Kupu Whakataki ki te Tātaritanga o te Rerekētanga
Ko te Tātari Rerekētanga (ANOVA) he tikanga tatauranga taketake e whakamahia ana hei mārama ki ngā rerekētanga o ngā toharite i waenga i ngā rōpū. He tino whai hua tēnei tikanga i roto i ngā momo marautanga pēnei i te hinengaro, te pāpori, te koiora, te ōhanga, me te maha atu. I roto i tēnei tuhinga, ka whakamāramahia e mātou ngā ariā taketake o te ANOVA , ōna momo, ngā whakapae matua, ngā mahi whakatinanatanga, me ngā tauira o tōna whakamahinga.
Te Mārama ki te Tātaritanga o te Rerekētanga
Ko te ANOVA he tikanga e whakamahia ana hei whakamātautau mēnā he rerekētanga nui i waenga i ngā toharite o ngā rōpū e rua, neke atu rānei. I whakaurua mai tēnei tikanga e Tā Ronald Fisher i te tīmatanga o te rautau 20. Ko te tikanga, ka whakataurite a ANOVA i te rerekētanga i waenga i ngā rōpū me te rerekētanga i roto i ngā rōpū hei whakatau mēnā he nui ake te rerekētanga o ngā toharite i waenga i ngā rōpū i te mea e tumanakohia ana mā te tauira matapōkere.
Ngā momo ANOVA
He maha ngā momo ANOVA e whakamahia whānuitia ana, arā:
1. ANOVA Kotahi-Ara:
Ka whakamahia tēnei tātaritanga ina kotahi te tauwehenga te taurangi motuhake rānei, ā, e hiahia ana ki te whakamātautau i te rerekētanga o te toharite i waenga i ngā rōpū e rua, neke atu rānei, i runga i taua taurangi.
2. ANOVA Ara-Rua:
Ka whakamahia ina e rua ā tātou āhuatanga, ngā taurangi motuhake rānei, ā, e hiahia ana tātou ki te whakamātautau i te awe o ngā āhuatanga e rua ki te taurangi whakawhirinaki i te wā kotahi.
3. ANOVA Inenga Whakahoki:
Ka whakamahia tēnei tātaritanga ina inehia te kaupapa kotahi i ngā wā rerekē, i raro rānei i ngā āhuatanga rerekē.
4. ANCOVA (Tātari i te Taurite):
He huinga tēnei o te ANOVA me te whakatauira e whakamahia ana hei whakahaere i ngā taurangi whakapoauau (ngā taurangi takirua).
Ngā Whakaaro ANOVA
I mua i te whakamahi i te ANOVA, he maha ngā whakapae me tutuki kia tika ai ngā hua e puta mai ana:
1. Te Auautanga: E kiia ana he auau ngā raraunga mai i ia rōpū. tohatoha noa.
2. Te Homokekatika: Me rite, me ōrite rānei te rerekētanga o ngā raraunga i waenga i ngā rōpū.
3. Te Tū motuhake: Me tū motuhake ngā kitenga o ngā raraunga tetahi i tetahi.
Mena kāore tētahi o ēnei whakapae e tutuki, tera pea ka pāngia ngā hua o te ANOVA, nō reira, me whai whakamātautau tuatahi me ētahi atu tikanga.
Ngā Hipanga mō te Whakatinana i te ANOVA
1. Te Hanga Whakaaro
Ko te whakatakotoranga o te whakapae he Te Whakaaro Kore (H0) e kī ana kāore he rerekētanga o te toharite i waenga i ngā rōpū, me te Whakapae Rerekē (H1) e kī ana he iti rawa i te kotahi takirua o ngā rōpū he rerekē ngā toharite.
Tauira o te Whakapae:
– H0 : µ1 = µ2 = µ3 (kāore he rerekētanga o te toharite i waenga i ngā rōpū)
– H1: Kotahi te takirua o ngā rōpū, he rerekē ngā toharite
2. Te Tātai i te Rerekētanga i waenganui i ngā Rōpū me roto i ngā Rōpū
Te tātaritanga o te rerekētanga e rua ngā momo rerekētanga e pā ana ki:
– Te Rerekētanga i Waenganui i te Rōpū: E ine ana i te rerekētanga i waenga i ngā toharite rōpū.
