Ngā Tātai Tatauranga i roto i te Rangahau
Ko te tatauranga he peka o te pāngarau e pā ana ki te kohikohi, te tātari, te whakamārama, me te whakaaturanga raraunga. I roto i te rangahau, ahakoa i roto i ngā pūtaiao, i te hangarau, i ngā pūtaiao pāpori, i ngā mahi tangata rānei, he mea nui te mahi a te tatauranga hei āwhina i ngā kairangahau ki te whakamātautau i ngā whakapae, ki te whakatakoto matapae, me te whakatau whakatau. Ka matapakihia e tēnei tuhinga ētahi tauira tatauranga taketake me tā rātou whakamahinga i roto i te rangahau.
1. Ngā Tatauranga Whakaahuatanga
E whakamahia ana ngā tatauranga whakaahua hei whakaahua i ngā raraunga i kohia i roto i tētahi rangahau. Kei roto i ēnei ko ngā mehua e whakarato ana i tētahi tirohanga whānui o ngā raraunga.
a. Toharite (Toharite)
Ko te toharite te uara e whakamahia whānuitia ana i roto i ngā tatauranga. Ko te tapeke o ngā uara katoa i roto i tētahi huinga raraunga ka wehea ki te maha o ngā uara.
\[ \text{Toharite} (\bar{x}) = \frac{\sum_{i=1}^{n} x_i}{n} \]
Kei hea:
– Ko te \( \sum \) te tohu tapeke, ko tōna tikanga ko te tāpiri i ngā uara katoa o \( x \) mai i te 1 ki te \( n \).
– Ko \( x_i \) ngā uara katoa o te huinga raraunga.
– Ko te \( n \) te tapeke o ngā uara i roto i te huinga raraunga.
b. Waenga
Ko te tau waenga ko te uara waenga i roto i tētahi huinga raraunga kua whakarōpūtia. Mena he tauhou te maha o ngā uara i roto i ngā raraunga, ko te tau waenga te uara waenga. Mena he taurite te maha o ngā uara, ko te tau waenga te toharite o ngā uara waenga e rua.
Aratau
Ko te aratau te uara e puta pinepine ana i roto i tētahi huinga raraunga. Tērā pea he aratau kotahi (unimodal), he aratau maha (multimodal), kāore rānei he aratau i roto i tētahi huinga raraunga.
d. Awhe
Ko te awhe te rerekētanga i waenga i ngā uara mōrahi me ngā uara mōkito i roto i tētahi huinga raraunga.
\[ \kuputuhi{Awhe} = \kuputuhi{Tōrahi}(x) – \kuputuhi{Iti}(x) \]
e. Paerewa Rerekētanga
Ko te paerewa rerekētanga he ine i te horapa, te marara rānei o ngā raraunga huri noa i te toharite. Ko te tātai mō te paerewa rerekētanga taupori ko:
\[ \sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i – \mu)^2}{N}} \]
Ā, hei tauira:
\[ s = \sqrt{\frac{\sum_{i=1}^{n} (x_i – \bar{x})^2}{n-1}} \]
Kei hea:
– Ko te paerewa rerekētanga o te taupori ko \( \sigma \).
– Ko te \( s \) te paerewa rerekētanga tauira.
– Ko \( x_i \) ngā uara katoa o te huinga raraunga.
– Ko te toharite o te taupori ko \( \mu \).
– Ko te toharite tauira te \( \bar{x} \).
– Ko te \( N \) te tapeke o ngā uara o te taupori.
– Ko te \( n \) te tapeke o ngā uara i roto i te tauira.
2. Ngā Tatauranga Whakatau
Mā ngā tatauranga whakatau tata ka taea e ngā kairangahau te whakatau i tētahi taupori i runga i tētahi tauira raraunga. Kei roto ko ngā momo tikanga, pērā i te whakamātautau whakapae, te whakatautaurite, me te tātari rerekētanga (ANOVA).
a. Whakamātautau Whakaaro
Ko te whakamātautau whakapae he tukanga tatauranga e whakamahia ana hei whakatau mena he nui ngā taunakitanga i roto i tētahi tauira raraunga hei whakatau he pono tētahi āhuatanga i roto i tētahi taupori.
i. Te Whakaaro Kore (H0) me te Whakaaro Rerekē (H1)
– Te Whakaaro Kore (H0): Kāore he rerekētanga, kāore hoki he pānga.
– Whakapae Rerekē (H1): He rerekētanga, he pānga rānei.
Ka whakamahia he tatauranga whakamātautau hei whakamātautau, pērā i te whakamātautau-t, te whakamātautau chi-square, te ANOVA rānei, me te whakatairite i te uara-p ki te taumata hiranga (\(\alpha\)), ko te tikanga he 0,05.
ii. whakamātautau-t
Ka whakamahia te whakamātautau-t hei whakatairite i ngā toharite o ngā rōpū e rua. He maha ngā momo rerekētanga o te whakamātautau-t, pērā i te whakamātautau-t tauira motuhake me te whakamātautau-t takirua.
