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\begin{aligned} p -value & = 2 P (F^{'} > F_{1 - α, {d f}_{a}, {d f}_{b}}) \\ = {\begin{cases} P (s_{1}^{2} / s_{2}^{2} > F_{1 - α, {d f}_{1}, {d f}_{2}}) + P (s_{2}^{2} / s_{1}^{2} \leq F_{1 - α, {d f}_{2}, {d f}_{1}}), & s_{1}^{2} / s_{2}^{2} \geq 1 \\ P (s_{1}^{2} / s_{2}^{2} \leq F_{1 - α, {d f}_{1}, {d f}_{2}}) + P (s_{2}^{2} / s_{1}^{2} > F_{1 - α, {d f}_{2}, {d f}_{1}}), & s_{1}^{2} / s_{2}^{2} < 1 \end{cases} \end{aligned}

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\begin{align*} p\mbox{-value} & = 2 P\left(F^{\prime } > F_{1-\alpha , \mr{df}_ a, \mr{df}_ b}\right) \\ & = \left\{ \begin{array}{ll} P\left(s_1^2/s_2^2 > F_{1-\alpha , \mr{df}_1, \mr{df}_2}\right) + P\left(s_2^2/s_1^2 \le F_{1-\alpha , \mr{df}_2, \mr{df}_1}\right) \; \; , & s_1^2/s_2^2 \ge 1 \\ P\left(s_1^2/s_2^2 \le F_{1-\alpha , \mr{df}_1, \mr{df}_2}\right) + P\left(s_2^2/s_1^2 > F_{1-\alpha , \mr{df}_2, \mr{df}_1}\right) \; \; , & s_1^2/s_2^2 < 1 \\ \end{array} \right. \end{align*}