6. 單迴歸
Source SS df MS F
MS Yˆ
Model (reg) SS Yˆ r SS Y
2
XY
1 SSY / 1 ~ F(1,n 2, 0.05)
MSE
SSe
Error SS e (1 rXY ) SS Y
2
n-2 S e2
n2
Total SSY n-1 MSE
7. 2
rXY SS Y
F
(1 rXY ) SS Y / n 2
2
rXY
t ~ t( n 2 )
(1 r )2
XY
n2
8. 複迴歸
Source SS df MS F
Model (reg) R 2 SS Y P MSR
~ F( p ,n p 1,0.05)
MSE
Error (1 R 2 ) SS Y N-P-1
Total SSY N-1 MSE=SSe
13. Parametric Statistics(母數統計法)
Dependent samples → paired t test D D
H0: μD=0 t ~ t ( n 1)
Two SD / n
N: pair數
samples Independent samples
( x1 x 2 ) ( 1 2 )
σ₁²σ₂² known → Z test Z ~Z
2
2
1
2
n1 n2
σ₁²=σ₂² unknown → tn1+n2‐2
( x1 x 2 ) ( 1 2 )
t ~ t ( n1 n 2 2)
2 1 1
SP ( )
n1 n2
σ₁²≠σ₂² unknown ~ t’(df’)
( x1 x 2 ) ( 1 2 )
t' ~ t ' ( df ')
2 2
S S
1 2
n1 n 2
14. Nonparametric Statistics(無母數統計法)
Dependent samples → Wilcoxon Sum of diff test
Signed Ranks test
Two samples Sign test
Independent samples → Wilcoxon Rank Sum test
Mann‐Whitney U test
Median test
15. More than two samples:
Parametric Statistics(母數統計法)
Dependent samples → repeated measures(重複量數)
Independent samples → Analysis of Variance(ANOVA,
變異數分析)
Nonparametric Statistics(無母數統計法)
Dependent samples → Friedman Rank test
Independent samples → Kruskal‐Wallis H test
29. Two types of error rate
(a) Error rate per comparison (αPC): the
probability of making a type Ι errors for
any of possible comparisons 每一個單一
比較的機率
PC = α’ C: number of comparisons
(b) Family error rate (αFW): the probability of
making one or more type Ι errors for
the full set of possible comparisons 至少
犯一個type Ι error的機率
FW 1 - (1 - ) c
30.
31.
32. Magnitude of experimental effect
• To describe the degree of association
between IV and DV
• (1) eta-square η2
SS B
2
SS T
• 優點:易理解計算
• 缺點:數值偏高,高估了IV和DV的關係程度
33. • (2) omega-square ω2
Y Y|X
2 2
2
Y2
SS B ( j 1) MSW
ˆ2
SS T MSW
• 優點:考慮自由度,不會高估IV和DV的相關程
度
38. • 優點
– Make no priori assumption about the shape of
the dist. i.e. weaker or no distributional
assumption
– No parameters assumed or estimated
– More sensitive to medium than mean
– Less affected by outliers ( usually we ranks)
– Simple calculation
– Small samples
39. • 缺點
– Information loss (magnitude, sign, rank)
– parametric statistic is more versatile
– Less powerful if assumption of parametric
tests are met