Bvunzo yeKruskal Wallis muStatistics
Bvunzo yeKruskal Wallis inzira yekuverenga isina parameter inoshandiswa kuenzanisa mutsauko uripo pakati pemapoka matatu kana anopfuura. Muzvidzidzo zvakawanda, vaongorori vanowanzoda kuona kana mapoka akati wandei aine kukosha kwakasiyana zvakanyanya kune chimwe chinhu chakasiyana. Kana data rikasangana nefungidziro yekuti zvinhu zvakafanana uye kuti zvinhu zvakafanana, bvunzo yeANOVA yenzira imwe chete ndiyo inowanzova sarudzo yekutanga. Zvisinei, kana fungidziro idzi dzikasazadzikiswa—semuenzaniso, data hariwanzo kugoverwa, pane zvinhu zvisingawanzoitiki, kana kuti chiyero chekuyera chiri chenguva dzose—bvunzo yeKruskal Wallis inzira ine simba uye inoshandiswa zvakanyanya.
Tsanangudzo uye Pfungwa Dzekutanga
Bvunzo yeKruskal–Wallis (inowanzonyorwa sebvunzo yeKruskal–Wallis H) ikuwedzera kwebvunzo yeMann–Whitney U, ichiiwedzera kumapoka anopfuura maviri. Nheyo yayo huru ndeyekuenzanisa "ranks" yedata, kwete kukosha chaiko. Nekuti yakavakirwa parank, bvunzo iyi haidi kugoverwa kwakajairika uye inodzivirira zvishoma kupesvedzero ye outliers.
Zvichienderana nepfungwa, kana mapoka akati wandei aine kugoverwa kwakafanana, huwandu hwedata mumapoka ese huchasanganiswa zvisina tsarukano. Kusiyana neizvi, kana mamwe mapoka aine huwandu hwakakwira kana hwakaderera, huwandu hwacho huchaunganidzwa pamwe chete uye huchaburitsa nhamba yakakura yebvunzo.
Kuedzwa kweKruskal Wallis kunoshandiswa riini?
Bvunzo yeKruskal Wallis inoshandiswa kana:
1. Huwandu hwemapoka i≥ 3, uye muongorori anoda kuenzanisa mutsauko uri pakati pemapoka (kazhinji pakati pemapoka).
2. Data harina kuzadzisa fungidziro dzeANOVA, kunyanya zvakajairika zvema residuals.
3. Zviyero zvedata reordinal (semuenzaniso zvibodzwa zvekugutsikana: kusagutsikana zvakanyanya kusvika kugutsikana zvakanyanya) kana data repakati/reratio risiri renguva dzose.
4. Mienzaniso yakazvimirira, zvichireva kuti nhengo dzeboka rimwe hadzina hukama kana kuti hadzina hukama nemamwe mapoka.
Muenzaniso: muongorori anoda kuenzanisa huwandu hwekugutsikana kwevarwere nemabasa ari muzvipatara zvitatu zvakasiyana achishandisa chikero cheLikert che1–5. Nekuti data racho harina kuzara, Kruskal Wallis isarudzo yakakodzera.
Kufungidzira kweKruskal Wallis paKuedza
Kunyangwe zvisiri zveparametric, Kruskal Wallis ichiri nepfungwa dzinoverengeka dzakakosha:
1. Kuzvimiririra kwekutarisa: data riri muboka rega rega rinofanira kubva kuvanhu vakasiyana.
2. Mhinduro inofanira kunge iri ordinal: data rinofanira kurongeka.
3. Maumbirwo ekugoverwa pakati pemapoka anofanira kunge akafanana: kana maumbirwo ekugoverwa akasiyana zvakanyanya, kududzira mutsauko kunogona kuoma. Bvunzo iyi inowanzo tsanangurwa semusiyano muvapakati, asi dudziro yepakati ndiyo inonyanya kukodzera kana maumbirwo ekugoverwa akafanana.
Fungidziro muKruskal Wallis Test
Mubvunzo yeKruskal Wallis, fungidziro iri kuyedzwa ndeiyi:
– H0 (fungidziro isina chinhu): kugoverwa (kana kuti pakati) kwemapoka ese kwakafanana.
– H1 (imwe pfungwa): pane boka rimwe chete rine kupararira kwakasiyana (kana kuti pakati) kwaro.
Zvinofanira kucherechedzwa kuti kana H0 yakarambwa, bvunzo yeKruskal-Wallis inongotaura kuti "pane musiyano," asi haitauri kuti ndeapi mapoka akasiyana. Izvi zvinoda kuongororwa kwakawedzerwa (post-hoc).
