ANOVA model

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ANOVA model

• Comparison between groups

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Basic model

• One-way ANOVA
• Yinµjeinµajein, set µjµaj
• µ is the total mean, aj is the grouping effect,
  ein is the residuals of model
• Two-way ANOVA
• Yijnµaißj(aß)ijeijn
• ßj is the second grouping effect, (aß)ij is the
  interaction between the first and second factor

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ANOVA modeling

• Ref, ANOVA modeling.doc

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Assumptions of ANOVA modeling

• Normality
• Independence
• Equality of variance

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Process of one-way ANOVA hypothesis testing
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Process of two-way ANOVA hypothesis testing
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Types of comparison

• Validity testing of total model
• H0 µ1µ2 µj, for all j, (H0 a1a2 aj0, for
  all j)
• H1 at least one µ unequal to others (H1 at
  least one a?0)
• The pair-wise comparison
• H0 µiµi, for any group i and i?i
• The sequential cell mean comparison (for two- or
  more factor-way ANOVA)
• H0 µijµij, for any cell ij and (i?i or j?j)
  
• The contrast comparison
• The testing for some particular comparisons

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One-way ANOVA table (for total testing)
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Two-way ANOVA table (for total testing)
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Degree of freedom

• DFMj-1 (jthe number of groups the types of
  experiments, etc.)
• Two-way DFM ab-1
• DFAa-1 (athe number of A type groups)
• DFBb-1 (bthe number of B type groups)
• DFAB(a-1)(b-1)
• DFE(n-1)-(j-1)n-j
• Two-way DFE(n-1)-(ab-1)n-ab
• DFTn-1 (nthe total sample size)

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Interaction between groups

• Plot the cell mean value along the two dimensions
  and watch out for the intersection