H_0:μ_(1∙)=μ_(2∙)=⋯=μ_(a∙) F=MSA/MSE F_(ν_1,ν_2 ) ν_1=a-1 ,
ν_2=ab(n-1)
H_0:μ_(∙1)=μ_(∙2)=⋯=μ_(∙b) F=MSB/MSE F_(ν_1,ν_2 ) ν_1=b-1 ,
ν_2=ab(n-1)
H_0: there is not interactions between factors F=(MS(AB))/MSE F_(ν_1,ν_2 ) ν_1=(a-1)(b-1),
ν_2=N-ab
Contrast
H_0:c_1 μ_1+c_2 μ_2+⋯c_k μ_k=0 ∑▒c=0 t=(∑_(i=1)^k▒〖c_i x ̅_i 〗)/(s_p √(∑_(i=1)^k▒(c_i^2)/n_i )) Student t(υ) ν=n_1+⋯+n_k-k
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Complete the following Two-Way ANOVA Table for x_ijk=μ_ij+ε_ijk=α_i+β_j+(αβ)_ij+ε_ijk where x ̂_ij=x ̅_(i.)+x ̅_(.j)-x ̅_(..); clearly label T, A, B, AB and E and include the amount of information present at each node: x_ijk, x_(ij∙), x ̂_(ij∙), x_(i∙∙),x_(∙j∙), and x_(∙∙∙).
Real depth Dr= Apparent depth/ refractive index of water Dr= Da / n water
The word depth has one syllable.
Depth is not a dimension of a cylinder. Also, depth is measured in feet, not sq feet.
Average depth. Depth of the deep end @ 8'. Depth of the shallow end 3'. Add the two together and divide by 2 = average. Ken