Whakamātautau F i roto i te Tātaritanga o te Rerekētanga
Pendahuluan
I roto i te rangahau tatauranga, ko tētahi o ngā whāinga matua ko te mārama mēnā he rerekētanga nui i waenga i ngā rōpū raraunga. Ko te whakamātautau-F tētahi tikanga e whakamahia ana mō tēnei kaupapa, inā koa i roto i te horopaki o te Tātari Rerekētanga (ANOVA). He mea nui tēnei whakamātautau i roto i te tātari raraunga whakamātautau, nā te mea ka taea e ngā kairangahau te aromatawai i te pono o ngā hua whakamātautau mēnā ka tutuki i a rātou ētahi whakapae tatauranga. I roto i tēnei tuhinga, ka tūhuratia e mātou te ariā, te tono, ngā whakapae, me te whakamāramatanga o te whakamātautau-F i roto i te tātari rerekētanga.
Ariā Taketake o te Whakamātautau F
I tapaina te whakamātautau-F pērā nā te mea e whai ana ōna uara i te tohatoha-F, he tohatoha tūponotanga tonu e whakamahia ana i roto i te tātaritanga o te rerekētanga. Ka whakamahia te tohatoha-F hei whakatairite i te rerekētanga i waenga i te rōpū me te rerekētanga i roto i te rōpū, e āwhina ana ki te whakatau mēnā he rerekētanga nui i waenga i ngā toharite rōpū.
Ko ngā wāhanga nui o te whakamātautau F ko:
1. Te rerekētanga i roto i te rōpū (Te rerekētanga i roto i ngā rōpū): E ine ana i te rerekētanga o ngā raraunga i roto i ia rōpū.
2. Te rerekētanga i waenga i ngā rōpū (Te rerekētanga i waenga i ngā rōpū): E ine ana i te rerekētanga toharite i waenga i ngā rōpū.
Mena he nui ake te rerekētanga i waenga i ngā rōpū i te rerekētanga i roto i ngā rōpū, he tino rerekētanga pea i waenga i ngā rōpū.
Te Whakamahinga o te Whakamātautau F i roto i te ANOVA
He tikanga tatauranga te ANOVA e whakamahia ana hei whakatairite i ngā toharite o ngā rōpū neke atu i te rua. He maha ngā momo ANOVA, tae atu ki te ANOVA kotahi-ara, te ANOVA rua-ara, me ētahi atu momo rerekētanga. Ko te rerekētanga matua i waenga i a rātou ka whakawhirinaki ki te āhua me te maha o ngā āhuatanga i akohia. I roto i tēnei tuhinga, ka arotahi mātou ki te ANOVA kotahi-ara hei tauira māmā hei whakaatu i te whakamahinga o te whakamātautau-F.
Ngā Hipanga Tātari me te ANOVA Kotahi-Ara
1. Te Hanga Whakaaro:
– Te whakapae kore ($H_0$): E kī ana he ōrite ngā toharite o te taupori katoa (kāore he rerekētanga i waenga i ngā rōpū).
– Te ariā rerekē ($H_1$): E kī ana he kotahi te toharite taupori rerekē, neke atu rānei.
2. Tātaihia te tatauranga F:
– Tapeke o ngā Tapawhā (SST):
\[
SST = \sum_{i=1}^{N}(X_i – \bar{X})^2
\]
Ka ine i te rerekētanga katoa o ngā raraunga.
– Te Tapeke o ngā Tapawhā i waenganui i te rōpū (SSB):
\[
SSB = \sum_{j=1}^{k} n_j (\bar{X_j} – \bar{X})^2
\]
Ka ine i te rerekētanga i waenga i ngā rōpū.
– Te Tapeke o ngā Tapawhā i roto i te rōpū (SSW):
\[
SSW = \sum_{j=1}^{k} \sum_{i=1}^{n_j} (X_{ij} – \bar{X_j})^2
\]
Ka ine i te rerekētanga o roto i ia rōpū.
– Tātaihia te tatauranga F:
\[
F = \frac{\text{MSB}}{\text{MSW}} = \frac{\text{SSB}/(k-1)}{\text{SSW}/(Nk)}
\]
Ko te MSB ko te Tapawhā Toharite i waenganui i ngā rōpū, ā, ko te MSW ko te Tapawhā Toharite i roto i ngā rōpū.
3. Te Hiranga o te Hiranga:
I muri i te tatau i te uara F, ka whakaritea e mātou tēnei uara ki te uara matua o te tohatoha F i runga i te taumata hiranga (\(\alpha\)) me ngā nekehanga herekoretanga. Mena he nui ake te uara F i tatauhia i te uara matua, ka whakakorehia e mātou te whakapae kore.
