# Implementation of Hypothesis test on R² for regressions in cross-sectional setup

I am confused by the paper of Kan et al. (2013 - "Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology") which proposes the execution of hypothesis tests on R² of regressions to assess whether the coefficients are different from each other. Consequently the following setup is tested: $$H_0=R²_A = R²_B \\ H_1=R²_A != R²_B$$

The test is based on a p-value for each of the R² - this is where my confusion starts. As I understood hypothesis tests the p-value results from the lookup of the z-value from the normal distribution, whereas the z-value follows $$z-value = \frac{x-\sigma}{\sqrt{n}}$$ For the implementation of such a test I do not have sufficient information or is it necessary to consider the standard deviation of included regression coefficients to make this calculation work?

I also thought about using the methodology to compare two mean-values, however, I still need a standard deviation of the tested models. Moreover, the paper by Kan describes the method only for a single cross section, not periodical cross-sections as described by Fama & MacBeth (1973). Do you know how to transform the calculation?

Many Thanks!