A new paper has just been published by a team of scientists with James Hansen as lead author in Proceedings of the Academy of Sciences (PNAS) under the title "Perception of Climate Change". The analysis is actually quite straightforward. Taking a reference period (1951-1980), representative for the climate state before the anthropogenically caused global warming of recent decades, assuming a normal distribution of the anomalies relative to the reference period, look at the change in the distribution and the frequency of the occurrence of extreme events, i.e., compare this frequency with the probability that these events would have happened under the climate conditions of the reference period. Doing this for each geographical location on the globe one can produce a map of the probabilities, e.g., for the seasonal average of the temperature, and study their change in time. One can also add up the area of the globe, which is covered by ranges of probabilities, and study by how much this area changes over time.
Events that have a very low probability to occur under the climate conditions of the reference period are of particular interest. Hansen et al. especially look at events that have a lower probability than three times the standard deviation (3-sigma events) of the normal distribution, and the area of the globe which is covered by those events. The probability of the occurrence of events outside of three times the standard deviation is about 0.13% at each tail of the normal distribution, or less than two times in a thousand years for either side. According to the analysis of the surface temperature anomalies by Hansen et al., the fractional area of the globe covered by hot events and by cold events has increased and decreased during Northern Hemispheric summer (June, July, August), respectively. The frequency distribution of the anomalies has become wider, i.e., the variability from year to year has increased over recent decades. The area covered by hot 3-sigma events, i.e., with a very low probability of occurrence has increased from almost 0% during the reference period to a range of 4 to 13% in the various years from 2006 to 2010. Analyzing land surface temperatures only, the fractional area covered by hot 3-sigma events has increased from almost 0% during the reference period to 9 to 21% in the recent years.
So, is the increase in the fractional area of the globe covered by hot 3-sigma events due to anthropogenically caused global warming? I would answer this question with Yes, the results of the study imply that most of the increase in the fractional area is due to it, if one accepts the evidence provided by a whole body of research in climate science that the global warming trend over recent decades compared to the reference period of 1951 to 1980 has been mostly man-made. The scope of the study by Hansen et al., itself is not to provide such evidence. Thus, it does not do that. If one does not accept the evidence from previous research in climate science, but believes in some other cause of the warming, then the metric applied by Hansen et al. would imply that the increase in the fractional area of hot 3-sigma events is due to this other cause.
A possible objection to the analysis that comes to my mind could be regarding the choice of the reference period. The period of 1951 to 1980 appears to be a reasonable choice, if one looks at the globally averaged temperature anomaly (e.g., from the analysis done at the NASA Goddard Institute for Space Studies, see here), since the temperature anomaly had reached a plateau after a previous warming period, although it was somewhat higher in the 1930ies and '40ies. However, is this also true for all the regions of the globe? For instance, surface temperatures in the contiguous United States (CONUS) were about in the same range in the 1930ies as in recent decades. The fractional area of CONUS is less than 1.6% of the globe, but it illustrates the point. Hansen et al. actually checked the robustness of the results from their analysis by looking at selected years of the 1930 and '40ies in the provided supplemental information. The fractional area of hot 3-sigma events goes up to about 3% of the total land surface areas of the globe in some years. This is still only a third or less of the fractional area of the total land surface of the globe, which was covered by hot 3-sigma events from 2006 to 2010.
The central panel of Figure 7 in the Hansen et al., paper shows the graph for the results from the analysis confined to the CONUS area. According to the time series starting in the year 1900 of the fractional area of CONUS covered by "Hot", "Very Hot", and "Extremely Hot" (3-sigma) events shown there, the fractional areas of CONUS covered by these events were about the same in the 1930ies or so as in recent years. Thus, indeed, if one looks only at the United States one can conclude recent heat waves with similar extreme temperatures could also have happened with about equal probability without anthropogenic global warming as backdrop. This also may be true for other regions of Earth due to the occurrence of regional warm anomalies during different time periods. It is still a problem to attribute the occurrence of single events to global warming. However, this misses the point of the analysis as I see it. The point is the simultaneity of the occurrence of extremely hot events at different locations all over the globe, as measured by the fractional area of the globe covered by such events. Extremely hot events can happen here and there also without global warming. But the probability is very low that those events would happen at different locations of the globe all at the same time without the global warming of recent decades.
I have not caught up yet with comments and possible criticism by other climate scientists of the Hansen et al. study. Thus, I am not going to comment here on those.
 Hansen, J., Mki. Sato, and R. Ruedy (2012), Perception of climate change, Proc. Natl. Acad. Sci., doi:10.1073/pnas.1205276109.