Power to detect a winning strategy

Question

You test whether a strategy's win rate exceeds $50\%$ : $H_0: p = 0.5$ against $H_1: p > 0.5$ , using $n = 100$ trades at one-sided $\alpha = 0.05$ . The strategy's true win rate is $p = 0.6$ .

What is the power, the probability the test confirms the edge?

Accepted Answer

Rejection threshold. Under H0, \hat p is approximately normal with mean 0.5 and standard deviation \sqrt{0.5 \cdot 0.5 / 100} = 0.05. A one-sided test at \alpha = 0.05 rejects when \hat p 0.5 + 1.645 	imes 0.05 = 0.5822. Distribution under the alternative. When p = 0.6, \hat p is approximately normal with mean 0.6 and standard deviation \sqrt{0.6 \cdot 0.4 / 100} = 0.049. Power. The probability of clearing the threshold when the edge is real: 	ext{Power} = P(\hat p 0.5822 \mid p = 0.6) = P\!\left(Z \frac{0.5822 - 0.6}{0.049}ight) = P(Z -0.363) = \Phi(0.363) \approx 0.64. So even with a ge…

Power to detect a winning strategy

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