Alternative Equation Formats

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MathML

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

Math Rendered as SVG

Math as LaTeX Source

\[ \mr{power} = \left\{ \begin{array}{ll} P\left[ R^2_{Y X_1|X_{-1}} \ge \frac{F_{1-\alpha }(p_1, N-p)}{F_{1-\alpha }(p_1, N-p) + \frac{N-p}{p_1}} \, \vert \, \rho _{Y X_1|X_{-1}} \right] & \mbox{two-sided} \\ P\left[ R_{Y X_1|X_{-1}} \ge \frac{t_{1-\alpha }(N-p-1)}{\left(t^2_{1-\alpha }(N-p-1) + N-p-1\right)^\frac {1}{2}} \, \vert \, \rho _{Y X_1|X_{-1}} \right] & \mbox{upper one-sided} \\ P\left[ R_{Y X_1|X_{-1}} \le \frac{t_{\alpha }(N-p-1)}{\left(t^2_{\alpha }(N-p-1) + N-p-1\right)^\frac {1}{2}} \, \vert \, \rho _{Y X_1|X_{-1}} \right] & \mbox{lower one-sided} \\ \end{array} \right. \]