Animated Distributions
2
8/18/2019 Animated Distributions http://slidepdf.com/reader/full/animated-distributions 1/2 General form for the F distribution with ν 1 and ν 2 degrees of freedom: f (F ; ν 1 , ν 2 ) = Γ ν 1 +ν 2 2 Γ ν 1 2 Γ ν 2 2 ν 1 ν 2 ν 1 2 F ν 1 −2 2 1 + ν 1 ν 2 F ν 1 +ν 2 2 Critical region for an F test for various degrees of freedom: F 5.3426 0 df 1 = 4 df 2 = 3 α = 0 . 10
Transcript of Animated Distributions
8/18/2019 Animated Distributions
http://slidepdf.com/reader/full/animated-distributions 1/2
General form for the F distribution with ν 1 and ν 2 degrees of freedom:
f (F ; ν 1, ν 2) = Γν 1+ν 2
2
Γ
ν 1
2
Γ
ν 2
2
ν 1
ν 2
ν12
F
ν1−2
21 +
ν 1
ν 2
F
ν1+ν22
Critical region for an F test for various degrees of freedom:
F 5.34260
df 1 = 4df 2 = 3
α = 0.10
8/18/2019 Animated Distributions
http://slidepdf.com/reader/full/animated-distributions 2/2
Statistical power in hypothesis testing:
−2 −1 0 1 2 30.658
Reject H
0
Fail to
reject H
0
H 0 is true:
α = 0.05(Type I error rate)
Effect size: 0.5
−2 −1 0 1 2 30.658
Reject H 0
Fail toreject H 0
H a is true:
Power = .346
β = .654
(Type II error rate)
