Correction for Gasparin et al., Combining exchangeable P-values

Correction for “Combining exchangeable P-values,” by Matteo Gasparin, Ruodu Wang, and Aaditya Ramdas, which published March 14, 2025; 10.1073/pnas.2410849122 (Proc. Natl. Acad. Sci. U.S.A. 122, e2410849122).

The authors note that, due to a production error, on page 9, right column, last paragraph, for “Proposition 7.2,” the below equation was incorrectly published. The authors explain that the term “(p” was erroneously deleted during the editing process. The online version has been corrected as follows:

$$F_{\mathrm{H}}^{\prime }(\mathbf{p}):=(T_K+1)H(\mathbf{p})$$

Additionally, on page 10, left column, first paragraph, in the “7.1. Exchangeable Harmonic Mean Combination Rule” section, the below equation was incorrectly published. The authors explain that an extra “u” was mistakenly added to the equation. The online version has been corrected as follows:

$$\begin{array}{cc}\hfill F_{\text{EH}}(\mathbf{p})& =inf\left\{\alpha \in (0,1):{\displaystyle \underset{\ell \le K}{\bigvee }}\frac{1}{\ell }{\displaystyle \sum _{i=1}^{\ell }}{\left(\frac{\alpha }{T_K{p}_i}-\frac{1}{T_K}\right)}_{+}\ge 1\right\};\hfill \\ \hfill F_{\text{EH}}^{\prime }(\mathbf{p})& =inf\left\{\alpha \in (0,1):{\displaystyle \underset{\ell \le K}{\bigvee }}\frac{1}{\ell }{\displaystyle \sum _{i=1}^{\ell }}\left(\frac{\alpha }{T_K{p}_i}-\frac{1}{T_K}\right)\ge 1\right\}.\hfill \end{array}$$