Summary - Statistics III (PSBE2-12)

2-ANOVA CI:
CI Df Where to use
𝑠𝑝 Df= n – g (one-way) The confidence interval of the population
𝑦𝑏𝑎𝑟𝑖 ± 𝑡 ∗
√𝑛𝑖 Df= n – (I x J) (two- mean.
way)
𝑠𝑖 Df= ni- 1 The confidence interval for an individual in
𝑦𝑏𝑎𝑟𝑖 ± 𝑡 ∗ group i.
√𝑛𝑖

1-ANOVA table regression:
SS Df MS F
Model Sum(yhati – ybar)2 p (= g – 1) SSM/Dfm MSM/MSE
Error Sum(yi – yhati)2 n–p–1 SSE/Dfe = s2 df1= dfm
Total Sum(yi – ybar)2 n–1 TSS/Dft= sy2 df2= dfe

1-ANOVA table groups:
SS Df MS F
Group Sum(ybari – ybar)2 g–1 SSGr/DfGr MSGr/MSE
Error Sum(yij – ybari)2 n–g SSE/DfE df1= dfgr
Total Sum(yij – ybar)2 n–1 TSS/DfT df2= dfe

2-ANOVA table:
SS Df MS F
Factor A SSA i–1 SSA/DfA MSA/MSE
Factor B SSB j–1 SSB/DfB MSB/MSE
Interaction SSAB (i – 1 )(j – 1) SSAB/DfAB MSAB/MSE
Error SSE n – (i x j) SSE/DfE = sp2 df1= dfa, dfb, dfab
Total TSS n-1 TSS/DfT = sy2 df2= dfe
Error = residual = within

Repeated measures ANOVA – Test of Within Subjects Effects
SS Df MS F
Factor A SSbetween J–1 MSA MSA/MSE
Residuals SSE (J – 1)(N – 1) MSE df1= dfa
df2= dfe
J= number of levels in Factor A
n= number of subjects
SSwithin subjects = SSbetween + SSE