Whakamātautau Chi-Square mō te Mana Motuhake
Ko te whakamātautau chi-square (χ²) mō te motuhaketanga he tikanga tatauranga kore-taurangi e whakamahia pinepine ana hei whakatau mena he hononga, he kore hononga rānei ngā taurangi kāwai e rua (tauine ingoa, tauine raupapa rānei). I roto i te maha o ngā rangahau pāpori, hauora, mātauranga, hokohoko, me te tātari kaupapa here, he maha ngā wā ka tūtaki ngā kairangahau ki ngā raraunga kāwai pēnei i te ira tangata (tāne/wahine), te tūnga momi hikareti (āe/kāo), te taumata mātauranga (kura tuarua/tohu paetahi/tohu paetahi), ngā manakohanga waitohu (A/B/C), me ētahi atu. Mā te whakamātautau chi-square mō te motuhaketanga ka āwhina i te whakautu i te pātai matua: he tino rerekē te tohatoha o tētahi taurangi puta noa i ētahi atu kāwai taurangi?
Ngā Ariā Taketake: He aha te Mana Motuhake?
E kiia ana he motuhake ngā taurangi e rua mēnā kāore ngā mōhiohio mō ngā kāwai i te taurangi tuatahi e āwhina i te matapae i ngā kāwai i te taurangi tuarua. Hei tauira, mēnā he motuhake te "ira tangata" me te "manakohanga inu", ka rite te ōwehenga o ngā manakohanga inu i roto i ngā rōpū tāne me ngā rōpū wahine. I tetahi atu taha, mēnā he rerekē rawa ngā ōwehenga, ko te tohu tēnei kāore ngā taurangi e rua i te motuhake (e hono ana).
Ko te whakamātautau chi-square mō te motuhaketanga ka mahi mā te whakataurite i ngā auau i kitea (ngā raraunga tūturu e kitea ana e tātou) me ngā auau e tumanakohia ana (ngā auau "me puta" mēnā he tino motuhake ngā taurangi e rua). Ko te nui ake o te rerekētanga i waenga i ngā uara i kitea me ngā uara e tumanakohia ana, ko te nui ake o te uara o te tatauranga χ², ā, ko te kaha ake o te taunakitanga o tētahi whanaungatanga.
Ripanga Āhuatanga
Kua whakaritea ngā raraunga mō tēnei whakamātautau ki roto i tētahi ripanga tūponotanga, e whakaatu ana i ngā auau mō ngā huinga kāwai o ngā taurangi e rua. Hei tauira, me tirotiro tātou i te whanaungatanga i waenga i te tūnga momi hikareti (Āe/Kāo) me te auau o te maremare mau tonu (Āe/Kāo). Ka hangaia e tātou he ripanga 2x2 kei roto ko te maha o ngā kaiwhakautu i roto i ia huinga.
I te nuinga o te wā, ka taea te 2×2, 2×3, 3×4, me ērā atu, i runga i te maha o ngā kāwai i roto i ia taurangi. Ka taea te whakamahi i te whakamātautau chi-square mō te tū motuhake mō ngā ripanga o tetahi rahi, mena ka tutukihia ētahi tikanga.
Whakamātautau Whakaaro
I roto i te whakamātautau chi-square mō te tū motuhake, ko te whakapae ko:
– H0 (whakapae kore): He motuhake ngā taurangi e rua (kāore he whanaungatanga/hononga).
– H1 (whakapae rerekē): Kāore ngā taurangi e rua e tū motuhake (he whanaungatanga/hononga kei reira).
Ko te whāinga o te whakamātautau he whakatau mēnā he rawaka ngā taunakitanga e whakaratohia ana e ngā raraunga hei whakakore i te H0.
Tātai Tatauranga Chi-Square
Ka tatauhia te tatauranga whakamātautau chi-square mā te whakamahi i te tātai:
\[
\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}
\]
Ngā Mōhiohio:
– Ko \(O_{ij}\) te auau tirotiro i te pūtau rarangi-i me te pou-j.
– Ko \(E_{ij}\) te auau e tumanakohia ana i roto i te pūtau o te rarangi-i me te pou-j.
Ka tatauhia te auau e tumanakohia ana mai i te tapeke o te rarangi me te tapeke o te pou:
\[
E_{ij} = \frac{(\text{Tapeke rarangi i}) \times (\text{Tapeke pou j})}{\text{Tapeke Whānui}}
\]
E whakaata ana tēnei tātai i te mea e tumanakohia ana ka puta mēnā kāore ngā tohatoha i ia rarangi me ia pou e awe ana tetahi i tetahi (he motuhake).
Ngā Nekehanga o te Herekoretanga
Ko ngā nekehanga herekore (df) mō tēnei whakamātautau ka whakatauhia e te rahi o te ripanga:
\[
df = (r – 1)(c – 1)
\]
me:
– \(r\) = te maha o ngā rarangi (te kāwai taurangi tuatahi)
– \(c\) = te maha o ngā pou (kāwai taurangi tuarua)
Ka pāngia te āhua o te tohatoha chi-square e ngā nekehanga herekoretanga e whakamahia ana hei whakatau i te uara-p.
Ngā Hipanga hei Mahi i te Whakamātautau Motuhake Chi-Square
Koinei te raupapa whānui mō te whakahaere i tēnei whakamātautau:
1. Whakaritea ngā raraunga ki roto i tētahi ripanga tūponotanga.
Kia tika te whakarite kei te whakaatuhia ngā raraunga hei auau, kaua hei ōrau.
