Te Whakatau i te Tauwehenga Hononga: Kupu Whakataki, Ngā Tikanga, me Ngā Whakamahinga
Ko te tauwehenga hononga he mehua tatauranga e whakatau ana i te kaha o te whanaungatanga i waenga i ngā taurangi e rua i roto i tētahi huinga raraunga. Ko ngā hononga kei waenganui i te -1 ki te 1. Ko te uara tauwehenga e tata ana ki te 1, ki te -1 rānei, e tohu ana i te whanaungatanga kaha i waenga i ngā taurangi e rua. Ko te uara tauwehenga e tata ana ki te 0 e tohu ana kāore he whanaungatanga kaha i waenga i ngā taurangi e rua. Ka matapakihia e tēnei tuhinga te tauwehenga hononga, ngā tikanga mō te tatau, tōna whakamārama, me ōna tono i roto i ngā momo mara.
He Kupu Whakataki ki te Tauwehenga Hononga
Mā te tauwehenga taunga ka kitea he tirohanga tau mō te tata o te whanaungatanga o ngā taurangi e rua. E rua ngā momo matua o ngā tauwehenga taunga i runga i te ahunga o te whanaungatanga:
1. Tauwehenga Hononga Pai: E tohu ana ina piki ake tētahi taurangi, ka piki ake anō hoki tētahi atu taurangi.
2. Tauwehenga Hononga Kino: E tohu ana ina piki tetahi taurangi, ka heke tetahi atu taurangi.
Ka taea hoki te wehewehe i te whanaungatanga i waenga i ngā taurangi e rua kia toru ngā momo i runga i te kaha o te whanaungatanga:
1. Hononga Kaha: E tata ana te tauwehenga ki te -1, ki te 1 rānei.
2. Hononga Taurite: Kei waenganui i te -0.5 ki te -1, i te 0.5 rānei ki te 1 te tauwehenga.
3. Hononga ngoikore: E tata ana te tauwehenga ki te 0.
Tikanga mō te Tatau i te Tauwehenga Hononga
He maha ngā tikanga noa e whakamahia ana hei tatau i te tauwehenga taunga, tae atu ki te taunga a Pearson, te taunga a Spearman, me te taunga a Kendall. Me matapakihia ia o ēnei tikanga me ētahi atu taipitopito.
1. Te Hononga Pearson
Ka whakamahia te tauwehenga taunga Pearson ina he tonu ngā taurangi e rua, ā, he tohatoha noa. Ko te tātai mō te tauwehenga taunga Pearson ko:
\[ r = \frac {n(\Sigma xy) – (\Sigma x)(\Sigma y)}{ \sqrt{ [n \Sigma x^2 – (\Sigma x)^2] [n \Sigma y^2 – (\Sigma y)^2 ] } } \]
Kei hea:
– \( r \) = tauwehenga taunga,
– \( n \) = te maha o ngā takirua raraunga,
– \( \Sigma xy \) = te tapeke o ngā hua o ngā takirua raraunga \( x \) me \( y \),
– \( \Sigma x \) = te tapeke o ngā uara \( x \),
– \( \Sigma y \) = te tapeke o ngā uara \( y \),
– \( \Sigma x^2 \) = te tapeke o ngā tapawhā o \( x \),
– \( \Sigma y^2 \) = te tapeke o ngā tapawhā o \( y \).
2. Te Hononga Tūnga o Spearman
Ka whakamahia te tauwehenga taunga Spearman mō ngā raraunga raupapa, ina kore rānei e taea te whakatutuki i te whakaaro o te āhua noa. Ko te tauwehenga Spearman e hangai ana ki te whakatauranga o ngā uara raraunga, kaua ki ō rātou uara tuturu. Ko te tātai mō te tauwehenga tauwehenga Spearman ko:
\[ \rho = 1 – \frac {6\Sigma d_i^2}{n(n^2-1)} \]
Kei hea:
– \( \rho \) = te tauwehenga taunga a Spearman,
– \( d_i \) = te rerekētanga i waenga i ngā tūnga o ngā takirua raraunga \( x \) me \( y \),
– \( n \) = te maha o ngā takirua raraunga.
