Whakamātautau Chi-Square i roto i ngā Tatauranga: Te Mārama me te Whakamahinga
I roto i ngā tatauranga, ka whakamahia ngā whakamātautau maha hei tātari raraunga me te whakatau tika i ngā whakatau pūtaiao. Ko tētahi o ngā whakamātautau tino nui i roto i ngā tatauranga ko te whakamātautau Chi-Square. He maha ngā whakamahinga o tēnei whakamātautau, inā koa i roto i te tātari raraunga kāwai . Ka matapakihia e tēnei tuhinga te whakamātautau Chi-Square me te hōhonu, tae atu ki ōna ariā taketake , ngā momo whakamātautau Chi-Square, ngā tikanga whakatinanatanga, me ngā whakamahinga i roto i ngā mara maha.
Ngā Ariā Taketake o te Whakamātautau Chi-Square
Ko te Whakamātautau Chi-Square he whakamātautau kore-taurite e whakamahia ana hei whakatau mena he rerekētanga nui i waenga i ngā tohatoha auau e tumanakohia ana me ngā tohatoha auau e kitea ana i roto i tētahi, i ētahi atu wāhanga rānei. I whakaurua mai tēnei whakamātautau e Karl Pearson i te tau 1900, ā, he maha ngā wā e whakamahia ana i roto i ngā rangahau pūtaiao maha e pā ana ki ngā raraunga kāwai.
Ko te tohu Chi-Square ka tuhia ki te reta Kariki χ², ā, ko te tātai taketake o tēnei whakamātautau ko:
\[ χ² = Σ \frac{(O_i – E_i)^2}{E_i} \]
me,
– Ko te auau e kitea ana ko \(O_i\),
– Ko te auau e tumanakohia ana ko \(E_i\).
Ngā Momo Whakamātautau Chi-Square
1. Whakamātautau Pai o te Taurite Chi-Square: Ka whakamahia tēnei whakamātautau hei whakatau mēnā he ōrite te huinga o ngā kitenga ki te tohatoha e tumanakohia ana. Hei tauira, ka hiahia pea te tangata ki te whakatau mēnā he tika te whiunga mataono mā te whakataurite i te tohatoha o ngā putanga i kitea me te tohatoha e tumanakohia ana (ka puta ia taha i te 1/6 o te wā).
2. Whakamātautau Chi-Square mō te Motuhaketanga: Ka whakamahia tēnei whakamātautau hei whakatau mēnā he motuhake ngā taurangi kāwai e rua. Hei tauira, ka taea te whakamahi i tēnei whakamātautau hei tirotiro i te whanaungatanga i waenga i te ira tangata me te manakohanga tae.
3. Whakamātautau Chi-Square mō te Homogeneity: He rite tēnei whakamātautau ki te whakamātautau motuhake, engari e whakamahia ana hei whakatau mena he ōrite te tohatoha o tētahi taurangi puta noa i ngā taupori, i ngā rōpū rerekē rānei. E tika ana kia rite te tohatoha o ia rōpū o te taurangi e whakamatautauria ana.
Te Tukanga Whakatinanatanga o te Whakamātautau Chi-Square
Ko te tukanga taketake mō te whakahaere i te whakamātautau Chi-Square he maha ngā mahi matua:
1. Whakatauhia te Whakapae: Tuhia te whakapae kore (H0) e kī ana kāore he rerekētanga i waenga i ngā tohatoha i kitea me ngā tohatoha e tumanakohia ana. E kī ana te whakapae rerekē (H1) he rerekētanga nui.
2. Waihangahia he Ripanga Āhuatanga: Waihangahia he ripanga āhuatanga kei roto ko te tohatoha auau tirohanga tuturu mō ngā kāwai raraunga katoa.
3. Te Tātai i te Auautanga e Tumanakohia ana: Mō ia pūtau i roto i te ripanga, tātaihia te auautanga e tumanakohia ana (E_i). Ko te auautanga e tumanakohia ana e ahu mai ana i te tohatoha ariā, i te ōwehenga rānei o te tauira katoa.
4. Te Tatau i ngā Tatauranga Chi-Square: Whakamahia te tātai χ² hei tatau i te uara tatauranga Chi-Square.
5. Te Whakatau i ngā Nekehanga Herekore: Ko ngā nekehanga herekore (df) mō te whakamātautau Chi-Square ka whakawhirinaki ki te momo whakamātautau e whakamahia ana. Mō te whakamātautau pai o te taunga, df = (te maha o ngā kāwai – 1). Mō te whakamātautau motuhake, df = (te maha o ngā rarangi – 1) (te maha o ngā pou – 1).
