# How to report significance of a Fischer's C-statistic test

I'm writing a piece about Phylogenetic Path Analysis.

Following Shipley 2014 I wrote:
"...if the data is generated according to a given causal graph, then probabilities of each independence claims are mutually independent; in other words, the data is well supported by the model. If all $$k$$ independence relationships are true then this statistic will follow a $$\chi^2$$ distribution with $$2k$$ degrees of freedom.
The hypothesis that the causal model fits the data is then accepted when the $$C$$ statistic is not significant ($$p$$-value $$>$$ 0.05)."

And a reviewer told me that stating "the $$C$$ (test) statistic is not significant" is wrong, because test statistics are not significant (in terms of significance claims).

How should I state this? What 'is' significant?

Is saying "The hypothesis that the causal model fits the data is then accepted if the $$C$$ statistic was significantly drawn from a $$\chi^2$$ distribution with $$2k$$ degrees of freedom." correct?