2. Tātaihia te auau e tumanakohia ana mō ia pūtau mā te whakamahi i te tātai \(E_{ij}\).
3. Tātaihia te uara o χ² mā te tāpiri i ngā wāhanga o \((OE)^2/E\) mō ngā pūtau katoa.
4. Whakatauhia te df mā te whakamahi i te \((r-1)(c-1)\).
5. Tātaihia te uara-p i runga i te tohatoha chi-square me te df (whakatairitea rānei te χ² i tātaihia ki te ripanga χ² i te taumata hiranga α, hei tauira 0,05).
6. Whakatauhia.
– Mēnā ko te uara-p ≤ α → te whakakore i te H0 → he whanaungatanga/whakawhirinakitanga kei reira.
– Ki te kore e taea te whakakore i te H0 i te uara-p > α → kāore he taunakitanga o te whanaungatanga.
7. Whakamāramatanga tūturu.
Whakamāramahia te tikanga o te whanaungatanga i roto i te horopaki o te rangahau, kaua ko te "hiranga" me te "kāore i te hiranga" anake.
Tauira Whakamārama (Kāore he Tātaitanga Taipitopito)
Me kī kei te aromatawai tētahi kairangahau i te whanaungatanga i waenga i te "tikanga ako" (motuhake/rōpū) me te "paetanga" (paahi/kore). Whai muri i te whakahaere i tētahi whakamātautau chi-square, ko te uara-p he 0,02. Me te α = 0,05, ko te whakatau ko te whakakore i te H0, e tohu ana i te whanaungatanga i waenga i te tikanga ako me te paetanga. Me whakatau e te kairangahau ko ēhea pūtau te mea nui rawa atu te rerekētanga (hei tauira, mēnā ka whakanuia e te ako rōpū te ōwehenga o ngā paetanga). I roto i te mahi, ka taea te whakawhānui ake i te tātari mā te tirotiro i ngā toenga paerewa, i ngā rahi pānga rānei.
Ngā Kupu me ngā Whakaaro Hira
Ahakoa he kore-taurite te chi-square, he maha ngā whakaritenga nui o tēnei whakamātautau:
1. Kei roto ngā raraunga i te āhua o ngā tatau (auau) ā, kotahi anake te kāwai e taka ai ia kaupapa (kāore e taea te wehe tetahi i tetahi).
2. Ngā tirohanga motuhake, arā, kāore e taea te tatau i tētahi kaiwhakautu neke atu i te kotahi, ā, kāore he whanaungatanga takirua i waenga i ngā tirohanga.
3. He nui te auau e tumanakohia ana. He ture whānui: ko te nuinga o ngā uara \(E_{ij}\) me ≥ 5. Mena he maha rawa ngā pūtau me ngā uara iti e tumanakohia ana, tera pea kāore e tika ngā hua o te whakamātautau chi-square.
Mō ngā ripanga 2×2 me ngā auau iti, ko tētahi atu huarahi ko te Whakamātautau Tika a Fisher. Mō ngā raraunga takirua (hei tauira, i mua-i muri i te kaiwhakautu kotahi), ko tētahi atu huarahi ko te whakamātautau a McNemar.
Rahi Pānga: Ehara i te mea he mea nui noa iho
Kāore te hua nui e tohu ana i te whanaungatanga "kaha". Nō reira, he mea nui kia ripoatahia te rahi o te pānga, hei tauira:
– Phi (φ) mō te tēpu 2×2
– Cramér's V mō ngā tēpu rahi ake
Ko te V a Cramér kei waenganui i te 0 ki te 1, ā, ko ngā uara nui ake e tohu ana i te hononga kaha ake. Mā te pūrongo i ngā rahi pānga ka āwhina i ngā kaipānui ki te mārama ki te kaha o te whanaungatanga, ehara i te mea ko tōna oranga anake.
Ngā Painga me ngā Here
Te taikaha:
– He māmā ki te whakamahi mō ngā raraunga kāwai.
– Kāore e hiahiatia te whakaaro he mea noa.
– He pai mō ngā mara rangahau maha.
Te Whakatakotoranga:
– He tairongo ki te rahi o te tauira: ka taea e ngā tauira nui te hanga i ngā rerekētanga iti hei "tino nui".
– Kāore e whakaatu tika ana i te ahunga o te whanaungatanga, engari ko te noho mai/te ngaro noa iho o tētahi hononga.
– He raruraru mēnā he iti ngā auau e tumanakohia ana i roto i ngā pūtau maha.
– Me tautoko te whakamāramatanga e ētahi atu tātaritanga (hei tauira, te tirotiro i ngā ōwehenga, i ngā toenga rānei).
Te Katinga
He taputapu nui te whakamātautau chi-square mō te motuhaketanga hei aromatawai i te noho, te ngaro rānei o te whanaungatanga i waenga i ngā taurangi kāwai e rua. Mā te hanga i tētahi ripanga tūpono, te tatau i ngā auau e tumanakohia ana, me te whakatairite i aua auau ki ngā auau i kitea mā te whakamahi i te tatauranga χ², ka taea e ngā kairangahau te whakamātautau i te ariā o te motuhaketanga. Heoi, hei whakaputa i tētahi tātari pakari, me neke atu ngā kairangahau i te whakatau mēnā he pānga nui kei te kitea, kāore rānei; me ripoata hoki e rātou ngā rahi pānga, me tirotiro i ngā whakaritenga auau e tumanakohia ana, me te hono i ngā kitenga ki te horopaki matua o te rangahau. Nō reira, ka nui atu te whakamātautau chi-square i te tukanga pāngarau noa iho, engari he wāhanga o te whakaaro pūtaiao e āwhina ana ki te mārama ki ngā tauira o ngā whanaungatanga i roto i ngā raraunga kāwai.
