Pfungwa Dzekutanga dzeOne-Way ANOVA
Nzira imwe chete ANOVA inzira inoshandiswa kuenzanisa nzira kubva kumapoka anopfuura maviri. Vanhu vazhinji vanoziva bvunzo ye-t yekuenzanisa nzira mbiri, asi kana huwandu hwemapoka hwapfuura maviri, kushandiswa kakawanda kwebvunzo ye-t kunowedzera njodzi yekuita sarudzo dzisiridzo. Apa ndipo panonyanya kukosha ANOVA yenzira imwe chete: inopa nzira chaiyo uye yakarongeka yekuedza kana paine misiyano yakakura mumatanho pakati pemapoka achienzaniswa zvichibva pane chimwe chinhu (chinhu chimwe chete chakasiyana).
1. Chii chinonzi One-Way ANOVA?
Izwi rekuti ANOVA rinobva paAnalysis of Variance. Pasinei nezita raro, "analysis of variance," chinangwa charo chikuru ndechekuedza mutsauko mune means. Pfungwa huru yeANOVA ndeiyi: kana means dzeboka dzakasiyana zvechokwadi, saka mutsauko uripo pakati pemapoka uchaonekwa wakakura kupfuura mutsauko uripo mukati memapoka.
Inonzi "nzira imwe chete" nekuti pane chinhu chimwe chete kana chimwe chete chinoshandiswa kugadzira mapoka aya. Semuenzaniso:
- Nzira dzekudzidza (dzakazvimirira, dzeboka, dzepamhepo) pamapoinzi ebvunzo.
– Rudzi rwefetereza (A, B, C, D) pakukohwa kwayo.
– Rudzi rwemushonga (mushonga 1, mushonga 2, placebo) paBP.
Mumuenzaniso uri pamusoro apa, "nzira yekudzidza", "rudzi rwefetereza", uye "rudzi rwemushonga" zvinhu chimwe chete chine mazinga akasiyana-siyana (mapoka).
2. One-Way ANOVA Inoshandiswa Rini?
Nzira imwe chete ANOVA inowanzo shandiswa kana:
1. Chinoshanduka-shanduka chiri muchimiro chenhamba/huwandu (mienzaniso: kukosha, huremu, nguva, BP).
2. Chinoshanduka-shanduka chakazvimiririra chinhu chimwe chete chine mapoka matatu (k ≥ 3).
3. Vaongorori vanoda kuziva kana paine boka rimwe chete rine avhareji yakasiyana nemamwe.
Kana paine mapoka maviri chete, bvunzo ye-t inowanzo kukwana. Zvisinei, ANOVA inogona kushandiswa kumapoka maviri uye ichapa mhedziso dzakaenzana nebvunzo ye-t (pasi pemamwe mamiriro).
3. Pfungwa Huru: Kusiyana Pakati Peboka vs. Pakati Peboka
ANOVA inoyera manyuko maviri ekusiyana:
- Kusiyana kwemukati meboka: kuti data rinosiyana zvakadii mukati meboka rega rega. Semuenzaniso, kunyangwe boka riine avhareji yakati, vanhu varo vanogona kunge vakapararira zvakanyanya kubva paavhareji.
- Kusiyana pakati pemapoka: kuti avhareji yeboka rega rega inosiyana zvakadii kubva kune rimwe nerimwe.
Kana musiyano uripo pakati pemapoka uri mukuru, musiyano uripo pakati pemapoka uchava mukuru. Kana data riri mumapoka rakapararira zvakanyanya, musiyano uripo mukati memapoka uchava mukuru. ANOVA inoenzanisa maviri aya ichishandisa chiyero chinonzi F statistical.
4. Fungidziro muANOVA
Nenzira imwe chete ANOVA, pfungwa yacho inogadzirwa seinotevera:
– H0 (fungidziro isina musoro): nzira dzese dzehuwandu hwevanhu muboka dzakafanana.
\[
\mu_1 = \mu_2 = \mu_3 = \dots = \mu_k
\]
– H1 (imwe pfungwa): pane avhareji yeboka rimwe chete rakasiyana.
Kureva kuti, hazvisi zvese \(\mu\) zvakafanana.
Zvakakosha kunzwisisa kuti ANOVA inongokuudza chete kana paine musiyano kana kuti kwete. Kana mhedzisiro yacho yakakosha, bvunzo dzakawanda dzinodiwa kuti uone kuti mapoka maviri api akasiyana.
5. Nhamba dzebvunzo: F Ratio
Nhamba huru yebvunzo muANOVA ndeye F:
\[
F = \frac{\text{Between-group variance (MSB)}}{\text{Within-group variance (MSW)}}
\]
Pano:
– MSB (Mean Square Between) = avhareji yemakwere ari pakati pemapoka, inotsanangura mutsauko uripo pakati pemapoka.
– MSW (Mean Square Within) = avhareji yemasikweya ari muboka, inotsanangura musiyano uri muboka.
Pfungwa yacho:
– Kana nzira dzemapoka ese dzakafanana, MSB idiki saka F iri pedyo ne1.
– Kana paine musiyano wakajeka pakati pemari, MSB inowedzera zvekuti F inova yakakura kupfuura 1.
– Kukosha kweF kwakakura zvakakwana (kana tichienzanisa neF yakakosha parusununguko rwakati) kunoita kuti tirambe H0.