Ngā Whakaaro Whakamātautau-F
He mea nui kia maumahara ko te whakamahinga o te whakamātautau-F e whakawhirinaki ana ki ētahi whakaaro taketake. Ki te kore ēnei whakaaro e tutuki, tera pea kāore e tika ngā hua o te whakamātautau-F. Kei roto i ēnei whakaaro:
1. Te Mana Motuhake:
Me tū motuhake ngā kitenga o ia rōpū tetahi i tetahi.
2. Te āhua noa:
Me whai ngā raraunga o ia rōpū i tētahi tohatoha noa. Ka taea te whakamātautau i ngā whakaaro noa mā te whakamahi i ngā whakamātautau noa pērā i te whakamātautau Shapiro-Wilk, mā te whakamahi rānei i ngā kauwhata QQ.
3. Te ōritetanga o te rerekētanga:
Me ōrite ngā rerekētanga i roto i ia rōpū. Ka taea te whakamātautau i tēnei whakaaro mā te whakamahi i te whakamātautau a Levene, i te whakamātautau rānei a Bartlett.
Mena kāore e tutuki ngā whakapae mō te ōritetanga, te ōritetanga rānei o te rerekētanga, ka taea te mahi i ngā panonitanga (pēnei i ngā logarithms, i ngā pakiaka tapawhā rānei) me ētahi atu whakamātautau kore-tawhā pēnei i te whakamātautau Kruskal-Wallis H kāore e hiahiatia ēnei whakapae.
Te Whakamārama i ngā Hua
I muri i te whakahaere i tētahi ANOVA me te whiwhi i te uara-F me te uara-p, ko te mahi e whai ake nei ko te whakamārama i ngā hua. Anei ētahi whakamāramatanga ka taea:
1. Mena ko te uara-p < \(\alpha\): Ka whakakahoretia te whakapae kore, e tohu ana he rerekētanga nui i waenga i ngā toharite rōpū. 2. Mena ko te uara-p > \(\alpha\): Kāore i te rawaka ngā taunakitanga hei whakakore i te whakapae kore, e tohu ana kāore he rerekētanga nui i waenga i ngā toharite rōpū.
Ahakoa ka whakakahoretia te whakapae kore, kāore te ANOVA e whakaatu ko ēhea ngā rōpū e rerekē ana. Me whai whakamātautau muri-hoc tēnei pērā i te HSD a Tukey (Honestly Significant Difference), te whakatikatika a Bonferroni, te whakamātautau a Sidak rānei, hei āwhina i te tautuhi ko ēhea ngā rōpū e tino rerekē ana.
Tauira tauira
Me whakaaro tātou ki te tauira māmā e whai ake nei:
E hiahia ana tētahi kairangahau ki te whakatau mēnā he rerekētanga nui kei roto i te whai huatanga o ngā momo tongi e toru ki te tipu o ngā tipu. Ka ine te kairangahau i te teitei o te tipu (i roto i te cm) i muri i te kotahi marama mō ngā rōpū tipu e toru e whakamahi ana i ngā tongi A, B, me C.
Raraunga Whakaaro:
| Tongi A | Tongi B | Tongi C |
|—————|————|————|
| 20 | 18 | 22 |
| 21 | 17 | 23 |
| 19 | 16 | 24 |
Ngā Hipanga Tātari:
1. Te Hanga Whakaaro:
– $H_0$: He rite tonu te teitei toharite o te tipu mō ngā maniua katoa.
– $H_1$: He rerekē te teitei toharite o te tipu kotahi, neke atu rānei.
2. Tātaihia te tatauranga F:
– Tātaihia te SST, te SSB, me te SSW, ka haere tonu ki te tātaitanga F.
3. Whakatauritea ki te Uara Hiranga:
– Mā te whakamahi i te ripanga tohatoha F me ngā nekehanga herekoretanga, ka whakatauhia mēnā he hiranga te uara F kua tatauhia.
Ngā tauira:
Mena e whakaatu ana te uara F he rerekētanga nui, ka taea e te kairangahau te whakahaere tonu i ngā whakamātautau whai muri i te whakamātautau hei whakatau ko ēhea rōpū he rerekē.
Whakamutunga
He taputapu tino whai hua te whakamātautau-F i roto i te tātaritanga o te rerekētanga hei whakatau mēnā he rerekētanga nui i waenga i ngā rōpū. Mā te whakatutuki i ngā whakapae tatauranga, ka taea e tēnei whakamātautau te whakarato i ngā māramatanga kaha ki ngā raraunga kua tātarihia. I roto i ngā tono mahi, he tino āwhina tēnei whakamātautau i roto i ngā momo mara rangahau pēnei i te koiora, ngā tikanga pāpori, te ōhanga, me ētahi atu. Mā te mōhio ki te wā me te pēhea te whakamahi i te whakamātautau-F, me te mārama ki ōna whakapae me ngā whakamaoritanga, ka whakapai ake i te kounga o te tātaritanga tatauranga, ā, ka whakarato i tētahi turanga pakari mō te whakatau kaupapa e ahu mai ana i ngā raraunga.
