Directional replicability: When can the factor of two be omitted

Directional replicability addresses the question of whether an effect studied across n independent studies is present with the same direction in at least r of them, for r≥2. When the expected direction of the effect is not specified in advance, the state of the art recommends assessing replicability separately by combining one-sided p-values for both directions (left and right), and then doubling the smaller of the two resulting combined p-values to account for multiple testing. In this work, we show that this multiplicative correction is not always necessary, and give a sufficient and necessary condition under which it can be safely omitted.