And this means that there is a 95% likelihood that the underlying warming, if you remove the short term variations, is within this range.

No, actually, it doesn’t. The 95% confidence refers to the fact that if the “experiment” were repeated many times, with identical sample sizes, and data used for a 95% CI each time, over the long run 95% of those intervals would contain the true slope. For any particular instance we have no way of assigning a probability of containment. (Caveat: this comment is based on the interval being a traditional “frequentist” style confidence interval which, as far as I can tell, it is. If it is based on Bayesian procedures than it is possible to assign a coverage probability.)

This does not contradict the overwhelming evidence and support for climate change.

An example might help.

The skeptical science calculator gives a trend of 0.178±0.033?/decade in GISTEMP since 1974. This means the confidence interval of the trend covers the range of trends from 0.145?/decade to 0.211?/decade. And this means that there is a 95% likelihood that the underlying warming, if you remove the short term variations, is within this range.

The range of trends from 0.145?/decade to 0.211?/decade is completely above the zero trend line so is statistically significant (by quite a long way).

“You wanna play that game? OK. Let’s take the difference between the lowest and highest annual averages after 1940. That gives a post-1940 warming of 0.85 deg.C.”
https://tamino.wordpress.com/2012/12/20/fake-skeptic-draws-fake-picture-of-global-temperature/

The trend in the 2010.9 period is unmistakeable, but I understand that the period is too short and the confidence intervals too large to speak of statistical significance.

I wasn’t sure whether the warming from 2014 and 2015 would mean that the trend from 1998 now is statistically significant. Thanks for clarifying this. Obviously, this would affect the significance of years with lower starting points.

“The definition [of when a trend is statistically significant] is when the confidence interval does not include the zero trend line. Or when the mean trend is further than 2 standard deviations above or below the zero trend line.”

This is still over my head – an illustration might help – but I understand a little more about statistical significance today than I did yesterday.

I share your view that the current warming, or, to use another word, reality, won’t change the the substance of the denialist narrative. But I’m wondering how long the current discrepancy between the satellite data and the surface data can continue. An honest peer-review of the latest set from UAH might discover why they now register even lower temperatures than before, and could make the denialist charges against surface records less credible and more difficult to maintain.

going from a low point to a high point

Until this year, the denialists’ point was that even starting at a low point, 1999 for example, it was not possible to get statistically significant warming over any following period. That situation no longer applies.

the degree of incline was horrifying

It has a very large confidence interval which is a demonstration that using very short intervals is not a very accurate source of information and not particularly meaningful. The same applies to a lesser degree to the somewhat longer period of 17 years but in spite of that, denialists endlessly droned on about “no statistically significant warming in 17 years” as if it was some huge revelation. There may be another 17 year period of no statistically significant warming one day but at least, for what it’s worth, the denialists can’t drone on about that again until that day.

when a trend is statistically significant

The definition is when the confidence interval does not include the zero trend line. Or when the mean trend is further than 2 standard deviations above or below the zero trend line.

the next denialist ploy will be to drop the no warming since 1998 or for x years claim, and to confuse the issue by claiming that the warming is not statistically significant

That’s what they’ve been doing, claiming no statistically significant warming since 1998 or whatever. What they’ve moved onto now is claiming that the surface records, apart from HADCrut3, are all the product of a global conspiracy and that only the satellite radio measurements are accurate.

Thanks for your reply. I don’t have a background in math and science, so I’m pushing my limits here. To start with your second suggestion. After looking at the SkS trend calculator I went over to Wood for Trees. Please correct me if I’m wrong, but I think you’re showing me an example of two can play this game, here doing the opposite of what denialists do, i.e. going from a low point to the El Niño influenced point we’re at today. It was indeed interesting, and the degree of incline was horrifying.

Regarding the trend since 1998, your suggestion didn’t provide me with the solid answer that it would have given those with an understanding of math, but your answer encouraged me to learn a little more than I knew before. This may be an unreasonable question, but do you have any idea where a math dummy like myself could learn enough about the relationship between trends and confidence intervals to be able to recognize when a trend is statistically significant? (I expect that the next denialist ploy will be to drop the no warming since 1998 or for x years claim, and to confuse the issue by claiming that the warming is not statistically significant, or not really real.)

would the warming trend since 1998 justify asserting that the trend from 1998 to 2015 is statistically significant?

This calculator will tell you the answer to that question: http://www.skepticalscience.com/trend.php

Also, try GISTEMP from 2010.9 (which includes December 2010) to now. You may be very interested in the result.

Based on what we know now, what would be the probability that 2015 is the warmest? What would be the probability that either 2014 or 2015 is the warmest?

Also, although (to my understanding) the amount of data we have since 1998 normally would make it difficult to speak of statistical significance, would the warming trend since 1998 justify asserting that the trend from 1998 to 2015 is statistically significant?

“Maybe you should give the good news to Lamar”

I would, but he would respond by subpoena demanding that I had over my underwear, which does not exist.

You got it!

No Warming Since 50,000,000 BCE.
(Maybe you should give the good news to Lamar.)