6. Zvikamu zveKuverenga: SST, SSB, uye SSW
MuANOVA, musiyano wese wedata wakakamurwa kuita zvikamu zviviri:
1. SST (Huwandu hweMaseko): huwandu hwese hwemaseko, hunotsanangura mutsauko we data rese uchienzaniswa neavhareji yese.
2. SSB (Huwandu hweMasikweya Pakati): huwandu hwemasikweya pakati pemapoka, musiyano unokonzerwa nekusiyana kwehuwandu hwemapoka.
3. SSW (Huwandu hweMasikweya Ari Mukati): huwandu hwemasikweya ari muboka, musiyano unokonzerwa nekusiyana kwemunhu mumwe nemumwe muboka.
Hukama hwakakosha:
\[
SST = SSB + SSW
\]
Zvadaro chimwe nechimwe chinokamurwa nemazinga erusununguko kuti chigadzire MSB neMSW.
7. Dhigirii reRusununguko
Dhigirii rerusununguko (df) nenzira imwe chete ANOVA:
– df pakati pemapoka: \(k – 1\)
(k = nhamba yemapoka)
– df muboka: \(N – k\)
(N = huwandu hwese hwezvakaonekwa)
– df huwandu: \(N – 1\)
Dhigirii dzerusununguko dzakakosha nekuti dzinoona chimiro chekugoverwa kweF kunoshandiswa kuyedza kukosha.
8. Kufungidzira kweOne-Way ANOVA
Kuti mhedzisiro yeANOVA ive inoshanda, fungidziro dzinoverengeka dzinowanzo dikanwa:
1. Kuzvimiririra: ruzivo pakati pevanhu/zvinoonekwa zvakazvimirira (hazvipesvedzeri mumwe nemumwe).
2. Kurongeka: data riri muboka rega rega rinowanzo goverwa (kana kuti zvasara zviri pedyo nezvinorongeka).
3. Kuenzana kwemusiyano (homoscedasticity): musiyano uripo pakati pemapoka wakafanana.
Mukuita, ANOVA "yakasimba" zvikuru pakutyorwa kwetsika kana saizi dzesamples dzakakura zvakakwana uye dzakaringana. Zvisinei, kutyorwa kwehumwe hwekusiyana kunogona kuva dambudziko guru, kunyanya kana saizi dzesamples dzeboka rega rega dzisina kuenzana. Miedzo yakaita seyaLevene kana yaBartlett inowanzo shandiswa kusimbisa fungidziro yehumwe hwekusiyana.
9. Kududzirwa kweMhedzisiro: p-value uye Sarudzo
Mhedzisiro yeANOVA inowanzo ratidzwa mutafura yeANOVA ine SSB, SSW, df, MSB, MSW, F value, uye p-value.
– Kana p-value ≤ α (semuenzaniso α = 0,05), saka ramba H0: pane musiyano mukuru muavhareji pakati pemapoka.
– Kana p-value > α , saka kundikana kuramba H0 : hapana humbowo hwakakwana hwekuti nzira dzacho dzakasiyana.
Zvisinei, "kukundikana kuramba H0" hazvirevi kuti nzira dzacho dzakafanana; zvinongoreva kuti data harina simba rekuratidza musiyano.
10. Bvunzo rePost Hoc Mushure meANOVA
Kana ANOVA ichikosha, danho rinotevera nderekuona kuti mapoka api akasiyana. Izvi zvinoitwa nebvunzo ye post hoc, semuenzaniso:
– Tukey HSD (inowanzo shandiswa pakuenzanisa mapeya ese).
– Bonferroni (anonyanya kuchengetedza).
– Scheffé (inochinjika pamhando dzakasiyana-siyana dzemisiyano).
– Games-Howell (zvakakodzera kana musiyano wacho usina kufanana).
Pasina kumwe kuyedza, tinongoziva chete kuti "pane musiyano," asi hatizivi kuti musiyano wacho uri papi.
11. Saizi yemhedzisiro
Pamusoro pekukosha, zvakakoshawo kutaura kuti chinhu chimwe chine simba rakadii pane dependent variable. Saizi dzakajairika dzemhedzisiro muANOVA ndeidzi:
– Eta yakaenzana nemativi mana (\(\eta^2\)): chikamu chekusiyana kwese kunotsanangurwa nekusiyana kwemapoka.
– Omega squared (\(\omega^2\)): vhezheni isina rusaruro rwakanyanya, kunyanya muzviyero zvidiki.
Saizi dzemhedzisiro dzinobatsira kuongorora kukosha kwezvinoitika, kwete kukosha kwehuwandu chete.
Mhedziso
Nzira imwe chete ANOVA chishandiso chakakosha chekuverenga nhamba chekuenzanisa nzira dzemapoka anopfuura maviri zvichibva pane chimwe chinhu chimwe chete. Pfungwa huru ndeyekuenzanisa musiyano uripo pakati pemapoka nekusiyana kuri mukati memapoka uchishandisa nhamba yeF. Kushandiswa kwayo kunoda fungidziro dzekuzvimiririra, kujairika, uye kufanana kwekusiyana kuti kuve nechokwadi chemhedziso dzakavimbika. Kana mhedzisiro yeANOVA ichiratidza misiyano yakakosha, ongororo inoenderera mberi nemiedzo ye post hoc kuti ione mapoka akasiyana uye kushuma saizi yemhedzisiro kuti vaongorore simba remhedzisiro yacho.
Kana muchida, ndinogona kuwedzera muenzaniso wenyaya yakazara (data diki), matanho akareruka ekuverenga nemaoko, kana muenzaniso wezvinobuda muANOVA kubva kuSPSS/R/Excel pamwe chete nemaverengero azvinoitwa.