– Te Rerekētanga i roto i te Rōpū: E ine ana i te rerekētanga i roto i te rōpū tonu.
3. Te Tātai i te Uara-F
Ko te Uara-F te ōwehenga i waenga i te Tapawhā Toharite i waenganui (MSB) me te Tapawhā Toharite i Roto (MSW):
\[ F = \frac{MSB}{MSW} \]
Kei hea:
\[ MSB = \frac{SSB}{dfB} \]
\[ MSW = \frac{SSW}{dfW} \]
Ko te SSB me te SSW ngā tapeke o ngā tapawhā i waenganui i ngā rōpū me roto i ngā rōpū, ko te dfB me te dfW ia ngā nekehanga herekore i waenganui i ngā rōpū me roto i ngā rōpū.
4. Whakatauritea ki te Uara Matua
Kātahi ka whakaritea te uara-F i whiwhihia ki te uara-F matua mai i te ripanga tohatoha -F me tētahi taumata hiranga (hei tauira, 0,05). Mena he nui ake te Uara-F i te uara matua, he whakatau tata tēnei kei reira te iti rawa i te kotahi te toharite rōpū rerekē.
5. Whakamātautau Whai muri i te Whakamātautau
Mena ka whakaatuhia e ngā hua ANOVA he rerekētanga nui, ko te mahi e whai ake nei ko te whakahaere i tētahi whakamātautau muri-hoc hei whakatau ko ēhea takirua rōpū e rerekē ana. Ko ētahi o ngā whakamātautau muri-hoc e whakamahia whānuitia ana ko Tukey, Scheffé, me Bonferroni.
Tauira o te Tono ANOVA
Me kī, me whakamātautau tātou i te whai huatanga o ngā tikanga whakaako e toru ki te whakatutukitanga o ngā ākonga. I roto i tēnei rangahau, ko te taurangi motuhake ko te tikanga whakaako (A, B, me C), ā, ko te taurangi whakawhirinaki ko ngā kaute whakamātautau a ngā ākonga.
Hipanga 1: Hangaia he Whakapae
– H0 : Kāore he rerekētanga o ngā kaute whakamātautau toharite i waenga i ngā tikanga whakaako A, B, me C.
– H1 : He rerekētanga kei roto i ngā kaute whakamātautau toharite mō te iti rawa i te kotahi takirua tikanga whakaako.
Hipanga 2: Te Kohikohi Raraunga
Me kī kua kohia e tātou ngā kaute whakamātautau mai i ngā ākonga i whakaakona ki ngā tikanga A, B, me C.
Hipanga 3: Te Tatau i te Rerekētanga
Tātaihia te SSB, te SSW, te MSB, me te MSW i runga i ngā raraunga i whiwhihia.
Hipanga 4: Te Tatau me te Whakataurite i ngā Uara-F
Tātaihia te Uara-F ka whakataurite ki te uara matua.
Hipanga 5: Whakamātautau Whai muri i te Whakamātautau
Mena e whakaatu ana te Uara-F i tētahi rerekētanga nui, me whakahaere he whakamātautau whai muri i te whakamātautau hei tautuhi ko tēhea tikanga whakaako he tino rerekē.
Whakamutunga
He taputapu kaha te tātari i te rerekētanga hei aromatawai i ngā rerekētanga nui i waenga i ngā rōpū. Ko te mārama me te whakamahi tika i te ANOVA me mārama pai ki ngā whakaaro me ngā mahi e whai wāhi ana. Mā tēnei ka taea te rangahau hōhonu ake me te whai mana nui ake o ngā hua.
Mā te mārama ki ngā momo ANOVA, ka taea e ngā kairangahau te whiriwhiri i te tikanga e tino pai ana mō tā rātou hoahoa whakamātautau me ngā raraunga. Kia mārama ki ngā whakapae matua o te ANOVA, ā, me whakahaere ngā tirotiro e tika ana i mua i te whakatau whakatau, kia pono ai, kia whakaaetia ai hoki ngā hua e puta mai ana e te hapori pūtaiao.