6. Whakatauritea ki te Uara Matua: Whakatauritea te uara tatau o χ² ki te uara matua o χ² i roto i te ripanga tohatoha Chi-Square i runga i te taumata hiranga kua whakaritea (α).
7. Whakatau: Mena he nui ake te uara χ² i tatauhia i te uara matua, ka whakakahoretia te whakapae kore, ko te tikanga he rerekētanga nui i waenga i ngā tohatoha i kitea me ngā tohatoha e tumanakohia ana.
Taupānga Whakamātautau Chi-Square
He whānuitia ngā whakamahinga o te whakamātautau chi-square i roto i ngā momo rangahau me ngā mara ahumahi. Ko ētahi o ngā whakamahinga mahi o tēnei whakamātautau ko:
1. Hapori me te Hinengaro: He maha ngā wā ka whakamahia te whakamātautau Chi-Square hei whakatau mēnā he whanaungatanga kei waenganui i ngā taurangi taupori pēnei i te tau, te ira tangata, te mātauranga me te whanonga, pēnei i ngā tikanga kai, ngā tikanga whakangahau rānei.
2. Pakihi me te Hokohoko: I roto i te mara pakihi, ka whakamahia te whakamātautau Chi-Square hei tirotiro mēnā he whanaungatanga kei waenganui i ngā kāwai e rua pēnei i te momo hua me te manakohanga a te kiritaki, i waenganui rānei i te tauwāhi toa me te rahinga hoko.
3. Hauora me te Hauora: I roto i ngā rangahau hauora, ka taea te whakamahi i te tātaritanga Chi-Square hei aromatawai i ngā raraunga haumanu, hei tauira, kia kite i te whanaungatanga i waenga i ētahi momo noho me te auau o ētahi mate.
4. Mātauranga: He maha ngā wā ka whakamahia te whakamātautau Chi-Square i roto i te tātari raraunga mātauranga hei aromatawai i te whanaungatanga i waenga i ngā taurangi pēnei i ngā tikanga whakaako me te whakatutukitanga a ngā ākonga, i waenga rānei i te papamuri o ngā ākonga me te whakatutukitanga mātauranga.
Tauira Whakamātautau Chi-Square
Me kī tātou kei te hiahia tātou ki te whakatau mēnā he rerekētanga nui i waenga i ngā hiahia inu (kawhe, tī, wai huarākau) i runga i te tūnga mahi (kaimahi wā-katoa, kaimahi wā-wāhanga, ākonga). I kohia ngā raraunga mai i tētahi rangahau o te 300 tāngata, ā, koinei te tohatoha o ngā kitenga i roto i tētahi ripanga āwangawanga:
| | Kawhe | Tī | Wai | Katoa |
|————————|——-|—–|—–|——-|
| Kaimahi Wā-Katoa | 50 | 30 | 20 | 100 |
| Kaimahi Wā-Wāhanga | 30 | 40 | 30 | 100 |
| Tauira | 20 | 10 | 70 | 100 |
| Tapeke | 100 | 80 | 120 | 300 |
Mā te tatau i ngā auau e tumanakohia ana, kātahi ka tatau i te uara tatauranga Chi-Square, ka taea e tātou te whakatau mēnā he hononga kei waenganui i ngā manakohanga inu me te tūnga mahi.
Te Katinga
He taputapu tatauranga kaha te whakamātautau chi-square mō te tātari i ngā raraunga kāwai. Mā te mārama ki ngā ariā taketake, ngā momo whakamātautau, me ngā tikanga whakatinanatanga, ka taea e ngā kairangahau te whakamahi i tēnei whakamātautau hei aromatawai i ā rātou whakapae i roto i ngā momo mara. Ko te tika o te whakamātautau chi-square e whakawhirinaki ana ki te tutuki i ētahi whakaaro, pērā i te rahi tauira e tika ana me te motuhake i waenga i ngā kāwai. Mā te mārama me te tono tika, ka taea e te whakamātautau chi-square te whakarato i ngā māramatanga whai hua hei tautoko i te whakatau kaupapa e ahu mai ana i ngā raraunga.
