The idea that global warning has paused in the past decade is based on the idea that if you look at recent global temperature

and add a line of best fit through it

We get a more or less flat line. We can even add an error range, for this line how what kind of range is needed for the true line to be within the area 95% of the time

The thing is, that is actually a rubbish line with no predictive power, which we see as soon as we add more points.

Now, let’s do this the way you are supposed to. We take a big time period to make a trend from, such as the thirty years before the last decade.

And let’s add a line of best fit to this data

Now let’s put in the 95% error range for expected values based on the line of best fit.

So how do the next 10 years in time (so 2004-2013) fit with this trend line?

Because the last decade fits the trend line really nicely, the conclusion we have to reach is that there is no reason to believe the rate of increase in world temperature has changed in a significant way, compared to 1973-2012. We need to assume this because if we are being scientific about it we are trying to reject the null hypothesis, and the null hypothesis is “the normally expected thing”/ “nothing unusual is going on”. In this case the climate increasing like it has been in past decades is the normal thing.

Now a final version of the graph, showing the code for creating it:

gtmp = c(-0.375, -0.19, -0.218, -0.29, -0.214, -0.203, -0.36, -0.447, -0.401, -0.348, -0.435, -0.464, -0.561, -0.366, -0.44, -0.333, -0.281, -0.34, -0.24, -0.266, -0.327, -0.341, -0.303, -0.287, -0.405, -0.406, -0.378, -0.056, 0.024, -0.264, -0.275, -0.231, -0.279, -0.323, -0.48, -0.451, -0.437, -0.477, -0.34, -0.204, -0.451, -0.373, -0.457, -0.44, -0.406, -0.374, -0.211, -0.22, -0.436, -0.282, -0.177, -0.225, -0.387, -0.461, -0.516, -0.354, -0.273, -0.447, -0.472, -0.522, -0.499, -0.53, -0.453, -0.422, -0.248, -0.177, -0.404, -0.499, -0.37, -0.312, -0.271, -0.204, -0.291, -0.269, -0.262, -0.227, -0.086, -0.19, -0.162, -0.337, -0.126, -0.07, -0.113, -0.277, -0.131, -0.17, -0.126, 0.017, 0.016, -0.01, 0.075, 0.061, 0.013, 0.05, 0.154, 0.025, -0.061, 0.007, -0.066, -0.119, -0.204, -0.027, 0.048, 0.112, -0.092, -0.159, -0.217, 0.013, 0.033, 0, -0.051, 0.027, 0.003, 0.035, -0.243, -0.141, -0.077, -0.04, -0.098, 0.042, -0.017, -0.153, -0.074, 0.059, -0.178, -0.121, -0.231, 0.059, -0.052, 0.034, 0.144, 0.19, -0.005, 0.179, 0.008, -0.005, 0.039, 0.166, 0.224, 0.113, 0.296, 0.287, 0.092, 0.133, 0.203, 0.333, 0.225, 0.384, 0.53, 0.289, 0.301, 0.455, 0.523, 0.521, 0.443, 0.587, 0.536, 0.563, 0.428, 0.554, 0.625, 0.487, 0.511, 0.544) #From Cowtan & Way
gyr <- 1850:2013
gdata <- data.frame(gyr, gtmp)

#empty plot
plot(NA,NA, xlim=c(1973,2013), ylim=c(-0.3,0.9), ylab="Global temperature anomaly", xlab="Year", frame.plot=F)

#no sig warming line of best fit and 95% error zone
lmline = lm(gtmp ~ gyr, data=gdata[gdata$gyr >= 2003,])
lmsd = sd(lmline$residuals)
xfrombottonleft=c(1972,1972,2014,2014)
yfrombottomleft= c(lmline$coefficients[1] + 1972 * lmline$coefficients[2] - 2*lmsd, lmline$coefficients[1] + 1972 * lmline$coefficients[2] + 2*lmsd, lmline$coefficients[1] + 2014 * lmline$coefficients[2] + 2*lmsd, lmline$coefficients[1] + 2014 * lmline$coefficients[2] - 2*lmsd)
polygon(xfrombottonleft, yfrombottomleft, col="#FF000011", border="#FF000011")

#long term line of best fit
reallmline = lm(gtmp ~ gyr, data=gdata[gdata$gyr >= 1973 & gdata$gyr < 2003,])
reallmsd = sd(reallmline$residuals)
xfrombottonleft=c(1972,1972,2014,2014)
yfrombottomleft= c(reallmline$coefficients[1] + 1972 * reallmline$coefficients[2] - 2*reallmsd, reallmline$coefficients[1] + 1972 * reallmline$coefficients[2] + 2*reallmsd, reallmline$coefficients[1] + 2014 * reallmline$coefficients[2] + 2*reallmsd, reallmline$coefficients[1] + 2014 * reallmline$coefficients[2] - 2*reallmsd)
polygon(xfrombottonleft, yfrombottomleft, col="#00000011", border="#00000011")

#plot the points
points(gdata$gyr[gdata$gyr >= 1973 & gdata$gyr < 2003 ],gdata$gtmp[gdata$gyr >= 1973 & gdata$gyr < 2003 ], pch=19)
points(gdata$gyr[gdata$gyr >= 2003],gdata$gtmp[gdata$gyr >= 2003 ], col="red", pch=19)
abline(lmline, col="red", lwd=2)
abline(reallmline, col="black")