Kwatanta Rukunoni Biyu
Wani lokaci muna son sanin ko bambancin da ke tsakanin rukunoni biyu na gaske ne ko kwatsam kawai. Shin daliban da suka halarci ajin karin karatu sun fi wadanda ba su halarci ba? Shin maganin sabuwa ya fi na da? T-test shine kayan aikin da ake amfani da shi don amsa irin wadannan tambayoyi.
Nau'o'in T-Test
1. T-Test na Samfuri Daya (One-Sample)
Kana kwatanta matsakaicin samfurinka da wata daraja da aka sani ko ake tsammanin ta.
Masana'antar sarrafa man gyada a Kano tana cewa kowace kwalba tana dauke da milimita 750. Hukumar NAFDAC ta dauki kwalabe 40 ta auna su:
- Matsakaicin samfuri: milimita 743
- Daidaiton bambanci: milimita 12
- H₀: Matsakaici = 750 ml
- H₁: Matsakaici ≠ 750 ml
T-test na samfuri daya zai kwatanta 743 da 750 ya gaya musu ko bambancin (7 ml) yana da mahimmancin kididdiga ko kwatsam ne saboda bambance-bambancen kwalabe.
2. T-Test na Samfurori Biyu Masu Zaman Kansu (Independent Two-Sample)
Kana kwatanta matsakaicin rukunoni biyu daban-daban.
Mai bincike yana son sanin ko sabon hanyar koyarwar lissafi ya fi na da. Ya raba dalibai zuwa rukunoni biyu:
- Rukuni A (hanya ta da): Dalibai 35, matsakaicin maki = 62, daidaiton bambanci = 10
- Rukuni B (sabon hanya): Dalibai 35, matsakaicin maki = 68, daidaiton bambanci = 11
Bambancin maki 6 ne. T-test zai gaya mana ko wannan bambancin yana da mahimmancin kididdiga ko kwatsam ne saboda dalibai daban-daban suna da iya daban-daban.
3. T-Test Mai Dangantaka (Paired)
Kana kwatanta matsakaicin mutane daya a lokuta biyu daban-daban - kafin da bayan wani abu.
Asibitin Aminu Kano yana gwadawa ko wani shirin abinci yana rage kiba. Sun auna nauyin marasa lafiya 25 kafin shirin kuma bayan watanni 3:
- Matsakaicin nauyi kafin: kilo 85
- Matsakaicin nauyi bayan: kilo 82
- Matsakaicin ragewa: kilo 3
Saboda mutane daya ne aka auna sau biyu, muna amfani da t-test mai dangantaka. Tambayar ita ce: shin raguwar kilo 3 ta fi abin da za a sa ran ta kwatsam?
Yadda T-Test Ke Aiki (Ba Tare da Lissafi Mai Wuya Ba)
T-test yana lissafa daraja ta "t" wacce take auna:
t = Bambancin da aka lura da shi ÷ Bambancin da ake sa ran ta kwatsam
Mafi girman daraja ta t, mafi karancin yiwuwar bambancin ya faru ta kwatsam. Lamba mai girma ta t tana nufin bambanci na gaske ne.
Sharadin T-Test
T-test yana aiki ne idan:
- Bayanai masu ci gaba ne: Nauyi, tsawon jiki, maki, kudi - ba rukunoni ba.
- Rarraba kusan na al'ada ne: Ko kuma samfuri ya isa girma (30+) don CLT ta shiga aiki.
- Ba a zabi samfuri da son kai ba: Bazuwar zabin.
- Bambancin yanayi iri daya ne (don t-test na samfurori biyu masu zaman kansu): Tarwatsewar ta rukunoni biyu ba ta bambanta sosai ba.
Fassara Sakamako
Binciken hanyar koyarwa ya ba mu: t = 2.45, df = 68, p-value = 0.017
- t = 2.45: Bambancin da aka lura da shi ya fi bambancin kwatsam da kusan sau 2.45
- df = 68: Degrees of freedom - yana shafar siffar rarrabar t
- p-value = 0.017: Kasa da 0.05, don haka bambancin yana da mahimmancin kididdiga
Sakamakon: Akwai shaida cewa sabon hanyar koyarwa yana inganta makin dalibai. Amma ka tuna: wannan bai gaya mana girman ingantawar ba. Don haka muna kallon bambancin matsakaici (maki 6) tare da p-value.
Ƙananan Samfurori da T-Distribution
T-test yana amfani da rarraba na t maimakon rarraba na al'ada na z. Bambancin shi ne cewa rarraba na t ya fi fadi a gefuna (thicker tails) - yana ba da karin kulawa ga rashin tabbas sa'ad da samfuri ya yi karami. Mafi girman samfuri, mafi kusancin rarraba na t zuwa rarraba na al'ada.
T-Test da Girman Tasiri
Koyaushe ka kalli bambancin matsakaici a zahiri tare da p-value. Girman tasiri kamar Cohen's d yana taimaka:
- d ≈ 0.2: Tasiri karami
- d ≈ 0.5: Tasiri na tsakiya
- d ≈ 0.8: Tasiri babba
T-test kayan aiki ne don gwada ko bambancin matsakaicin da ke tsakanin rukunoni biyu (ko tsakanin samfuri da daraja ta musamman) na gaske ne ko kwatsam. Akwai nau'uka uku: samfuri daya, samfurori biyu masu zaman kansu, da mai dangantaka. Sakamakon ya haɗa da daraja ta t da p-value. Ka tuna ka kalli girman tasiri tare da mahimmancin kididdiga - bambancin "na gaske" a kididdiga na iya zama maras muhimmanci a aikace.