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statistiek 2 samenvatting statistische testen

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samenvatting van de statistische testen, alles wat je theoretisch per test moet weten om de oefeningen te kunnen maken

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  • July 6, 2024
  • 9
  • 2023/2024
  • Summary
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1


Ongepaarde t-test
- Continue variabele die normaal verdeeld is in elke groep
- Gelijke varianties
 test van levene (resultaat krijg je door t-test te runnen)

altijd α= 0.05

H 0 : μ1=μ2 2 2
H 0 : σ 1=σ 2
H 1 : eenzijdig μ1 > μ2 of μ1 < μ2
tweezijdig μ1 ≠ μ2 H 1 : σ 21 ≠ σ 22


Teststatistiek





x 1−x 2 pooled standaarddeviatie S
t= t n +n −2 ( n1 −1 ) S21 +(n2−1) S 22

√ 1 1 1 2 S=
S + n1 +n2−2
n1 n 2


100(1-α)% betrouwbaarheidsinterval


[
tweezijdig ( x 1−x 2 )−t
n1+ n2−2 , 1−
α
2
∗S
√ 1 1
+ , ( x −x ) +t
n1 n2 1 2 n +n −2 ,1− α2
∗S
1
1 1
+
n1 n2
2 √ ]
linkszijdig ¿−∞ , ( x 1−x 2 )−t n +n −2 ,1−α ∗S
1 2
√ 1 1
+ ¿¿
n1 n2

rechtszijdig ¿
Descriptieve statistiek + grafische voorstelling
gemiddelde x
standaarddeviatie s

boxplot

, 2


Mann-Whitney U-test
- Continue variabele die niet normaal verdeeld is of bij ordinale variabele


H 0 :beide groepen hebben dezelfde distributie
H 1 : beide groepen hebben verschillende distributie

Teststatistiek
U−μ U U =min ( U 1 ,U 2 ) Rangsom W
z= N (0,1) Correctie voor ties t (= aantal
σU n1 (n 1+1) gelijke waarden)
U 1=n1 n 2+ −W 1 Totale steekproefgrootte
2 N=n1+ n2
n2 (n 2+1)
U 2=n1 n 2+ −W 2
2

n1 n2
μU =
2

σ U = √ n1 n2 ¿ ¿ ¿




Procedure

 Rangschik elke observatie (groepen samen gerangschikt maar apart genoteerd) van klein naar groot
 Ken een rangwaarde toe (rangen voor de 2 groepen samen maar apart genoteerd)
o Indien ties: een gemiddelde rang toekennen
o Indien ties: bereken t 3−t
 Bereken rangsom per groep: W 1 en W 2

Descriptieve statistiek + grafische voorstelling
Mediaan
interkwartielinterval

boxplot

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