He aha ka Loiloi Pili?
ʻO ka loiloi pilina kahi ʻenehana helu i hoʻohana ʻia e ana i ka pilina ma waena o ʻelua a ʻoi aku paha mau loli. Ma ke ʻano o ka ʻikepili a me ka noiʻi, makemake pinepine nā mea noiʻi e hoʻomaopopo i ka pilina ma waena o nā loli a lākou e aʻo nei. No ka laʻana, makemake paha kahi mea noiʻi waiwai e hoʻomaopopo i ka pilina ma waena o ka loaʻa kālā a me ka hoʻolilo ʻana o nā mea kūʻai aku, a makemake paha kahi psychologist e nānā i ka pilina ma waena o nā pae kaumaha a me ka huahua hana.
Nā Manaʻo Kumu o ka Nānā Pilina
Ana ke ʻano pili i ke kuhikuhi a me ka ikaika o ka pilina linear ma waena o nā loli ʻelua. ʻEkolu mau ʻano nui o nā pilina pili:
1. Pilina Maikaʻi: Ke piʻi aʻe kekahi loli, e piʻi pū kekahi loli ʻē aʻe.
2. Pilina Maikaʻi ʻole: Ke piʻi aʻe kekahi loli, e emi ana kekahi loli ʻē aʻe.
3. ʻAʻohe Pilina: ʻAʻohe ʻano maopopo i ka pilina ma waena o nā loli ʻelua.
Ma ke ʻano makemakika, ua hōʻike ʻia ka ikaika a me ke kuhikuhi o kahi pilina ma ke ʻano he coefficient pilina, hiki ke piʻi mai -1 a i 1. ʻO kahi coefficient pilina maikaʻi kokoke i 1 e hōʻike ana i kahi pilina maikaʻi ikaika, ʻoiai ʻo kahi coefficient maikaʻi ʻole kokoke i -1 e hōʻike ana i kahi pilina maikaʻi ʻole ikaika. ʻO ka waiwai o 0 e hōʻike ana ʻaʻohe pilina linear.
Nā ʻAno o nā Koepili Pili
Aia kekahi mau ʻano o nā coefficients correlation i hoʻohana pinepine ʻia, kēlā me kēia me kāna mau hoʻohana ponoʻī ma muli o ke ʻano a me ke ʻano o ka ʻikepili e kālailai ʻia nei. ʻO kekahi o nā ʻano maʻamau o nā coefficients correlation:
1. Ka helu pilina Pearson
ʻO ke Pearson Correlation Coefficient ka mea i hoʻohana pinepine ʻia a ana i ka pilina linear ma waena o ʻelua mau loli hoʻomau. ʻO ke ʻano hana:
\[ r = \frac{n(\sum xy) – (\sum x)(\sum y)}{\sqrt{[n\sum x^2 – (\sum x)^2][n\sum y^2 – (\sum y)^2]}} \]
Ma hea:
– ʻo \( n \) ka helu o nā hui ʻikepili,
– ʻO \( \sum xy \) ka huina o nā hoʻonui ma waena o nā hui ʻikepili,
– ʻO \( \sum x \) a me \( \sum y \) nā huina o kēlā me kēia loli,
– ʻO \( \sum x^2 \) a me \( \sum y^2 \) nā huina o nā huinahā o kēlā me kēia loli.
2. Ka helu hoʻopili Spearman
Hoʻohana ʻia ke koina pilina Spearman i ka wā ʻaʻole linear ka ʻikepili e kālailai ʻia ana a i ʻole i ka wā he ordinal ka ʻikepili (ʻikepili hiki ke kauoha ʻia). Ana ʻo Spearman i ke kūlike o ke kūlana ma waena o nā loli ʻelua. Ua helu ʻia me ka hoʻohana ʻana i ke ʻano:
\[ r_s = 1 – \frac{6\sum d^2}{n(n^2 – 1)} \]
Ma hea:
– ʻo \( d \) ka ʻokoʻa ma waena o nā kūlana o nā nānā ʻelua,
– ʻO \( n \) ka helu o nā nānā ʻana.
