Ngā Ariā Taketake o te ANOVA Kotahi-Ara
Ko te ANOVA Ara-Kotahi he tikanga tatauranga e whakamahia ana hei whakataurite i ngā toharite mai i ngā rōpū neke atu i te rua. He tokomaha te hunga e mōhio ana ki te whakamātautau-t hei whakataurite i ngā toharite e rua, engari ki te neke atu i te rua te maha o ngā rōpū, mā te whakamahi anō i te whakamātautau-t ka nui ake te tūponotanga o te whakatau hē. Koinei te wāhi e hiranga ai te ANOVA ara-kotahi: ka whakaratohia he huarahi tika ake, he huarahi pūnaha ake hoki hei whakamātautau mēnā he rerekētanga nui kei roto i ngā toharite i waenga i ngā rōpū e whakatauritea ana i runga i tētahi āhuatanga kotahi (he taurangi kāwai kotahi).
1. He aha te ANOVA Ara-Kotahi?
I ahu mai te kupu ANOVA i te Analysis of Variance. Ahakoa tōna ingoa, "analysis of variance", ko tōna kaupapa matua he whakamātautau i ngā rerekētanga o ngā toharite. Ko te whakaaro matua o te ANOVA koia tēnei: mēnā he rerekē ngā toharite rōpū, ka nui ake te rerekētanga i waenga i ngā rōpū i te rerekētanga i roto i ngā rōpū.
Ka kiia tēnei he "ara-kotahi" nā te mea kotahi anake te tauwehe, kotahi rānei te taurangi motuhake kāwai e whakamahia ana hei hanga i ngā rōpū. Hei tauira:
– Ngā tikanga ako (takitahi, rōpū, ipurangi) mō ngā kaute whakamātautau.
– Momo tongi (A, B, C, D) mō te hua o te kotinga.
– Momo rongoā (rongoā 1, rongoā 2, rongoā kore-whakaora) mō te toto toto tiketike.
I te tauira i runga ake nei, ko te "tikanga ako", te "momo tongi", me te "momo rongoā" he āhuatanga takitahi e maha ngā taumata (kāwai).
2. Āhea te whakamahinga o te ANOVA Kotahi-Ara?
Ko te ANOVA kotahi-ara te tikanga e whakamahia ana ina:
1. Kei roto i te āhua tau/taurangi te taurangi whakawhirinaki (hei tauira: uara, taumaha, wā, toto toto).
2. Ko te taurangi motuhake he tauwehe kāwai kotahi me te iti rawa o ngā rōpū e toru (k ≥ 3).
3. E hiahia ana ngā kairangahau ki te mōhio mēnā he rerekē te toharite o tētahi rōpū i ētahi atu.
Mena e rua noa ngā rōpū, he rawaka te whakamātautau-t. Heoi anō, ka taea tonu te whakamahi i te ANOVA mō ngā rōpū e rua, ā, ka puta he whakatau e rite ana ki te whakamātautau-t (i raro i ētahi tikanga).
3. Whakaaro Matua: Rerekētanga i waenganui i te rōpū me te rerekētanga i roto i te rōpū
E ine ana a ANOVA i ngā pūtake rerekētanga e rua:
– Te rerekētanga i roto i te rōpū: te nui o te rerekētanga o ngā raraunga i roto i ia rōpū. Hei tauira, ahakoa he toharite motuhake tō tētahi rōpū, tera pea ka marara noa atu ōna takitahi i te toharite.
– Te rerekētanga i waenga i ngā rōpū: te nui o te rerekētanga o te toharite o ia rōpū tetahi i tetahi.
Mena he nui te rerekētanga i waenga i ngā toharite rōpū, ka nui te rerekētanga i waenga i ngā rōpū. Mena he tino horapa ngā raraunga i roto i ngā rōpū, ka nui te rerekētanga i roto i ngā rōpū. Ka whakatauritea e ANOVA ngā mea e rua mā te whakamahi i te ōwehenga e kiia nei ko te tatauranga F.
