The pause is something whose definition belongs to climate sceptics like me who first identified it and named it. I personally was using it as long ago as 2007/8. It is in my climategate submission of 2009.
And because sceptics key concern is whether the forecasts of impending warming were correct, the pause has always been and will always be defined in terms of whether these forecasts of warming are correct. Thus the “pause” is anything less than the predicted warming.
And whilst there may be other forecasts, I personally have always used the 2001 IPCC prediction of between 1.4 and 5.8C warming by 2100 as being the key test. This is because 2001 was after the 1998 peak or the 1970-2000 warming and because it was a period without net change for a few years, it was not biased by the particular year chosen for the start, because being “flat” for a few years, one could use any date from 2001 onwards and get fairly much the same trend.
And as not one of those metrics for global temperature predicted to warm in 2001 has warmed at even the lowest rate, I can be 100% confidence that there is a 100% statistical significance that 100% of the metrics show a pause.  (Although obviously if one later fabricates “metrics” with the intent of not showing a pause …. )
But unfortunately, given the massive PR budget of the troughers, there’s been a lot of frankly daft stories about the pause. Most come down to some climate extremist academic cherry picking a period for the “pause”, dreaming up a false statistical test and then claim “proves” it doesn’t exist. No it does not. It just proves it does exist, because they wouldn’t spend so much time and effort on the pause, unless the actual definition based on the failure of the forecasts was real.
So, that is the first reason for this post: to spell out in black and white that the definition of the pause. To state it belongs to people like me who are the discovers and not a bunch of pause-denying climate extremists academics with their snouts in the trough of public money trying to keep the pig swill flowing. But most importantly to point out that “statistically significance” can only refer to the number of climate forecasts and/or number of metrics (running at the time of the forecast) that failed.

Statistical significance in climate

The second reason for this post, is to condemn the idiotic notion that we can know what is  “statistically significant” over the period for which we have global temperature data (However, obviously a bigger problem is that we don’t have any actual temperature data except the satellite as there is unequivocal evidence that what I term “human adjusted” data is constantly being “upjusted”.)
But in terms of general statistical significance … what is the normal variation we expect over 100 years of climate?And the correct answer is we know … we don’t know. That is because we only have 150 years of pseudo global data and so we only have basically one full century of data.
We cannot use the same single time period to both decide what is “normal” and what is “abnormal”.
It is like taking a plant out the ground and finding the roots have red spots. If this is the first time the plant has been seen, we cannot know whether this is a one of case for that plant or something that is general to the species.
So, it would be false to say we have “statistically significant” warming over a century. It is no more “statistically significant” than finding a new plant species and then claiming for the one isolated specimen that it is “statistically bigger than normal”.
So, what about part of the century? Here it gets complicated. Because global temperature is the sum of many changes, some occurring day-to-day, some week-to-week, some month-to-month, some year-to-year, some decade-to-decade, some century-to-century, some millennium-to-millenium, etc. That means, we can be in the middle of a natural century or even millennium long warming (or cooling) trend. As such warming would be the expected trend within a century. Moreover, if there are also natural cycles such as the suggested 60year one, then NORMALLY there can be periods of substantial warming.
So, given we know there are large long-term trends in the climate as well as many cycles like El Nino, PDO, NAO, etc, the only meaningful test that can be made on the global temperature is to compare like with like. Is the period we are interested in, significantly different from similar periods?

The formal proof that there is no statistically significant warming or cooling is shown in this article: Proof: recent temperature trends are not abnormal

But, the simple way to explain it is thus: From 1970-2000 it warmed by 0.48C. Is this abnormal? Well, if we look we find that from 1910-1940 it also warmed by 0.48C. So, such warming is far from abnormal as being only 1/5 of the data, we find the same scale of warming occurring twice. Indeed, if we look at the longest temperature series in central England we find the 1970-2000 rise in temperature is dwarfed by the 1690-1730 temperature rise.

Finally

1. None of the human-adjusted temperature metrics have any credibility. Firstly, the stations are cherry picked so as to remove those showing cooling. Secondly, they are “upjusted” using bogus criteria which is supposed to compensate for things like known urban heating – but usually actually boost the effect of urban heating rather than remove it. Finally, the troughers producing these metrics lost all credibility when they gave up all pretence of impartiality and clearly and blatantly changed the metric to fabricate a warming trend because of the pause. And it is such a blatant fraud, because they all disagree with the only impartial, non-human adjusted, non trougher metric from the satellites (18 years without warming and still going!)
2. But even though the “troughers” have shown themselves to be climate extremists with no intention of impartiality and so they have been “upjusting” the metrics, they still were incapable of showing warming. That is why the pause is so important. It’s not that we sceptics were producing something that was impartial and happened to show a pause. It is that those people who clearly and overtly adjust the data to fabricate warming, couldn’t fabricate even the lowest predicted trend. And the reason is clear from the 18 years the satellites show without warming.
3. To use a betting analogy: if you bet on a horse, you cannot then claim to have won, by e.g. changing the way the winner is decided AFTER THE RACE. Likewise, in real science, one sets the criteria for “winning” at the start and that is the criteria used to decide whether the data fits the test. Therefore, whilst the metric available in 2001 were far from ideal … the IPCC told us this was their measure of global temperature, and they said this would rise by at least 0.14C/decade**. Therefore the criteria for the pause being real is that THOSE METRICS PREDICTED TO RISE did not rise by at least the minimum trend predicted.

**The actual prediction was >1.4C to 2100.