Is the “sigmaless” option systematically more or less conservative than the “sigmamore” one in Hausman test?

[Federico Tedeschi]

Dear Statalisters,

I’m using Stata SE 17.0.

According to what I read in the paper here: https://www.mdpi.com/2225-1146/11/4/25

between page 15 and 16, by using the “sigmamore” option

more likely it would be to favor (even unduly) the rejection of the null hypothesis

when h>1, with h being the ratio between the squared error terms of the models (the ones of the efficient and of the consistent one).
If I well understand, this would imply “sigmamore” being less conservative than “sigmaless” when the residual error in the consistent model is lower (that I think is the case where statistical significance may be found, since the p-value should be below 0.5) and more conservative when it is higher than the one in the efficient model.
By trying such analyses with a dataset of mine (where I was specifically testing random- vs fixed- effect models), however, I find exactly the opposite: higher p-values (thus, more conservatiness) for “sigmamore” in correspondence with p-values below 0.5, and viceversa.
Thus, is there any systematic difference in p-values to be expected between these two options?

[Federico Tedeschi]

In a private communication with the authors, I was told that there was a typo on the sign of the inequality.
The typo will be corrected soon directly in the online version of the paper.
Thus, I would conclude that “sigmamore” is more conservative than “sigmaless” when the residual error in the consistent model is lower (that I think is the case where statistical significance may be found, since the p-value should be below 0.5) and less conservative when it is higher than the one in the efficient model.