Reading significance straight off a confidence interval

Question

A report gives you two confidence intervals for a strategy's mean daily edge (in basis points) but no p-value. The 95% confidence interval is $[0.2,\ 4.8]$ . The 99% confidence interval is $[-0.8,\ 5.8]$ .

Using only these intervals, decide whether the edge is significant at the 5% level and at the 1% level, and state the rule that lets you do this.

Accepted Answer

The duality rule. A two-sided test of "the true value equals v" rejects at level \alpha exactly when the (1-\alpha) confidence interval excludes v. For testing a zero edge, the null value is 0: the edge is significant at level \alpha if and only if the matching (1-\alpha) interval does not contain 0. Apply it. - The 95% interval [0.2,\ 4.8] excludes 0, so the edge is significant at the 5% level. - The 99% interval [-0.8,\ 5.8] contains 0, so the edge is not significant at the 1% level. Putting the two together, the two-sided p-value lies between 0.01 and 0.05. Why it works. A confidence inter…

Reading significance straight off a confidence interval

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