[acover]

From the paper:

"shows our estimate that there is only a 0.5% chance that the observed retreat of Kaskawulsh Glacier happened in the absence of a climate trend"

The 0.5% has nothing to do with the river. It is their confidence that the retreat of the glacier could occur in the absence of a climate trend based on their model.

[archgoon]

Can you clarify why it is incorrect to reverse that into the statement "We estimate that there is a 99.5 percent chance that the observed retreat did not happen in the absence of a climate trend."? I confess to a fair amount of confusion at this point :) I'm sure there is something subtle (or perhaps obvious, and my brain is failing) that I'm missing.

What is the properly worded complement?

[archgoon]

This seems similar, but not identical, to the statement:

If there is not a climate trend, we would expect this to happen with a .05 chance.

If they meant the latter, my confusion is resolved.

[acover]

This is the blind leading the blind.

Fundamental truth: bayes theorem.

P(evidence | null hypothesis) = P(null hypothesis | evidence) * P (evidence) / P (null hypothesis)

The P-value test determines:

P(evidence | null hypothesis) = 0.5%

= there is a 0.5% chance of the observed evidence given the null hypothesis

The statement "We estimate that there is a 99.5 percent chance that the observed retreat did not happen in the absence of a climate trend."

translates to P(!null hypothesis | evidence) = 99.5%

By Bayes theorem:

P(!null hypothesis | evidence) = P(evidence | !null hypothesis) * P (!null hypothesis) / P (evidence)

We know almost none of these terms. The answer is not as simple as 99.5.

[archgoon]

Oh I thought we were having an interesting discussion about the linguistic mapping between probability and regular English. Sorry for wasting your time. :(