anova model
DESCRIPTION
ANOVA model. Comparison between groups. Basic model. One-way ANOVA Y in =μ j+ e in =μ+α j +e in , set μ j =μ+α j μ is the total mean, α j is the grouping effect, e in is the residuals of model Two-way ANOVA Y ijn =μ+α i +β j +(αβ) ij +e ijn - PowerPoint PPT PresentationTRANSCRIPT
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ANOVA model
Comparison between groups
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Basic model One-way ANOVA
Yin=μj+ein=μ+αj+ein, set μj=μ+αj μ is the total mean, αj is the grouping effe
ct, ein is the residuals of model Two-way ANOVA
Yijn=μ+αi+βj+(αβ)ij+eijn βj is the second grouping effect, (αβ)ij is t
he 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: μ1=μ2… =μj, for all j, (H0: α1=α2… =αj=0, for all j) H1: at least one μ unequal to others (H1: at least one α
≠0) The pair-wise comparison
H0: μi=μi’, for any group i and i≠i’ The sequential cell mean comparison (for two- or more
factor-way ANOVA) H0: μij=μi’j’, 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 DFM=j-1 (j=the number of groups; the types
of experiments, etc.) Two-way DFM= ab-1 DFA=a-1 (a=the number of A type groups) DFB=b-1 (b=the 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
DFT=n-1 (n=the 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