Ko te tātai taketake mō te whakamātautau-t mō ngā tauira motuhake ko:
\[ t = \frac{\bar{x}_1 – \bar{x}_2}{\sqrt{\left( \frac{s_1^2}{n_1} \right) + \left( \frac{s_2^2}{n_2} \right)}} \]
b. Whakamuri
Ka whakamahia te whakatauira i te whanaungatanga i waenga i tētahi, i ētahi rānei o ngā taurangi motuhake (ngā matapae) me tētahi taurangi whakawhirinaki (te urupare).
i. Whakamuritanga Raina Māmā
Ka whakatauirahia e te whakatauira raina māmā te whanaungatanga i waenga i tētahi taurangi motuhake me tētahi taurangi whakawhirinaki.
Ko te whārite whakatauira rārangi māmā ko:
\[ y = \beta_0 + \beta_1 x + \epsilon \]
Kei hea:
– Ko \( y \) te taurangi whakawhirinaki.
– Ko te taurangi motuhake ko \( x \).
– Ko \( \beta_0 \) te haukoti.
– Ko te tauwehenga taurite te \( \beta_1 \).
– He hapa a \( \epsilon \).
ii. Te Whakamuritanga Raina Maha
Ka whakatauirahia e te whakatauira raina maha te whanaungatanga i waenga i ngā taurangi motuhake maha me te taurangi whakawhirinaki kotahi.
Ko te whārite whakatautaurangi rārangi maha ko:
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_p x_p + \epsilon \]
Kei hea:
– Ko \( y \) te taurangi whakawhirinaki.
– Ko te taurangi motuhake ko \( x_1, x_2, \ldots, x_p \).
– Ko \( \beta_0 \) te haukoti.
– Ko \( \beta_p \) te tauwehenga whakatautau mō te taurangi motuhake \( p \).
– He hapa a \( \epsilon \).
c. Tātaritanga Rerekētanga (ANOVA)
Ka whakamahia te ANOVA hei whakatairite i ngā toharite o ngā rōpū e toru, neke atu rānei. Ka whakatauhia e te ANOVA mēnā he rerekētanga nui i waenga i ngā toharite rōpū mā te whakatairite i te rerekētanga i waenga i ngā rōpū ki te rerekētanga i roto i ngā rōpū.
Ko te tātai taketake mō te ANOVA ko:
\[ F = \frac{\text{Rēreretanga i waenganui i te rōpū}}{\text{Rēreretanga i roto i te rōpū}} \]
Ka tatauhia te tatauranga-F, ka whakaritea ki te uara matua o te tohatoha F hei whakatau mēnā he rerekētanga nui i waenga i ngā toharite rōpū.
3. Hononga
Ka ine te hononga i te kaha me te ahunga o te whanaungatanga rārangi i waenga i ngā taurangi e rua.
a. Tauwehenga Taurite Pearson (r)
Ko te tauwehenga taunga a Pearson te mehua e whakamahia whānuitia ana hei ine i te tauwehenga rārangi i waenga i ngā taurangi e rua.
Ko te tātai mō te tauwehenga taunga Pearson ko:
\[ r = \frac{\sum_{i=1}^{n} (x_i – \bar{x})(y_i – \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i – \bar{x})^2} \sqrt{\sum_{i=1}^{n} (y_i – \bar{y})^2}} \]
Kei hea:
– Ko te tauwehenga taunga Pearson te \( r \).
– Ko \( x_i \) me \( y_i \) ngā uara o ngā taurangi e rua.
– Ko \( \bar{x} \) me \( \bar{y} \) ngā toharite o ngā taurangi e rua.
Ko te uara \( r \) kei waenganui i te -1 (hononga kino tino tika) ki te +1 (hononga pai tino tika), me te 0 e tohu ana kāore he hononga.
Te Katinga
He taputapu rangahau nui ngā tatauranga hei āwhina i ngā kairangahau ki te whakaatu, ki te tātari, me te whakatau i ngā whakatau mai i ngā raraunga. E kapi ana tēnei tuhinga i ētahi tauira taketake noa iho i roto i ngā tatauranga whakaahua me ngā tatauranga whakatau, tae atu ki te hononga. Ahakoa he māmā noa iho, ko te māramatanga hōhonu ki ēnei tauira te mea nui ki te whakahaere tātaritanga tika me te whakatau whakatau tika mai i ngā raraunga rangahau. Mā te mōhio ki ngā tatauranga, ka taea e ngā kairangahau te whakarite kia ahu mai ā rātou kitenga i runga i te tātaritanga pakari me te pono.