3. Te Hononga Tau a Kendall
Ka ine te tauwehenga hononga a Kendall i te kaha o te whanaungatanga i waenga i ngā taurangi raupapa e rua. Kāore i rite ki a Spearman, ka aro nui te tauwehenga hononga a Kendall ki te maha o ngā takirua ōrite me ngā takirua kore ōrite. Ko te tātai mō te tauwehenga hononga a Kendall ko:
\[ \tau = \frac{ (C – D)} { \sqrt{(C + D + T) (C + D + U) } } \]
Kei hea:
– \( \tau \) = te tauwehenga taunga a Kendall,
– \( C \) = te maha o ngā takirua ōrite,
– \( D \) = te maha o ngā takirua taupatupatu,
– \( T \) = te maha o ngā takirua raupapa i roto i te taurangi \( x \),
– \( U \) = te maha o ngā takirua raupapa i roto i te taurangi \( y \).
Te Whakamārama i te Tauwehenga Hononga
Ko te whakamāramatanga o te tauwehenga hononga e whakawhirinaki ana ki te uara o te tauwehenga i whiwhihia:
– Tauwehenga +1: He whanaungatanga tino pai.
– Tauwehenga 0.7 ki te 0.9: He whanaungatanga pai kaha.
– Tauwehenga 0.4 ki te 0.6: He whanaungatanga pai āhua pai.
– Tauwehenga 0.1 ki te 0.3: He ngoikore te whanaungatanga pai.
– Tauwehenga 0: Kāore he whanaungatanga.
– Tauwehenga -0.1 ki te -0.3: He ngoikore te whanaungatanga kino.
– Tauwehenga -0.4 ki te -0.6: He whanaungatanga kino āhua-waenga.
– Tauwehenga -0.7 ki te -0.9: He whanaungatanga kino kaha.
– Tauwehenga -1: He whanaungatanga tino kino.
Te Whakamahinga Taurite Hononga
He whānuitia ngā whakamahinga o te tauwehenga taunga i roto i ngā momo mara, tae atu ki te ōhanga, te pūtaiao pāpori, te hauora, te mātauranga, me ētahi atu. Anei ētahi tauira:
1. Ōhanga: Te whakatau i te whanaungatanga i waenga i te pikinga utu me te kore mahi, i waenga rānei i te whakapaunga a ngā kaihoko me te moni whiwhi.
2. Ngā Pūtaiao Pāpori: Te whakatau i te whanaungatanga i waenga i te mātauranga me te moni whiwhi, i waenga rānei i te pāpāho pāpori me te oranga hinengaro.
3. Hauora: Te whakatairite i te whanaungatanga i waenga i ngā tikanga momi hikareti me ngā mate pukupuku pūkahukahu, i waenga rānei i te āhua noho hihiko me te hauora o te ngākau.
4. Mātauranga: Te tirotiro i te whanaungatanga i waenga i te wā ako me ngā hua o te whakamātautau, i waenga rānei i te rahi o te akomanga me te whakatutukitanga o ngā ākonga.
Ngā Tauira Whaihua e Whakamahi ana i ngā Huinga Raraunga
Me kī he huinga raraunga tā tātou kei roto ko ngā kaute whakamātautau pāngarau me te wā ako i roto i ngā hāora mō te 10 ākonga penei:
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Ngā Hāora Ako a ngā Tauira Ngā Māka Pāngarau
1 5 85
2 3 78
3 6 90
4 2 76
5 4 80
6 6 88
7 5 85
8 3 82
9 7 91
10 5 87
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Ka taea e tātou te tatau i te taunga taunga a Pearson i waenga i ngā Hāora_Ako me te Kaute_Pāngarau. Mā te whakamahi i te tātai a Pearson, ka tatauhia e tātou a \( \Sigma x \), \( \Sigma y \), \( \Sigma xy \), \( \Sigma x^2 \), me \( \Sigma y^2 \) i te tuatahi, kātahi ka whakakapia ēnei uara ki te tātai hei tiki i te uara o \( r \).
Whakamutunga
He taputapu kaha te tauwehenga hononga i roto i te tātari raraunga hei whakatau i te kaha me te ahunga o te whanaungatanga i waenga i ngā taurangi e rua. He mea nui te mārama ki te ariā, ngā tikanga tatau, me te whakamārama i te tauwehenga hononga mō te tātari raraunga whai hua. Mā te mārama tika, ka taea e tātou te whakatau pai ake i ngā whanaungatanga i waenga i ngā taurangi i roto i ngā momo mara, ā, ka taea hoki e tātou te whakatau whai whakaaro, e ahu mai ana i ngā raraunga.
