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Summary - Statistics III (PSBE2-12)
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  • Course
  • Statistics III (PSBE212)
  • Institution
  • Rijksuniversiteit Groningen (RuG)

This document contains an overview of all the ANOVA tables and what their boxes mean, as well as all the assumption checks for regression, regular ANOVA assumptions, and RM-ANOVA assumptions.

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Document information

  • July 26, 2024
  • 4
  • 2022/2023
  • Summary

Subjects

  • assumption check
  • anova tables

Written for

  • Rijksuniversiteit Groningen (RuG)
  • Psychologie
  • Statistics III (PSBE212)
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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

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