4. Te whakapae i roto i te ANOVA
I roto i te ANOVA kotahi-ara, ka whakatakotoria te ariā penei:
– H0 (whakapae kore): he ōrite ngā toharite o te taupori rōpū katoa.
\[
\mu_1 = \mu_2 = \mu_3 = \dots = \mu_k
\]
– H1 (whakapae rerekē): kotahi te toharite rōpū rerekē, neke atu rānei.
Ara, ehara i te mea he rite katoa ngā \(\mu\).
He mea nui kia mārama ko te ANOVA anake te mea e whakaatu ana mēnā he rerekētanga whānui, kāore rānei. Mena he hiranga ngā hua, me whakamātautau anō kia kitea ai ko ēhea takirua rōpū e rerekē ana.
5. Ngā Tatauranga Whakamātautau: Ōwehenga F
Ko te tatauranga whakamātautau matua i roto i te ANOVA ko F:
\[
F = \frac{\text{Rerekētanga i waenganui i te rōpū (MSB)}}{\text{Rerekētanga i roto i te rōpū (MSW)}}
\]
Anei:
– MSB (Mean Square Between) = te toharite o ngā tapawhā i waenga i ngā rōpū, e whakaahua ana i te rerekētanga i waenga i ngā toharite rōpū.
– MSW (Mean Square Within) = te toharite o ngā tapawhā i roto i tētahi rōpū, e whakaahua ana i te rerekētanga i roto i tētahi rōpū.
Te arorau:
– Mena he ōrite ngā toharite o ngā rōpū katoa, he iti te MSB, nō reira e tata ana a F ki te 1.
– Mēnā he mārama te rerekētanga o ngā toharite, ka piki ake te MSB kia nui ake ai te F i te 1.
– Mā te uara F nui rawa (ki te whakataurite ki te uara F tino nui i tētahi taumata herekoretanga) ka whakakahoretia e tātou a H0.
6. Ngā Wāhanga Tātai: SST, SSB, me te SSW
I roto i te ANOVA, ka wehea te rerekētanga katoa o ngā raraunga kia rua ngā wāhanga:
1. SST (Tapeke o ngā Tapawhā): ko te tapeke o ngā tapawhā, e whakaahua ana i te rerekētanga katoa o ngā raraunga katoa ki te toharite whānui.
2. SSB (Tapeke o ngā Tapawhā i waenganui): te tapeke o ngā tapawhā i waenganui i ngā rōpū, te rerekētanga nā ngā rerekētanga o ngā toharite rōpū.
3. SSW (Tapeke o ngā Tapawhā i Roto): te tapeke o ngā tapawhā i roto i tētahi rōpū, he rerekētanga nā ngā rerekētanga takitahi i roto i te rōpū.
Te whanaungatanga taketake:
\[
SST = SSB + SSW
\]
Kātahi ka wehea ia e ngā nekehanga herekoretanga hei whakaputa i te MSB me te MSW.
7. Ngā Nekehanga o te Herekoretanga
Ngā nekehanga herekore (df) i roto i te ANOVA kotahi-ara:
– df i waenga i ngā rōpū : \(k – 1\)
(k = te maha o ngā rōpū)
– df i roto i te rōpū : \(N – k\)
(N = te tapeke o ngā kitenga katoa)
– tapeke df : \(N – 1\)
He mea nui ngā nekehanga herekore nā te mea ka whakatau i te āhua o te tohatoha F e whakamahia ana hei whakamātautau i te hiranga.
8. Ngā Whakaaro o te ANOVA Kotahi-Ara
Kia tika ai ngā hua o te ANOVA, he maha ngā whakapae e hiahiatia ana:
1. Te tū motuhake: he tū motuhake ngā raraunga i waenga i ngā kaupapa/ngā kitenga (kāore e pā tetahi ki tetahi).
2. Te Auautanga: he ōrite te tohatoha o ngā raraunga o ia rōpū (he tata rānei ngā toenga ki te auautanga).
3. Te ōritetanga o te rerekētanga (homoscedasticity): he ōrite te rerekētanga i waenga i ngā rōpū.
I roto i te mahi, he tino "kaha" te ANOVA ki te takahi i te ōritetanga o te rerekētanga mēnā he nui, he taurite hoki ngā rahi tauira. Heoi anō, ka nui ake te raruraru o te takahi i te ōritetanga o te rerekētanga, inā koa mēnā he kore ōrite ngā rahi tauira o ia rōpū. He maha ngā wā ka whakamahia ngā whakamātautau pēnei i a Levene, i a Bartlett rānei hei manatoko i te whakaaro o te ōritetanga o te rerekētanga.
