Bvunzo yaMann-Whitney muStatistics
Nhamba dzezviverengero ibazi remasvomhu rine chekuita nekuunganidza, kuongorora, kududzira, uye kuratidzwa kwedata. Nhamba dzezviverengero dzinoshandiswa munzvimbo dzakasiyana siyana kuita sarudzo dzinotungamirirwa nedata. Imwe nzira inowanzoshandiswa munhamba dzezviverengero iMann-Whitney test (inozivikanwawo seMann-Whitney U test kana Wilcoxon rank-sum test). Iyi inzira isiri yeparametric inoshandiswa kuona kana paine musiyano mukuru pakati pemapoka maviri asina kubatana.
Nhanganyaya yeMann-Whitney Test
Bvunzo yeMann-Whitney yakaunzwa naHenry Mann naDonald Whitney muna 1947 senzira isina parameterical pane t-test. Nzira iyi haidi fungidziro yekuti yakajairika. Saka, inobatsira zvikuru kana data risingatevedzere kugoverwa kwakajairika kana kana saizi yesampuro iri diki zvakanyanya kuti isimbise fungidziro yekuti yakajairika.
Nheyo dzekutanga dzeMann-Whitney Bvunzo
Bvunzo yeMann-Whitney inoshandiswa kuenzanisa ma median emapoka maviri. Musimboti wekutanga ndewekuti:
1. Kuongororwa kweZvinzvimbo: Data rese kubva kumapoka ese ari maviri rinosanganiswa uye rinorongwa kubva padiki kusvika pakuru. Kana paine kukosha kwakafanana, kucherechedzwa kwega kwega kunorongwa neavhareji yenzvimbo yacho chaiyo.
2. Kuverengera Nhamba Yekuongorora: Nhamba yekuongorora nhamba (U) inoverengerwa zvichienderana nehuwandu hwemapoka eboka rega rega. Kune nzira mbiri dzekuverenga: imwe inotanga neboka rekutanga uye imwe neboka rechipiri.
- Fomura yakajairika yeU ndeiyi:
\[
U_1 = n_1 \nguva n_2 + \frac{n_1 \nguva (n_1 + 1)}{2} – R_1
\]
kana
\[
U_2 = n_1 \nguva n_2 + \frac{n_2 \nguva (n_2 + 1)}{2} – R_2
\]
di mana:
– \(n_1\) uye \(n_2\) ndiwo huwandu hwezvakacherechedzwa muboka rega rega,
– \(R_1\) uye \(R_2\) ndiwo huwandu hwemapoka ari muboka rega rega.
3. Kuedza Kukosha: Kuedza kukosha kunoitwa kuti paonekwe kukosha kwep. Mumamiriro ezvinhu ehukuru hwesampuro, kugoverwa kweU kunogona kufungidzirwa nekugoverwa kwakajairika.
Mafungiro muMann-Whitney Test
Kunyangwe bvunzo yeMann-Whitney isiri bvunzo yeparametric uye isingade kufungidzira kwekugoverwa kwakajairika, kune fungidziro dzakawanda dzakabatana dzinofanira kuzadzikiswa kuti mhedzisiro ive yechokwadi:
1. Kuzvimiririra: Kucherechedzwa kwega kwega mumapoka ese ari maviri kunofanira kunge kwakazvimirira.
2. Chikero cheOrdinal kana Interval: Data rinofanira kunge riri pa ordinal kana interval scale. Izvi zvinoreva kuti data rinogona kurongwa uye rine ruzivo rwekuronga.
3. Kupararira kwemapoka ese ari maviri: Kupararira kwemapoka ese kunofanira kunge kwakafanana (kunyangwe pakati pemapoka acho kungave kwakasiyana).
Matanho Ekuita Bvunzo yeMann-Whitney
Matanho anowanzo teverwa kuita Mann-Whitney Bvunzo ndeaya anotevera:
1. Sanganisa uye Ronga Data: Sanganisa data kubva kumapoka ese ari maviri worironga rose. Kurongwa kunopihwa zvichienderana nehurongwa nekugadziriswa kwenzvimbo kwakabatana neavhareji kukosha.
