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Samenvatting Statistiek hoorcollege 12
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Statistiek HC12Chi-kwadraat toetsen
Chi-kwadraat test voor toetsen ‘Goodness-of-fit’
Hypothesen over verdeling van 1 nominale variabele
- Welk sociaal netwerk is het populairst?
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Voorbeeld 1 – χ2 toetsen
Hypothesen
H0 : de steekproef is representatief voor de populatie α = 0,01
H1 : de steekproef is niet representatief voor de populatie
Principe χ2 toets -> vergelijk de geobserveerde frequenties met de verwachte
frequenties onder H0 -> hoe groter de verschillen, hoe meer bewijs tegen H0
Stap 1
H0 : verhouding
VMBO MBO HBO WO
35% 40% 15% 10%
Stap 2
H1 : verhouding
VMBO MBO HBO WO Totaal
Observed 15 18 8 9 50
Expected 17,5 20 7,5 5 50
Obs – exp -2,5 -2 0,5 4 0
Stap 3
χ2 = sigma cel = (Ocel – Ecel)2 = (15 – 17,5)2 + (18 – 20)2 + (8 – 7,5)2 + (9 – 5)2 = 3,79
Ecel 17,5 20 7,5 5
Stap 4
χ2 kan niet kleiner zijn dan 0 -> kwadraat
χ2 is dus altijd positief
Grafiek -> scheef naar links
α ligt altijd maar aan 1 kan -> rechts
df = aantal cellen – 1 = 4 – 1 = 3
Tabel C.4
Upper percentage -> alleen rechts -> gelijk aan α -> 0,01 of 1%
Aantal vrijheidsgraden -> 3
χ2 cv = 11,345
Stap 5
We zouden H0 verwerpen als χ2 obs groter is dan 11,345
We kunnen H0 dus niet verwerpen
Er is onvoldoende bewijs om H0 te verwerpen
De steekproef is dus representatief voor de populatie
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