9. Te Whakamārama i ngā Hua: te uara-p me te Whakatau
Ko ngā hua o te ANOVA ka whakaaturia i roto i tētahi ripanga ANOVA kei roto ko te SSB, SSW, df, MSB, MSW, te uara F, me te uara-p.
– Mena ko te uara-p he ≤ α (hei tauira, α = 0,05), kātahi ka whakakahoretia te H0: he rerekētanga nui kei roto i te toharite i waenga i ngā rōpū.
– Mena he nui ake te uara-p i te α, kāti kāore e taea te whakakore i te H0: kāore i te rawaka ngā taunakitanga e whakaatu ana he rerekē ngā toharite.
Heoi, ko te "korenga e whakakore i te H0" ehara i te kī he tino ōrite ngā tikanga; ko tōna tikanga kāore i te kaha ngā raraunga hei whakaatu i tētahi rerekētanga.
10. Whakamātautau Post Hoc i muri i te ANOVA
Mena he mea nui te ANOVA, ko te mahi e whai ake nei ko te kimi ko ēhea ngā rōpū e rerekē ana. Ka mahia tēnei mā te whakamātautau muri-hoc, hei tauira:
– Tukey HSD (e whakamahia ana mō te whakatairite i ngā takirua katoa).
– Bonferroni (he hunga āta whakaaro).
– Scheffé (he ngāwari mō ngā momo rerekētanga).
– Games-Howell (he pai ake mēnā kāore te rerekētanga i te ōrite).
Ki te kore he whakamātautau atu, ko tā tātou e mōhio ana ko "he rerekētanga" anake, engari kāore tātou e mōhio kei hea te rerekētanga.
11. Rahi Pānga
Haunga te hiranga, he mea nui anō hoki kia ripoatahia te nui o te awe o tētahi āhuatanga ki te taurangi whakawhirinaki. Ko ngā rahi pānga noa i roto i te ANOVA ko:
– Eta tapawhā (\(\eta^2\)) : te ōwehenga o te rerekētanga katoa e whakamāramahia ana e ngā rerekētanga rōpū.
– Omega tapawhā (\(\omega^2\)) : he putanga iti ake te whakaaro pōhēhē, inā koa i roto i ngā tauira iti.
Ka āwhina ngā rahi pānga ki te aromatawai i te hiranga ā-tinana, ehara i te hiranga tatauranga anake.
Whakamutunga
Ko te ANOVA ara-kotahi he taputapu tatauranga taketake mō te whakatairite i ngā toharite o ngā rōpū neke atu i te rua i runga i te kotahi āhuatanga. Ko te ariā taketake ko te whakatairite i te rerekētanga i waenga i ngā rōpū me te rerekētanga i roto i ngā rōpū mā te whakamahi i te tatauranga F. Me whakamahi i ngā whakaaro mō te motuhaketanga, te āhua noa, me te ōritetanga o te rerekētanga hei whakarite i ngā whakatau pono. Mēnā ka whakaatuhia e ngā hua o te ANOVA ngā rerekētanga nui, ka haere tonu te tātari me ngā whakamātautau muri-hoc hei tautuhi i ngā rōpū motuhake me te ripoata i ngā rahi pānga hei aromatawai i te kaha o te awe i roto i te mahi.
Ki te hiahia koe, ka taea e au te tāpiri i tētahi tauira take katoa (raraunga iti), ngā mahi tatau ā-ringa māmā, tētahi tauira rānei o te putanga ANOVA mai i te SPSS/R/Excel me te pēhea te pānui.
