# Compare p-values of equal sample sizes: What does it mean if a p-value of kaplan-meier log rank test is larger than the other?

I'm analysing detection rates of carcasses for birds and mammals in either open fields or in forests, using kaplan-meier survival functions. The p-value is determined by log rank test.

I found that birds detected carcasses in open fields significantly faster than in forests (n = 34, chi^2 = 11.11, df = 1, p = 0.00086), whereas mammals detected carcasses in forests significantly faster than in open fields (n = 34, chi^2 = 8.01, df = 1, p = 0.0047).

My question is whether or not I can say anything about the fact that the relation of habitat (open/forest) is stronger for birds than it is for mammals, given the statistics mentioned above? And if so, what?

On the internet I read different opinions on this matter. Some say it does not make sense to compare two p-values between each other, some argue otherwise. However, everybody talks about comparing not necessarily the p-values, but the effect sizes. But how do I calculate the effect sizes for log rank tests?

Here (What sense does it make to compare p-values to each other?) it is stated that if the sample size is fixed (which is the case here: both are based on the same 34 carcasses), then p-values are monotonically related to Cohen's d. Does that mean that (because the sample sizes are equal) I can compare the p-values?

If I could compare the p-values with each other, what could I say about it? Is the relation between habitat and detection rates of birds 5.5 times stronger / more evident / clearer / ... than for mammals?