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?