2. Verenga Nhamba Yezvinzvimbo: Verenga nhamba yezvikamu zveboka rega rega.
3. Kuona kukosha kweU-Value yeStatistics: Shandisa fomura yakatsanangurwa kare kuti uverenge kukosha kweU-value yemapoka ese ari maviri.
4. Kuona Kukosha Kunokosha kana kuti P-Value: Enzanisa kukosha kweU kwakawanikwa nemutengo unokosha kubva patafura yekugovera yeU (kana kuverenga kukosha kwep) kuti uone kana musiyano uripo pakati pemapoka wakakosha.
Semuenzaniso, ngatitii tine seti mbiri dzedata A neB. Data iri rinogona kumiririra nzira mbiri dzakasiyana dzekurapa chirwere chimwe chete, uye tinoda kuziva kana imwe nzira yekurapa ichishanda kupfuura imwe.
Muenzaniso Unoshanda
Ngatitii tine mapoka maviri ekurapa:
– Kurapa A: [85, 90, 88, 75, 91]
– Kurapa B: [80, 78, 95, 87, 92]
1. Kubatanidza uye Kuronga Data:
– Zvinosanganiswa: [85, 90, 88, 75, 91, 80, 78, 95, 87, 92]
– Kurongeka uye Kurongwa: [75(1), 78(2), 80(3), 85(4), 87(5), 88(6), 90(7), 91(8), 92(9), 95(10)]
2. Kuverenga Nhamba yeZvinzvimbo:
– Nhamba yekurapwa kweA: 4 + 7 + 6 + 1 + 8 = 26
– Nhamba yekurapwa kweB: 3 + 2 + 10 + 5 + 9 = 29
3. Kuverenga Kukosha kweU:
\[
U_A = n_1 \nguva n_2 + \frac{n_1 \nguva (n_1 + 1)}{2} – R_A = 5 \nguva 5 + \frac{5 \nguva (5 + 1)}{2} – 26 = 25 + 15 – 26 = 14
\]
\[
U_B = n_1 \nguva n_2 + \frac{n_2 \nguva (n_2 + 1)}{2} – R_B = 5 \nguva 5 + \frac{5 \nguva (5 + 1)}{2} – 29 = 25 + 15 – 29 = 11
\]
Sarudza kukosha kudiki kweU, kureva U = 11.
4. Kuziva Kukosha:
Enzanisa U-value yakawanikwa neU-value inokosha kubva patafura yekugovera yeMann-Whitney kana kuverenga p-value. Kana U iri pasi pecritical value kana p-value iri pasi pealpha (semuenzaniso, 0,05), tinoramba null hypothesis togumisa kuti pane musiyano mukuru pakati pemapoka maviri aya.
Zvakanakira uye Zvipingamupinyi zveMann-Whitney Test
Superiority:
1. Nonparametric: Hazvidi kuti pave nekufungidzira kwekugoverwa kwakajairika.
2. Kuchinjika: Inogona kushandiswa kana data iri pachiyero che ordinal kana kuti ine zvinhu zvisingawanzoitiki.
3. Zviri Nyore uye Zvinoshanda: Zviri nyore kuverenga nekududzira.
Keterbatasan:
1. Kurasikirwa Nekushanda: Mukugoverwa kwakajairika, bvunzo ye-t inoshanda zvakanyanya.
2. Kufunga nezveFomu reKugovera Rimwechete: Bvunzo iyi inofungidzira fomu rekuparadzira rimwechete pakati pemapoka maviri aya.
3. Yakasungirirwa paSaizi Dzesampuro Dzidiki: Kugoverwa kweasymptotic kungave kusina kururama pasampuro diki kwazvo.
Mhedziso
Bvunzo yeMann-Whitney chishandiso chine simba uye chinochinjika chisiri cheparametric chekuona musiyano uripo pakati pemapoka maviri asina kubatana. Nekunzwisisa misimboti yayo yekutanga uye matanho ekushandisa, tinogona kushandisa bvunzo iyi mumhando dzakasiyana dzemashandisirwo munzvimbo dzakasiyana siyana dzekutsvagisa. Kunyange zvazvo iine zvimwe zvipingamupinyi, zvakanakira zvayo pasi pemamwe mamiriro ezvinhu zvinoita kuti ive nzira inobatsira zvikuru muhuwandu.
