  The location-scale model is usually present in physics and chemistry in
connection to the Birge ratio method for the adjustment of fundamental physical
constants such as the Planck constant or the Newtonian constant of gravitation,
while the random effects model is the commonly used approach for meta-analysis
in medicine. These two competitive models are used to increase the quoted
uncertainties of the measurement results to make them consistent. The intrinsic
Bayes factor (IBF) is derived for the comparison of the random effects model to
the location-scale model, and we answer the question which model performs
better for the determination of the Newtonian constant of gravitation. The
results of the empirical illustration support the application of the Birge
ratio method which is currently used in the adjustment of the CODATA 2018 value
for the Newtonian constant of gravitation together with its uncertainty. The
results of the simulation study illustrate that the suggested procedure for
model selection is decisive even when data consist of a few measurement
results.
