanele.
2. Ukubalwa Kokuhlolwa Kwezibalo: Inani lokuhlolwa kwezibalo (U) libalwa ngokusekelwe kwinani lezigaba zeqembu ngalinye. Kunezindlela ezimbili zokubala: enye iqala ngeqembu lokuqala kanti enye iqala ngeqembu lesibili.
– Ifomula ejwayelekile ye-U yile:
\[
U_1 = n_1 \izikhathi n_2 + \frac{n_1 \izikhathi (n_1 + 1)}{2} – R_1
\]
noma
\[
U_2 = n_1 \izikhathi n_2 + \frac{n_2 \izikhathi (n_2 + 1)}{2} – R_2
\]
Kuphi:
– \(n_1\) kanye \(n_2\) yinani lokubonwa eqenjini ngalinye,
– \(R_1\) kanye \(R_2\) yinani lezikhundla eqenjini ngalinye.
3. Ukuhlolwa Kokubaluleka: Ukuhlolwa kokubaluleka kwenziwa ukuze kutholakale inani le-p. Ezimweni zosayizi omkhulu wesampula, ukusatshalaliswa kwe-U kungalinganiswa ngokusabalalisa okuvamile.
Izinkolelo-mbono ekuhlolweni kweMann-Whitney
Nakuba ukuhlolwa kwe-Mann-Whitney kuyisivivinyo esingeyona ipharamitha futhi kungadingi ukucabanga ngokusatshalaliswa okuvamile, kunezinkolelo eziningana ezihlobene okumele kuhlangatshezwane nazo ukuze kuqinisekiswe imiphumela:
1. Ukuzimela: Ukubuka ngakunye kwamaqembu womabili kumele kube okuzimela komunye nomunye.
2. Isikali Esijwayelekile noma Esiphakathi: Idatha kumele ibe sezingeni elijwayelekile noma eliphakathi. Lokhu kusho ukuthi idatha ingahlelwa futhi iqukethe ulwazi lokubeka ezingeni.
3. Uhla Lokusabalalisa: Ukusatshalaliswa kwamaqembu womabili kumele kube nesimo esifanayo (yize i-median ingase ihluke).
Izinyathelo Zokwenza Ukuhlolwa Kwe-Mann-Whitney
Okulandelayo yizinyathelo ezivame ukulandelwa ukwenza iMann-Whitney Test:
1. Hlanganisa bese Uhlela Idatha: Hlanganisa idatha evela kumaqembu womabili bese uyihlela iyonke. Izikhundla zabelwa ngokwe-oda kanye nokulungiswa kwesikhundla okuhlobene nenani elimaphakathi.
2. Bala Inani Lezikhundla: Bala inani lezikhundla zeqembu ngalinye.
3. Ukunquma i-U-Value yezibalo: Sebenzisa ifomula echazwe ngaphambilini ukuze ubale i-U-value yamaqembu womabili.
4. Ukunquma Inani Elibalulekile noma Inani le-p: Qhathanisa inani le-U elitholiwe nenani elibalulekile elivela kuthebula lokusabalalisa le-U (noma ubale inani le-p) ukuze unqume ukuthi umehluko phakathi kwamaqembu ubalulekile ngokwezibalo.
Isibonelo, ake sithi sineziqoqo ezimbili zedatha u-A no-B. Le datha ingase imele izindlela ezimbili zokwelapha ezihlukene zesifo esithile, futhi sifuna ukwazi ukuthi ngabe ukwelashwa okukodwa kusebenza kangcono kunokunye.
Isibonelo Esiwusizo
Ake sithi sinamaqembu amabili okwelapha:
– Ukwelashwa A: [85, 90, 88, 75, 91]
– Ukwelashwa B: [80, 78, 95, 87, 92]
1. Ukuhlanganisa Nokuhlunga Idatha:
– Inhlanganisela: [85, 90, 88, 75, 91, 80, 78, 95, 87, 92]
– Ukuhleleka kanye Nokuqokwa: [75(1), 78(2), 80(3), 85(4), 87(5), 88(6), 90(7), 91(8), 92(9), 95(10)]
2. Ukubala Inani Lamazinga:
– Inani lezilinganiso ze-Therapy A: 4 + 7 + 6 + 1 + 8 = 26
– Inani lezilinganiso ze-Therapy B: 3 + 2 + 10 + 5 + 9 = 29
3. Ukubala Inani le-U:
\[
U_A = n_1 \izikhathi n_2 + \frac{n_1 \izikhathi (n_1 + 1)}{2} – R_A = 5 \izikhathi 5 + \frac{5 \izikhathi (5 + 1)}{2} – 26 = 25 + 15 – 26 = 14
\]
\[
U_B = n_1 \izikhathi n_2 + \frac{n_2 \izikhathi (n_2 + 1)}{2} – R_B = 5 \izikhathi 5 + \frac{5 \izikhathi (5 + 1)}{2} – 29 = 25 + 15 – 29 = 11
\]
Khetha inani elincane le-U, okungukuthi u-U = 11.
4. Ukunquma Ukubaluleka:
Qhathanisa inani le-U elitholiwe nenani le-U elibalulekile elivela kuthebula lokusabalalisa le-Mann-Whitney noma ubale inani le-p. Uma u-U engaphansi kwenani elibalulekile noma inani le-p liphansi kune-alpha (isb., 0,05), siyayenqaba i-null hypothesis bese siphetha ngokuthi kukhona umehluko omkhulu phakathi kwamaqembu amabili.
Izinzuzo kanye nokulinganiselwa kokuhlolwa kweMann-Whitney
Izinzuzo:
1. Okungeyona ipharamitha: Akudingi ukucabanga ngokusatshalaliswa okuvamile.
2. Ukuzivumelanisa nezimo: Kungasetshenziswa uma idatha isezingeni elijwayelekile noma inezingaphandle.
3. Kulula Futhi Kuyasebenza: Kulula ukubala nokutolika.
Imikhawulo:
1. Ukulahlekelwa Ukusebenza Kahle: Ekusabalaleni okuvamile, ukuhlolwa kwe-t kusebenza kahle kakhulu.
2. Ukuthathwa Kwefomu Lokusabalalisa Elifanayo: Lolu vivinyo luthatha ifomu lokusabalalisa elifanayo phakathi kwamaqembu amabili.
3. Kuboshwe Osayizi Abancane Besampula: Ukusatshalaliswa kwe-asymptotic kungase kungabi nembambo kakhulu kumasampula amancane kakhulu.
Isiphetho
Ukuhlolwa kwe-Mann-Whitney kuyithuluzi elinamandla neliguquguqukayo elingalingani neliyi-parametric lokuhlonza umehluko phakathi kwamaqembu amabili angabhangqiwe. Ngokuqonda izimiso zalo eziyisisekelo kanye nezinyathelo zokusebenzisa, singasebenzisa lolu vivinyo ezinhlotsheni ezahlukene zezicelo kuzo zonke izinkambu zocwaningo ezahlukene. Nakuba kunemikhawulo ethile, izinzuzo zalo ngaphansi kwezimo ezithile zikwenza kube yindlela ewusizo kakhulu kwizibalo.
