And we can say, based on Tamino's post, that the time period Lucia used is too short to say anything meaningful about climate trends. Which Lucia must know because she isn't stupid, and yet she persists.
The point is moot. Especially given the analysis I was pointed to by Tamino is not germaine to measuring and testing estaimtes of trends.
It is a simple point. We apply statistical methods to gauge whether what we witness as some form of explained variation in the data is sufficiently large relative to unexplained vairation for us to make some probability statements.
Tamino can't get around an appropriate and correctly applied statistical analysis that shows the measured trend (over any period) is sufficiently different from that hypothesised as supposed to be occurring over time.
It is an unassailable fact that testing the hypothesised statement that "the world is warming by 0.2 degrees per decade over time" - the basis of the last IPCC report on the matter - shows the data we have actually collected since then would be very unlikely to have occurred. The statistical analysis shows that quite clearly:
Tamino can say that the more comlex process allows for such deviations over, say, 10 years, but that does of course imply that we will need to witness subsequently higher trends above 0.2 per decade in the future to "catch up" to the hypothesis. He may be right, he may be wrong, but that brings us back to crystal ball gazing, which is of no inferential value. Tamino also sticks to some unexplained choices in his analysis that tend to increase the size of his error bands unecessarily. I would recommend Lucia as a superior statistician and her analysis more useful.
We still come back to the hard data we have:
If there was an underlying trend of warming of 0.2 degrees per century, then, after accounting for the year to year
unexplained (i.e. random) variation in the data, it is very unlikely (significantly less than one chance in 20, maybe one chance in 200) that we would have had the run of data we have had.
The only response for a statistician is to keep watching the data as it unfolds.