A z of 1.4 that clears neither bar

Question

A pairs-trading signal is tested with a pre-registered upper-tail alternative (edge $> 0$ ). The result is $z = 1.4$ .

Compute the one-sided p-value for $z = 1.4$ , and state whether the signal is significant at the 5% level even under this more generous one-sided test.

Accepted Answer

The one-sided computation. For the upper-tail alternative, take the area beyond z in the predicted tail: p{	ext{one}} = 1 - \Phi(1.4) = 1 - 0.9192 = 0.0808 \approx 0.081. The verdict. Even the one-sided test, which is the friendlier of the two because it does not split the alpha across both tails, gives p \approx 0.081 0.05. So the signal is not significant at the 5% level. (The two-sided p would be 0.162, even further from significance.) Why this is a useful check. When a result fails even the one-sided test, there is no honest way to rescue it by switching test types. Only when a two-sided…

A z of 1.4 that clears neither bar

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