Radius of hydride (H⁻) ion
Unfortunately, there is no caliper-like tool to measure ionic radii directly.
They are determined based on experimental data such as crystal structure or crystal lattice energy using empirical relationships.
The exact value would inevitably deviate from one method to another.

Pauling [1, pp. 150–152] used a hard-sphere model which doesn't account for overlap in crystal lattice and was predicting higher interatomic distances compared to the crystallographic data, hence an overestimated value of the anionic radii.

Several limitations of the hard-sphere model can be resolved by applying a soft-sphere model.
According to the recent work by Lang and Smith [2], who also compared applicability of both hard- and soft-sphere models, $r_\mathrm{i}(\ce{H-}) = \pu{139.9 pm}.$

CRC Handbook of Chemistry and Physics [3, p. 12-22] lists the value of thermochemical radius determined using Kapustinskii equation from a set of known lattice energies: $r_\mathrm{i}(\ce{H-}) = \pu{(148 ± 19) pm}.$

References


Pauling, L. The Chemical Bond; Cornell University: Ithaca NY, 1960.
Lang, P. F.; Smith, B. C. Ionic Radii for Group 1 and Group 2 Halide, Hydride, Fluoride, Oxide, Sulfide, Selenide and Telluride Crystals. Dalton Trans. 2010, 39 (33), 7786. DOI: 10.1039/c0dt00401d.
Haynes, W. M.; Lide, D. R.; Bruno, T. J. CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 97th ed.; Taylor &amp; Francis Group (CRC Press): Boca Raton, FL, 2016. ISBN 978-1-4987-5429-3.