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MathML

\begin{aligned} p o w e r & = {\begin{cases} P [(N - 2 - p^{⋆})^{\frac{1}{2}} \frac{R_{Y X_{1} | X_{- 1}}}{{(1 - R_{Y X_{1} | X_{- 1}}^{2})}^{\frac{1}{2}}} \geq t_{1 - α} (N - 2 - p^{⋆})], & upper one-sided \\ P [(N - 2 - p^{⋆})^{\frac{1}{2}} \frac{R_{Y X_{1} | X_{- 1}}}{{(1 - R_{Y X_{1} | X_{- 1}}^{2})}^{\frac{1}{2}}} \leq t_{α} (N - 2 - p^{⋆})], & lower one-sided \end{cases} \\ = {\begin{cases} P [R_{Y | (X_{1}, X_{- 1})} \geq \frac{t_{1 - α} (N - 2 - p^{⋆})}{{(t_{1 - α}^{2} (N - 2 - p^{⋆}) + N - 2 - p^{⋆})}^{\frac{1}{2}}}], & upper one-sided \\ P [R_{Y | (X_{1}, X_{- 1})} \leq \frac{t_{α} (N - 2 - p^{⋆})}{{(t_{α}^{2} (N - 2 - p^{⋆}) + N - 2 - p^{⋆})}^{\frac{1}{2}}}], & lower one-sided \end{cases} \end{aligned}

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Math as LaTeX Source

\begin{align*} \mr{power} & = \left\{ \begin{array}{ll} P\left[ (N-2-p^\star )^\frac {1}{2} \frac{R_{Y X_1|X_{-1}}}{\left(1 - R^2_{Y X_1|X_{-1}}\right)^\frac {1}{2}} \ge t_{1-\alpha }(N-2-p^\star )\right], & \mbox{upper one-sided} \\ P\left[ (N-2-p^\star )^\frac {1}{2} \frac{R_{Y X_1|X_{-1}}}{\left(1 - R^2_{Y X_1|X_{-1}}\right)^\frac {1}{2}} \le t_{\alpha }(N-2-p^\star )\right], & \mbox{lower one-sided} \\ \end{array} \right. \\ & = \left\{ \begin{array}{ll} P\left[ R_{Y|(X_1,X_{-1})} \ge \frac{t_{1-\alpha }(N-2-p^\star )}{\left(t^2_{1-\alpha }(N-2-p^\star ) + N-2-p^\star \right)^\frac {1}{2}} \right], & \mbox{upper one-sided} \\ P\left[ R_{Y|(X_1,X_{-1})} \le \frac{t_{\alpha }(N-2-p^\star )}{\left(t^2_{\alpha }(N-2-p^\star ) + N-2-p^\star \right)^\frac {1}{2}} \right], & \mbox{lower one-sided} \\ \end{array} \right. \\ \end{align*}