Take: Misalin Tambayoyin Tattaunawa Kan Jarrabawa
Gwajin chi-square (χ² gwajin) wata hanya ce ta ƙididdiga da ake amfani da ita don gwada hasashe game da rarrabawar mitar masu canjin rarrabuwa. Wannan gwajin yana da matukar amfani wajen tantance ko akwai wata muhimmiyar alaƙa tsakanin masu canjin rarrabuwa guda biyu masu zaman kansu. Wannan labarin zai tattauna ainihin manufar gwajin chi-square kuma ya ba da misalai da yawa na tambayoyi da tattaunawarsu.
Pendahuluan
Gwajin Chi-Square yana ɗaya daga cikin gwaje-gwajen da ba na parametric ba da aka fi amfani da su don nazarin bayanai na rukuni. Babban manufarsa ita ce gwada girman bambancin da ke tsakanin rarrabawar da aka lura da kuma rarrabawar da ake tsammani bisa ga hasashen da ba shi da ma'ana.
Hasashe mara tushe (H0) a cikin gwajin ma'auni yawanci yana nuna cewa babu wata alaƙa tsakanin masu canji guda biyu, yayin da madadin hasashe (H1) ya bayyana cewa akwai dangantaka tsakanin masu canji guda biyu.
Ka'idoji na Asali na Gwajin Chi-Square
Da farko, bari mu fahimci wasu muhimman ra'ayoyi a cikin gwajin Chi-Square:
1. Yawan Lura (O): Wannan shine adadin lura da kuka lura a cikin wani takamaiman nau'in bayanai.
2. Mita da ake tsammani (E): Wannan shine adadin abubuwan da ake tsammani a cikin wani nau'i na musamman bisa ga rarrabawar ka'ida ko kuma hasashen da ba shi da ma'ana.
3. Tsarin Gwaji na Chi-Square:
\[
\chi² = \sum \frac{(O_i - E_i)²}{E_i}
\]
Inda \(O_i\) shine mitar da aka lura da ita da kuma \(E_i\) shine mitar da ake tsammani don nau'in i-th.
4. Digiri na 'Yanci (df): Ana ƙididdige wannan azaman (adadin layuka - 1) (adadin ginshiƙai - 1) don teburin gaggawa.
5. Matsayin Muhimmanci (\(\alpha\)): Ma'aunin da ake amfani da shi don tantance ko sakamakon gwajin ƙididdiga yana da mahimmanci. Gabaɗaya, ana amfani da kashi 0,05 ko 5% a matsayin matakin mahimmanci.
Tambayoyi da Tattaunawa Samfura
Bari mu duba wani bincike domin fahimtar amfani da gwajin Chi-Square.
Misali Tambaya ta 1:
An gudanar da wani bincike domin tantance ko akwai alaƙa tsakanin fifikon nau'in kiɗa da matakin ilimi. An tattara bayanai masu zuwa daga masu amsa 200.
| | Pop | Rock | Jazz | Jimilla |
|—————— |—–|———|———-|
| Makarantar Sakandare | 20 | 30 | 50 | 100 |
| Digiri na farko | 35 | 25 | 40 | 100 |
| Jimilla | 55 | 55 | 90 | 200 |
Tambaya: Akwai alaƙa tsakanin nau'in kiɗan da aka fi so da matakin ilimi?
Matakan Tattaunawa:
1. Ƙayyade Hasashe:
– H0: Babu wata alaƙa tsakanin fifikon nau'in kiɗa da matakin ilimi.
– H1: Akwai alaƙa tsakanin fifikon nau'in kiɗa da matakin ilimi.
2. Lissafa Mita da ake tsammani (E):
Lissafin mitar da ake tsammani ga kowace tantanin halitta na teburin abubuwan da ke faruwa. Tsarin lissafin E shine:
\[
E_{ij} = \frac{(\text{Jimlar Layi}_i \times \text{Jimlar Column}_j)}{\text{Jimlar Jimilla}}
\]
Misali, yawan da ake tsammanin ɗaliban makarantar sakandare waɗanda ke son Pop su samu shine:
\[
E_{SMA, Pop} = \frac{(sau 100 55)}{200} = 27.5
\]
Haka kuma, muna lissafin dukkan ƙwayoyin halitta:
| | Pop | Rock | Jazz |
|—————— |—–|———|———-|
| Makarantar Sakandare | 27.5 | 27.5 | 45 |
| Digiri na farko | 27.5 | 27.5 | 45 |
3. Lissafin Chi-Square (χ²):
Amfani da dabarar:
\[
\chi² = \sum \frac{(O - E)²}{E}
\]
Lissafa gudummawar kowace tantanin halitta da jimillarta:
– Ga Makarantar Sakandare da Pop:
\[
\chi²_{SMA, Pop} = \frac{(20 – 27.5)²}{27.5} \kimanin 2.04
\]
– Ana yin irin wannan lissafin ga kowane haɗin gwiwa:
\[
Chi² = 2.04 + 0.23 + 0.56 + 0.23 + 0.23 + 0 + 1.96 = 5.25
\]
4. Lissafa Digirin 'Yanci:
\[
df = (3-1) \sau (3-1) = 4
\]
5. Tantance Muhimman Dabi'u da Shawarwari:
Ta amfani da teburin rarraba Chi-Square tare da \(\alpha = 0.05\) da df = 4, ƙimar mahimmanci ita ce 9.488. Tun daga 5.25 < 9.488, mun kasa ƙin H0. Kammalawa: Babu wata muhimmiyar alaƙa tsakanin fifikon nau'in kiɗa da matakin ilimi a matakin mahimmanci na 0.05. Kammalawa Gwajin Chi-Square kayan aiki ne mai matuƙar amfani don nazarin bayanai na rukuni a fannoni daban-daban na bincike. Ta hanyar fahimtar yadda ake ƙididdigewa da kimanta sakamakon gwajin Chi-Square, masu bincike za su iya yin kyakkyawan ƙarshe game da bayanan su. Nazarin shari'ar da aka tattauna yana ba da misali mai amfani na yadda gwajin Chi-Square ke aiki da kuma yadda ake fassara sakamakon. Baya ga nazarin hannu, amfani da software na ƙididdiga kamar SPSS ko R suma abu ne da aka saba yi don sauƙaƙe lissafi da ƙarin bincike. A cikin aikace-aikacen gaske, ban da kula da sakamakon ƙididdiga, yana da mahimmanci a yi la'akari da mahallin binciken kuma a fassara ƙididdiga cikin hikima.
