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186 Ho et al.Fig. 7. The power curves of ECF x|y, ENT, |ρ 1− ρ 2|, and ECF y|x.vertically aligned, that is when θ is around π/4. To investigate further the reasonfor this behavior, note that the rotated data points (x′, y′) of genes 1 and 2 can beexpressed in term of the original points (x, y) as:x′ = cosθx−sin θy,y′ = sin θ x+cos θy.The resulting variance and correlation of the data in phenotypic class 2 afterrotation can be written as:2σ = 1−2cos θsinθρ(12)x2ρ2=2σ = 1+ 2cos θsinθρy22 2(cos θ − sin θ ) ρ( 1− 2cos θsin θρ) ( 1+2cos θsin θρ)(13)(14)The ECF-statistics is shown in Eq. 7. In the simulation, set µ x1= µ x2= µ y1=µ y2= 0, and σ = σ = 1,x1x2 and therefore the ECF-statistic can be expressed as afunction of θ and ρ alone. The value of ECF y|xwhen the class 1 data is fixed and