Taitara: Tauira o ngā Pātai Kōrero Whakamātautau-Whaiaro
Ko te whakamātautau chi-square (whakamātautau χ²) he tikanga tatauranga e whakamahia ana hei whakamātautau i ngā whakapae mō te tohatoha auau o ngā taurangi kāwai. He tino whai hua tēnei whakamātautau hei whakatau mēnā he whanaungatanga nui kei waenganui i ngā taurangi kāwai motuhake e rua. Ka matapakihia e tēnei tuhinga te ariā taketake o te whakamātautau chi-square, ā, ka whakaratohia he tauira pātai me te matapakinga mō ēnei.
Pendahuluan
Ko te whakamātautau Chi-Square tētahi o ngā whakamātautau kore-taurite e whakamahia whānuitia ana mō te tātari raraunga kāwai. Ko tōna kaupapa matua he whakamātautau i te whānuitanga o te rerekētanga i waenga i te tohatoha i kitea me te tohatoha e tumanakohia ana i runga i te whakapae kore.
Ko te whakapae kore (H0) i roto i te whakamātautau tohutoro whakawhiti e kī ana kāore he whanaungatanga i waenga i ngā taurangi kāwai e rua, ko te whakapae rerekē ia (H1) e kī ana he whanaungatanga i waenga i ngā taurangi e rua.
Ngā Ariā Taketake o te Whakamātautau Chi-Square
Tuatahi, kia mārama tātou ki ētahi ariā taketake o te whakamātautau Chi-Square:
1. Auautanga Tirotiro (O): Koinei te maha o ngā kitenga ka kitea e koe i roto i tētahi kāwai raraunga.
2. Auautanga e Tumanakohia ana (E): Koinei te maha o ngā kitenga e tumanakohia ana e koe i roto i tētahi kāwai motuhake i runga i te tohatoha ariā, i te whakapae kore rānei.
3. Tātai Whakamātautau Chi-Square:
\[
\chi² = \sum \frac{(O_i – E_i)²}{E_i}
\]
Ko \(O_i\) te auau e kitea ana, ā, ko \(E_i\) te auau e tumanakohia ana mō te kāwai-i.
4. Ngā Nekehanga Herekore (df): Ka tatauhia tēnei hei (te maha o ngā rarangi – 1) (te maha o ngā pou – 1) mō tētahi ripanga tūponotanga.
5. Taumata Hiranga (\(\alpha\)): Ko te paepae e whakamahia ana hei whakatau mena he hiranga ngā hua o tētahi whakamātautau tatauranga. Ko te tikanga, ko te 0,05, ko te 5% rānei te taumata hiranga.
Ngā Pātai Tauira me te Kōrero
Me titiro tātou ki tētahi rangahau take hei mārama ki te whakamahinga o te whakamātautau Chi-Square.
Tauira Pātai 1:
I whakahaerehia tētahi rangahau hei whakatau mēnā he hononga kei waenganui i ngā momo waiata e pai ana ki a rātou me te taumata mātauranga. Ko ngā raraunga e whai ake nei i kohia mai i te 200 o ngā kaiwhakautu.
| | Pop | Rock | Jazz | Katoa |
|——————— |—–|——|——-|——-|
| Kura Tuarua | 20 | 30 | 50 | 100 |
| Paetahi | 35 | 25 | 40 | 100 |
| Tapeke | 55 | 55 | 90 | 200 |
Pātai: He hononga kei waenganui i te momo puoro tino pai ki te taumata mātauranga?
Ngā Hipanga Kōrero:
1. Whakatauhia te Whakapae:
– H0: Kāore he whanaungatanga i waenga i te manakohanga momo puoro me te taumata mātauranga.
– H1: He whanaungatanga kei waenganui i ngā manakohanga momo puoro me te taumata mātauranga.
2. Tātaihia te Auautanga e Tumanakohia ana (E):
Tātaihia te auau e tumanakohia ana mō ia pūtau o te ripanga tūponotanga. Ko te tātai mō te tātai i a E ko:
\[
E_{ij} = \frac{(\text{Rārangi Katoa}_i \times \text{Tīwae Katoa}_j)}{\text{Tapeke Whānui}}
\]
Hei tauira, ko te auau e tumanakohia ana mō ngā ākonga kura tuarua e pai ana ki a Pop ko:
\[
E_{SMA, Pāpāho} = \frac{(100 \times 55)}{200} = 27.5
\]
Waihoki, ka tatauhia e mātou mō ngā pūtau katoa:
| | Pop | Rock | Jazz |
|——————— |—–|——|——-|
| Kura Tuarua | 27.5 | 27.5 | 45 |
| Paetahi | 27.5 | 27.5 | 45 |
3. Tātaihia te Chi-Square (χ²):
Mā te whakamahi i te tātai:
\[
\chi² = \sum \frac{(O – E)²}{E}
\]
Tātaihia te takoha o ia pūtau me te tapeke:
– Mō te Kura Tuarua me te Pop:
\[
\chi²_{SMA, Pānui} = \frac{(20 – 27.5)²}{27.5} \approx 2.04
\]
– Ka mahia ngā tataunga ōrite mō ia huinga:
\[
\chi² = 2.04 + 0.23 + 0.56 + 0.23 + 0.23 + 0 + 1.96 = 5.25
\]
4. Tātaihia ngā Nekehanga o te Herekoretanga:
\[
df = (3-1) \times (3-1) = 4
\]
5. Whakatauhia ngā Uara me ngā Whakataunga Tino Hira:
Mā te whakamahi i te ripanga tohatoha Chi-Square me te \(\alpha = 0.05\) me te df = 4, ko te uara matua ko te 9.488. Mai i te 5.25 < 9.488, kāore mātou i te whakakore i te H0. Whakatau: Kāore he whanaungatanga nui i waenga i te manakohanga momo puoro me te taumata mātauranga i te taumata hiranga 0.05. Whakatau He taputapu tino whai hua te whakamātautau Chi-Square mō te tātari raraunga kāwai i roto i ngā momo mara rangahau. Mā te mārama ki te tatau me te aromatawai i ngā hua o te whakamātautau Chi-Square, ka taea e ngā kairangahau te whakatau pai ake mō ā rātou raraunga. Ko te rangahau take kua kōrerohia e whakarato ana i tētahi whakaahua mahi mō te mahi a te whakamātautau Chi-Square me te whakamārama i ngā hua. Haunga te tātari ā-ringa, he mea noa hoki te whakamahi i ngā pūmanawa tatauranga pēnei i te SPSS, R rānei i roto i te mahi hei whakahaere i ngā tatau me te tātari atu. I roto i ngā tono tūturu, hei tāpiri atu ki te aro ki ngā hua tatauranga, he mea nui kia whakaarohia te horopaki o te rangahau me te whakamārama i ngā tatauranga me te whakaaro nui.
