no warming since 1998”

But you might have heard claims like “there’s been no warming since 1998”, so let us have a look at temperatures starting in 1998 (the year sticking out most above the trend line in the previous graph)
I will be using the HadCRUT4 hybrid data, which have the most sophisticated method to fill data gaps in the Arctic with the help of satellites,

Keith Woollard said You lose me at the first graph. If you use the satellite data you cannot make any of the points you raise.

[Response: Of course the same points about the meaning of significance and confidence intervals could have been made also with satellite data. But here we are interested in the evolution of global surface temperatures, which cannot be measured by satellites. – stefan]
I’m curious, why aren’t they using the satellite data?
[Response: Satellite data doesn’t measure the same thing and has different levels of signal and noise. – gavin]

The issue is that claims like “there’s been no warming since 1998” relate to the satellite data which do show a pause for that time no matter how you try to deny it.
You cannot both incorporate satellite data and then dismiss it.