3. Ka helu pilina o Kendall
ʻO ke Coefficient Correlation a Kendall kekahi koho ʻē aʻe no ka ʻikepili ordinal a he mea pono ia i ke ana ʻana i ka pilina monotonic ma waena o nā loli ʻelua. ʻO ke ʻano hana:
\[ \tau = \frac{(Helu\, o\, kūlike\, mau hui) – (Helu\, o\, kūlike\, mau hui)}{n(n-1)/2} \]
Nā Hoʻohana a me nā Noi o ka Loiloi Pilina
Hoʻohana ʻia ka loiloi pilina ma nā ʻano like ʻole e like me ka hoʻokele waiwai, ka psychology, ka sociology, ka biology, a me nā mea hou aku. ʻO kekahi mau laʻana o nā noi kūpono:
1. Hoʻokele waiwai
I loko o ka hoʻokele waiwai, hiki ke hoʻohana ʻia ka loiloi pilina e wānana pehea e pili ai kekahi loli hoʻokele waiwai, e like me ka hoʻonui ʻana o ke kumukūʻai, i kekahi loli ʻē aʻe, e like me ka helu hana ʻole a i ʻole ka ulu ʻana o ka hoʻokele waiwai. No ka laʻana, ka pilina ma waena o nā uku paneʻe a me ka hoʻopukapuka kālā ʻoihana.
2. ʻIke loea
I loko o ka psychology, hoʻohana pinepine nā kānaka noiʻi i ka loiloi pilina e hoʻomaopopo i ka pilina ma waena o nā loli psychological. No ka laʻana, ka loaʻa ʻana o kahi loulou ma waena o nā pae kaumaha o ke kanaka a me ka hauʻoli, a i ʻole ma waena o nā ʻano hiamoe a me ka hana hoʻonaʻauao.
3. Mahiʻai
Ma ka mahiʻai, hiki i ka loiloi pilina ke kōkua i nā mahiʻai a me nā kānaka ʻepekema e hoʻomaopopo i ka pilina ma waena o nā mea loli e like me ka hoʻohana ʻana i ka mea hoʻouluulu a me nā hua o nā mea kanu. Kōkua kēia i ka hoʻoholo ʻana i nā hoʻoholo maikaʻi e pili ana i nā hana mahiʻai.
4. Ola kino
I ka ʻepekema olakino, ua noiʻi pinepine ʻia ka pilina ma waena o nā mea pilikia e like me ka puhi paka a me nā maʻi cardiovascular. Kōkua kēia i ka hoʻokumu ʻana i nā ʻōlelo aʻoaʻo a me nā kulekele olakino i hoʻokumu ʻia i nā hōʻike.
Nā Pōmaikaʻi a me nā Palena o ka Nānā Pilina
ʻOi aku
1. Maʻalahi: Maʻalahi e hoʻomaopopo a hoʻokō.
2. Ka pono: Hiki ke holo wikiwiki no ka ʻikepili nui.
3. Nā Wānana Mua: Hāʻawi i nā ʻike mua i nā pilina ma waena o nā loli i hiki ke ʻimi hou ʻia.
Nā Palena
1. ʻAʻole Hōʻike i kahi Pilina Kumu: ʻAʻole manaʻo ka pilina i ke kumu. Hiki ke pili pono nā loli ʻelua me ka ʻole o kekahi e hoʻoulu i kekahi.
2. Ka Mana o nā Loli Huna: Hiki ke hoʻopili ʻia ka pilina ma waena o ʻelua mau loli e nā loli ʻē aʻe i kālailai ʻole ʻia.
3. Nā Palena o nā ʻAno ʻIkepili: ʻAʻole kūpono nā ʻano ʻikepili āpau no nā ʻano pilina āpau. No ka laʻana, ʻaʻole kūpono ʻo Pearson no ka ʻikepili ordinal.
Ka hopena
He mea hana helu ikaika ka loiloi pilina no ka hoʻomaopopo ʻana i nā pilina ma waena o nā loli ma nā ʻano like ʻole o ke aʻo ʻana. He mea nui ka hoʻomaopopo maikaʻi ʻana i ke kumumanaʻo ma hope o nā coefficients correlation a me kā lākou hoʻohana pono ʻana e hoʻonui i nā pono o kēia ʻano hana. ʻOiai kona mau palena, e like me ka hōʻoia ʻole ʻana i nā pilina kumu, ʻo ka loiloi pilina ke ʻano mua nui i ka ʻimi ʻana i nā pilina ma waena o nā loli ma mua o ka neʻe ʻana i nā loiloi paʻakikī.
