Mutu: Chitsanzo cha Mafunso Okambirana pa Mayeso Osiyanasiyana
Mayeso a chi-square (χ² test) ndi njira yowerengera yomwe imagwiritsidwa ntchito poyesa malingaliro okhudza kufalikira kwa ma frequency a ma classical variables. Mayeso awa ndi othandiza kwambiri podziwa ngati pali ubale wofunikira pakati pa ma classical variables awiri odziyimira pawokha. Nkhaniyi ikambirana za lingaliro loyambira la mayeso a chi-square ndikupereka mafunso angapo a zitsanzo ndi kukambirana kwawo.
Pendauluan
Mayeso a Chi-Square ndi amodzi mwa mayeso osagwiritsa ntchito ma parametric omwe amagwiritsidwa ntchito kwambiri posanthula deta yamagulu. Cholinga chake chachikulu ndikuyesa kusiyana pakati pa kugawa komwe kwawonedwa ndi kugawa komwe kumayembekezeredwa kutengera lingaliro lopanda pake.
Hypothesis yopanda kanthu (H0) mu mayeso obwerezabwereza nthawi zambiri imanena kuti palibe ubale pakati pa zosintha ziwiri zamagulu, pomwe hypothesis ina (H1) imanena kuti pali ubale pakati pa zosintha ziwirizi.
Malingaliro Oyambira a Mayeso a Chi-Square
Choyamba, tiyeni timvetse mfundo zina zoyambira mu mayeso a Chi-Square:
1. Kuchuluka kwa Kuwona (O): Ichi ndi chiwerengero cha zomwe mumawona mu gulu linalake la deta.
2. Kuchuluka Koyembekezeredwa (E): Ichi ndi chiwerengero cha zomwe mukuyembekezera mu gulu linalake kutengera kugawa kwa chiphunzitso kapena lingaliro lopanda pake.
3. Fomula Yoyesera ya Chi-Square:
\[
\chi² = \sum \frac{(O_i – E_i)²}{E_i}
\]
Kumene \(O_i\) ndi pafupipafupi yomwe yawonedwa ndipo \(E_i\) ndi pafupipafupi yomwe ikuyembekezeka pa gulu la i-th.
4. Madigiri a Ufulu (df): Izi zimawerengedwa ngati (chiwerengero cha mizere - 1) (chiwerengero cha mizati - 1) pa tebulo la contingency.
5. Mulingo Wofunika (\(\alpha\)): Mulingo wogwiritsidwa ntchito kudziwa ngati zotsatira za mayeso a ziwerengero ndi zofunika. Kawirikawiri, 0,05 kapena 5% imagwiritsidwa ntchito ngati mulingo wofunika.
Mafunso ndi Kukambirana Zitsanzo
Tiyeni tiwone chitsanzo cha kafukufuku kuti timvetse bwino momwe mayeso a Chi-Square amagwiritsidwira ntchito.
Chitsanzo cha Funso 1:
Kafukufuku wachitika kuti adziwe ngati pali ubale pakati pa zomwe amakonda pa nyimbo ndi maphunziro ake. Deta yotsatirayi inasonkhanitsidwa kuchokera kwa anthu 200 omwe anayankha.
| Pop | Rock | Jazz | Zonse |
|——————— |—–|——|——-|——-|
| Sukulu Yasekondale | 20 | 30 | 50 | 100 |
| Ophunzira Omaliza Maphunziro | 35 | 25 | 40 | 100 |
| Chiwerengero | 55 | 55 | 90 | 200 |
Funso: Kodi pali ubale pakati pa mtundu wa nyimbo zomwe mumakonda ndi kuchuluka kwa maphunziro?
Njira Zokambirana:
1. Dziwani Lingaliro Loyerekeza:
– H0: Palibe ubale pakati pa zomwe amakonda mtundu wa nyimbo ndi kuchuluka kwa maphunziro.
– H1: Pali ubale pakati pa zomwe amakonda pa mtundu wa nyimbo ndi maphunziro ake.
2. Werengani Mafupipafupi Oyembekezeredwa (E):
Werengerani kuchuluka kwa ma frequency omwe akuyembekezeka pa selo lililonse la tebulo la contingency. Fomula yowerengera E ndi iyi:
\[
E_{ij} = \frac{(\text{Total Row}_i \times \text{Total Column}_j)}{\text{Grand Total}}
\]
Mwachitsanzo, kuchuluka komwe ophunzira aku sekondale omwe amakonda Pop amayembekezera ndi:
\[
E_{SMA, Pop} = \frac{(100 \times 55)}{200} = 27.5
\]
Mofananamo, timawerengera maselo onse:
| Pop | Rock | Jazz |
|—————— |—–|——|——-|
| Sukulu Yasekondale | 27.5 | 27.5 | 45 |
| Bachelor | 27.5 | 27.5 | 45 |
3. Werengani Chi-Square (χ²):
Kugwiritsa ntchito fomula iyi:
\[
\chi² = \sum \frac{(O - E)²}{E}
\]
Werengerani gawo la selo lililonse ndi chiwerengero chonse:
- Kwa Sukulu Yasekondale ndi Pop:
\[
\chi²_{SMA, Pop} = \frac{(20 – 27.5)²}{27.5} \pafupifupi 2.04
\]
- Kuwerengera kofanana kumachitika pa kuphatikiza kulikonse:
\[
\chi² = 2.04 + 0.23 + 0.56 + 0.23 + 0.23 + 0 + 1.96 = 5.25
\]
4. Werengani Madigiri a Ufulu:
\[
df = (3-1) \nthawi (3-1) = 4
\]
5. Dziwani Makhalidwe ndi Zisankho Zofunika Kwambiri:
Pogwiritsa ntchito tebulo logawa la Chi-Square lomwe lili ndi \(\alpha = 0.05\) ndi df = 4, mtengo wofunikira ndi 9.488. Popeza 5.25 < 9.488, talephera kukana H0. Kutsiliza: Palibe ubale wofunikira pakati pa kukonda mtundu wa nyimbo ndi maphunziro pamlingo wofunikira wa 0.05. Kutsiliza Kuyesa kwa Chi-Square ndi chida chothandiza kwambiri pakusanthula deta m'magawo osiyanasiyana ofufuza. Pomvetsetsa momwe mungawerengere ndikuwunikira zotsatira za mayeso a Chi-Square, ofufuza amatha kupanga malingaliro abwino okhudza deta yawo. Kafukufuku wamilandu womwe wafotokozedwawu umapereka chithunzi chothandiza cha momwe mayeso a Chi-Square amagwirira ntchito komanso momwe angatanthauzire zotsatira. Kuphatikiza pa kusanthula kwamanja, kugwiritsa ntchito mapulogalamu owerengera monga SPSS kapena R ndikofala kwambiri m'machitidwe kuti athandize kuwerengera ndi kusanthula kwina. Mu ntchito zenizeni, kuwonjezera pa kuyang'ana zotsatira za ziwerengero, ndikofunikira kuganizira za momwe kafukufukuyu akukhudzira ndikutanthauzira ziwerengero mwanzeru.
