|Data: GISS. Baseline: 1951-1980 average (14.00ºC).|
Z-scores are one of the simplest statistical tests both to calculate and interpret. The formula is
What z-scores tell us is how many standard deviations any one data point is above or below the average. We can then use the normal distribution to calculate the chances any data point will be that many standard deviations away from the average. Using the 1880s average anomaly (x̄ = -0.2111ºC) and standard deviation (s = 0.1271ºC), I calculated the chances of global temperature during a single month matching the average for the 1950s (x = -0.0455ºC) and the last ten years (x = 0.5803ºC) if no global warming had occurred. The results?
|1950s - 1880s|
1 in 270,270.3
|Last 10 - 1880s|
Mind you, this is the z-score of any one month in thd 1880s matching what is today the average. Today's average has shifted so far above the temperatures of the 1880s that the chances of any one month then matching today's average is zero. Now does that mean that we won't ever see months wherein global average temperatures are similar to those of the 1880s and 1950s? Not yet. The coldest months of today still overlap the warmest months of the 1880s and 1950s, as the graph shows. So we could see a global monthly temperature today that is similar to months in those decades—if you want to call a very cold month of today matching a very warm month of yesteryear "similar."
In short, the global temperature distribution has clearly shifted to the right. And it's that shift in distribution that is the main signature of global warming.