Alternative Equation Formats

\begin{aligned} V_{L P} & = G_{1}^{2} S_{P}^{4} + H_{3}^{2} S_{P O}^{4} + G_{13} S_{P}^{2} S_{P O}^{2} \\ V_{U P} & = H_{1}^{2} S_{P}^{4} + G_{3}^{2} S_{P O}^{4} + H_{13} S_{P}^{2} S_{P O}^{2} \\ V_{L M} & = G_{2}^{2} S_{O}^{4} + G_{3}^{2} (p - 1)^{2} S_{P O}^{4} + G_{4}^{2} p^{2} (r - 1)^{2} S_{E}^{4} \\ V_{U M} & = H_{2}^{2} S_{O}^{4} + H_{3}^{2} (p - 1)^{2} S_{P O}^{4} + H_{4}^{2} p^{2} (r - 1)^{2} S_{E}^{4} \\ V_{L T} & = G_{1}^{2} p^{2} S_{P}^{4} + G_{2}^{2} o^{2} S_{O}^{4} + G_{3}^{2} (p o - p - o)^{2} S_{P O}^{4} + G_{4}^{2} (p o)^{2} (r - 1)^{2} S_{E}^{4} \\ V_{U T} & = H_{1}^{2} p^{2} S_{P}^{4} + H_{2}^{2} o^{2} S_{O}^{4} + H_{3}^{2} (p o - p - o)^{2} S_{P O}^{4} + H_{4}^{2} (p o)^{2} (r - 1)^{2} S_{E}^{4} \\ L_{R} & = \frac{p (1 - G_{1}) (S_{P}^{2} - F_{1} S_{P O}^{2})}{p o (r - 1) S_{E}^{2} + o (1 - G_{1}) F_{3} S_{O}^{2} + o (p - 1) S_{P O}^{2}} \\ U_{R} & = \frac{p (1 + H_{1}) (S_{P}^{2} - F_{2} S_{P O}^{2})}{p o (r - 1) S_{E}^{2} + o (1 + H_{1}) F_{4} S_{O}^{2} + o (p - 1) S_{P O}^{2}} \\ G_{1} & = 1 - F_{α / 2 : \infty, p - 1} \\ G_{2} & = 1 - F_{α / 2 : \infty, o - 1} \\ G_{3} & = 1 - F_{α / 2 : \infty, (p - 1) (o - 1)} \\ G_{4} & = 1 - F_{α / 2 : \infty, p o (r - 1)} \\ H_{1} & = F_{1 - α / 2 : \infty, p - 1} - 1 \\ H_{2} & = F_{1 - α / 2 : \infty, o - 1} - 1 \\ H_{3} & = F_{1 - α / 2 : \infty, (p - 1) (o - 1)} - 1 \\ H_{4} & = F_{1 - α / 2 : \infty, p o (r - 1)} - 1 \\ F_{1} & = F_{1 - α / 2 : p - 1, (p - 1) (o - 1)} \\ F_{2} & = F_{α / 2 : p - 1, (p - 1) (o - 1)} \\ F_{3} & = F_{1 - α / 2 : p - 1, o - 1} \\ F_{4} & = F_{α / 2 : p - 1, o - 1} \\ G_{13} & = \frac{(F_{1} - 1)^{2} - G_{1}^{2} F_{1}^{2} - H_{3}^{2}}{F_{1}} \\ H_{13} & = \frac{(1 - F_{2})^{2} - H_{1}^{2} F_{2}^{2} - G_{3}^{2}}{F_{2}} \\ K & = s_{P}^{2} + s_{O}^{2} - s_{P O}^{2} \\ C & = \frac{s_{P}^{2} \sqrt{F_{1 - α : 1, p - 1}} + s_{O}^{2} \sqrt{F_{1 - α : 1, o - 1}} - s_{P O}^{2} \sqrt{F_{1 - α : 1, (p - 1) (o - 1)}}}{K} \end{aligned}

\begin{align*} V_{LP} & = G^2_1 S^4_ P + H^2_3 S^4_{PO} + G_{13} S^2_ P S^2_{PO} \\ V_{UP} & = H^2_1 S^4_ P + G^2_3 S^4_{PO} + H_{13} S^2_ P S^2_{PO} \\ V_{LM} & = G^2_2 S^4_ O + G^2_3(p-1)^2 S^4_{PO} + G^2_4 p^2 (r-1)^2 S^4_ E \\ V_{UM} & = H^2_2 S^4_ O + H^2_3(p-1)^2 S^4_{PO} + H^2_4 p^2 (r-1)^2 S^4_ E \\ V_{LT} & = G^2_1 p^2 S^4_ P + G^2_2 o^2 S^4_ O + G^2_3(po-p-o)^2 S^4_{PO} + G^2_4(po)^2 (r-1)^2 S^4_ E \\ V_{UT} & = H^2_1 p^2 S^4_ P + H^2_2 o^2 S^4_ O + H^2_3(po-p-o)^2 S^4_{PO} + H^2_4(po)^2 (r-1)^2 S^4_ E \\ L_ R & = \frac{p(1-G_1)(S^2_ P - F_1 S^2_{PO})}{ po(r-1)S^2_ E + o(1-G_1)F_3 S^2_ O + o(p-1)S^2_{PO}} \\ U_ R & = \frac{p(1+H_1)(S^2_ P - F_2 S^2_{PO})}{ po(r-1)S^2_ E + o(1+H_1)F_4 S^2_ O + o(p-1)S^2_{PO}} \\ G_1 & = 1 - F_{\alpha /2:\infty ,p-1} \\ G_2 & = 1 - F_{\alpha /2:\infty ,o-1} \\ G_3 & = 1 - F_{\alpha /2:\infty ,(p-1)(o-1)} \\ G_4 & = 1 - F_{\alpha /2:\infty ,po(r-1)} \\ H_1 & = F_{1-\alpha /2:\infty ,p-1} - 1 \\ H_2 & = F_{1-\alpha /2:\infty ,o-1} - 1 \\ H_3 & = F_{1-\alpha /2:\infty ,(p-1)(o-1)} - 1 \\ H_4 & = F_{1-\alpha /2:\infty ,po(r-1)} - 1 \\ F_1 & = F_{1-\alpha /2:p-1,(p-1)(o-1)} \\ F_2 & = F_{\alpha /2:p-1,(p-1)(o-1)} \\ F_3 & = F_{1-\alpha /2:p-1,o-1} \\ F_4 & = F_{\alpha /2:p-1,o-1} \\ G_{13} & = \frac{(F_1 - 1)^2 - G^2_1 F^2_1 - H^2_3}{F_1} \\ H_{13} & = \frac{(1 - F_2)^2 - H^2_1 F^2_2 - G^2_3}{F_2} \\ K & = s^2_ P + s^2_ O - s^2_{PO} \\ C & = \frac{s^2_ P\sqrt{F_{1-\alpha :1,p-1}} + s^2_ O\sqrt{F_{1-\alpha :1,o-1}} - s^2_{PO}\sqrt{F_{1-\alpha :1,(p-1)(o-1)}}}{K} \end{align*}

Alternative Equation Formats

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