- One choose a data set of global tropospheric (e.g., UAH, RSS) or surface temperature estimates (e.g., NASA/GISS, NOAA/NCDC, HadCRU), preferably one that has the strongest bias to the cool side.
- One finds a time interval in the data set, which is sufficiently short enough so that a statistical trend estimate does not provide any statistically significant warming trend. The large variability within the data on the short time interval makes sure of this. Even better, if the statistical estimate of the trend is close to Zero or negative. In latter case, one can claim "global cooling!" Statistical significance does not matter in this case. It only matters, if it comes to denying a global warming trend.
trend calculator at the Skeptical Science blog, which is based on ) of the trend is 0.012 Kelvin/Decade. The 2-sigma (about 95%) confidence interval is +/-0.229 Kelvin/Decade. As one can see, it is quite large. Then there is the recent "global cooling" from 1997 to today with a trend of (-0.003+/-0.229) Kelvin/Decade. No statistically significant cooling, but what "skeptic" is going to care about that, as long as "cooling" can be claimed.
What about the small interval between the "global warming standstills"? The positive trend estimate in this small time interval is not statistically significantly different from a Zero-trend either: (0.164+/-1.689) Kelvin/Decade. Therefore, since none of the separate time intervals shows any statistically significant global warming, the brave "skeptic" concludes, there has not been any global warming for 34 years at all! It is all a lie, a big global warming hoax! Invented by sinister forces for their own mean purposes.
What now? Now we repeat the statistical trend estimate for the whole time interval from 1979 to today:
The statistical estimate for the trend over the whole time interval is (0.133+/-0.073) Kelvin/Decade. There is a clear global warming trend, which is statistically significantly different from a Zero-trend by more than 3-sigma, which means that the probability to have a false positive signal relative to the noise in the data within the time interval is less than three out of a thousand.
No global warming and presence of global warming cannot be both true at the same time. A statement and its negation cannot be true at the same time. One of the two approaches must be wrong. And it is not the second one.
What does this teach us?
- One can get easily fooled by noise, if one chooses too short time intervals of the data in time series analysis. In any time series, on
ce always can find a time interval short enough, for which the noise becomes so large it masks any trend in the data series.
- A failure to find a statistically significant trend in a time series does not refute the hypothesis of the presence of such a trend, since one cannot logically exclude the possibility that the lack of statistical significance is only due to a too small sampling size of the data.
- Empirical, statistical evidence for a true global warming "standstill" or at least for a trend change could be provided by showing that the trend over the recent shorter time interval is statistically significantly different from the statistically significant warming trend that has been observed over the whole of the recent decades. This is not the case for the RSS data set above (and neither for any of the other mentioned ones). The 2-sigma interval for the RSS temperature data since 1997 is +/-0.229 Kelvin/Decade. The multi-decadal trend from 1979 to today lies well within its boundaries. Therefore, claims about a "global warming standstill", using too short time intervals from these data sets and flawed conclusions from statistical trend analysis, do not have any scientific validity.