H_0:μ_(1∙)=μ_(2∙)=⋯=μ_(a∙) F=MSA/MSE F_(ν_1,ν_2 ) ν_1=a-1 ,
ν_2=(a-1)(b-1)
H_0:μ_(∙1)=μ_(∙2)=⋯=μ_(∙b) F=MSB/MSE F_(ν_1,ν_2 ) ν_1=b-1 ,
ν_2=(a-1)(b-1)
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H_0:μ_1=μ_2=⋯=μ_k F=MSA/MSE F_(ν_1,ν_2 ) ν_1=a-1 , ν_2=N-a
Null hypothesis of a one-way ANOVA is that the means are equal. Alternate hypothesis a one-way ANOVA is that at least one of the means are different.
same as one way anova population variance equal among groups noramlly distributed independent samples
In a two-way ANOVA on the surface, the relate in an equation the total variation, , where i=1,2,…,a and j=1,2,…,b; the explained variation by the "treatment" or first factor is , the explained variation by the "block" or second factor is and the unexplained variation . SST= SSA+SSB +SSE Degrees of freedom N-1 a-1 b-1 (a-1)(b-1) N=ab
ANOVA is an inferential statistic used to test if 3 or more population means are equal or to test the affects of interactions.