Matanho Ekuverenga
Muchidimbu, matanho ebvunzo yeKruskal Wallis ndeaya:
1. Sanganisa data rese kubva kumapoka ese.
2. Chinja kubva padiki kusvika pahukuru. Kana paine zvibodzwa, shandisa avhareji yenzvimbo.
3. Wedzerai zvinzvimbo muboka rega rega.
4. Verenga nhamba yebvunzo H.
Fomura yehuwandu hwehuwandu hweH ndeye:
\[
H = \frac{12}{N(N+1)} \sum_{i=1}^{k} \frac{R_i^2}{n_i} – 3(N+1)
\]
Information:
– \(N\) = huwandu hwese hwezvakaonekwa
– \(k\) = nhamba yemapoka
– \(n_i\) = nhamba yezvakaonekwa muboka re i-th
– \(R_i\) = nhamba yemapoka ari muboka re i-th
H value inobva yaenzaniswa ne chi-square distribution (\(\chi^2\)) ine \(k-1\) degrees of freedom. Kana p-value iri diki pane significance level (semuenzaniso, 0,05), saka H0 inorambwa.
Muenzaniso Unoratidza
Ngatitii mudzidzisi anoda kuziva kana paine musiyano pakati pemapoinzi ebvunzo dzehuwandu pakati penzira nhatu dzekudzidza: A, B, naC. Mushure mekuunganidza data, zvinoonekwa kuti mapoinzi haawanzo kugoverwa nekuti pane zvakawanda zvakawandisa. Mudzidzisi anobva ashandisa bvunzo yeKruskal Wallis.
Kana mhinduro dzebvunzo dzichiratidza p-value ye0,01 (pasi pe0,05), zvinogumiswa kuti pane musiyano mukuru pakati penzira mbiri dzekudzidza. Zvisinei, mudzidzisi haasati aziva kana nzira A iri nani pane B kana C. Apa ndipo panodiwa ongororo ye post-hoc.
Bvunzo rePost-hoc Mushure meKruskal Wallis
Kana bvunzo yeKruskal Wallis yakakosha, danho rinotevera nderekuenzanisa zvinhu zviviri. Dzimwe nzira dzakajairika ndedzinotevera:
1. Bvunzo raDunn: rinonyanya kushandiswa paKruskal Wallis mushure mekuvhiyiwa.
2. Pairwise Mann–Whitney nekugadziriswa (Bonferroni, Holm, kana Benjamini-Hochberg) kudzora zvikanganiso zvinokonzerwa nekuongororwa kwakawanda.
Chinangwa chekugadzirisa uku ndechekudzivirira kuwedzera kwemukana wekukanganisa kwerudzi rwekutanga (kutaura musiyano kana pasina musiyano) nekuda kwekuenzanisa kakawanda.
Saizi yemhedzisiro
Pamusoro pekukosha, zvidzidzo zvakawanda zvemazuva ano zvinosimbisa hukuru hwemhedzisiro kuti zvibatsire vaverengi kunzwisisa hukuru hwemusiyano. Humwe hukuru hwemhedzisiro hunowanzobatanidzwa neKruskal-Wallis model hunosanganisira:
– Eta-squared (η²) yakavakirwa paH:
\[
\eta^2 = \frac{H – k + 1}{N – k}
\]
– Epsilon-squared (ε²) senzira yekuchengetedza zvakanyanya.
Saizi dzemhedzisiro dzinobatsira kutsanangura kana musiyano uri mudiki, wepakati, kana mukuru, kwete kungoti "wakakosha kana kwete."
Zvakanakira uye Zvisina Kukwana
Kelebihan
1. Hazvidi kuti munhu afungidzire kuti zvinhu zvakajairika.
2. Yakakodzera data re ordinal.
3. Yakasimba zvikuru kana ichienzaniswa nedzisiri dzepamusoro kupfuura nzira dzeparametric.
Miganhu
1. Hazviratidzi kuti mapoka api akasiyana pasina post-hoc.
2. Kududzirwa semusiyano uri pakati pevaviri kunonyanya kushanda kana chimiro chekugoverwa kwemapoka chakafanana.
3. Kana data chairo riri rakajairika uye rakafanana, ANOVA inogona kuva nesimba guru (simba rakakwirira).
Penutup
Bvunzo yeKruskal-Wallis chishandiso chakakosha muhuwandu hwekuongorora, kunyanya kana vaongorori vari kubata nedata risingasvike pafungidziro dzenzira dzeparametric. Nenzira yayo yakavakirwa padanho, bvunzo iyi inobvumira kuenzanisa kwakasununguka kwemapoka matatu kana anopfuura, kunyanya kune data re ordinal kana risiri remazuva ese. Zvisinei, kushandiswa kwayo kuchiri kuda kunzwisisa fungidziro, kududzirwa kwemhedzisiro, uye kudiwa kwekuongorora kwe post-hoc kuti uone mapoka akasiyana emapoka. Nekubatanidza p-values, saizi yemhedzisiro, uye imwe ongororo yakakodzera, bvunzo yeKruskal-Wallis inogona kupa mhedziso dzakasimba uye dzakakodzera munzvimbo dzakasiyana-siyana dzekutsvagisa, kubva kuhutano nedzidzo kusvika kubhizinesi nesainzi yemagariro evanhu.
