Proof that the recent slowdown is statistically significant (correcting for autocorrelation)
Guest essay by Sheldon Walker
In my last article I attempted to present evidence that the recent slowdown was statistically significant (at the 99% confidence level).
Some people raised objections to my results, because my regressions did not account for autocorrelation in the data. In response to these objections, I have repeated my analysis using the AR1 model to account for autocorrelation.
By definition, the warming rate during a slowdown must be less than the warming rate at some other time. But what “other time” should be used. In theory, if the warming rate dropped from high to average, then that would be a slowdown. That is not the definition that I am going to use. My definition of a slowdown is when the warming rate decreases to below the average warming rate. But there is an important second condition. It is only considered to be a slowdown when the warming rate is statistically significantly less than the average warming rate, at the 90% confidence level. This means that a minor decrease in the warming rate will not be called a slowdown. Calling a trend a slowdown implies a statistically significant decrease in the warming rate (at the 90% confidence level).
In order to be fair and balanced, we also need to consider speedups. My definition of a speedup is when the warming rate increases to above the average warming rate. But there is an important second condition. It is only considered to be a speedup when the warming rate is statistically significantly greater than the average warming rate, at the 90% confidence level. This means that a minor increase in the warming rate will not be called a speedup. Calling a trend a speedup implies a statistically significant increase in the warming rate (at the 90% confidence level).
The standard statistical test that I will be using to compare the warming rate to the average warming rate, will be the t-test. The warming rate for every possible 10 year interval, in the range from 1970 to 2017, will be compared to the average warming rate. The results of the statistical test will be used to determine whether each trend is a slowdown, a speedup, or a midway (statistically the same as the average warming rate). The results will be presented graphically, to make them crystal clear.
The 90% confidence level was selected because the temperature data is highly variable, and autocorrelation further increases the amount of uncertainty. This makes it difficult to get a significant result using higher confidence levels. People should remember that Karl et al – “Possible artifacts of data biases in the recent global surface warming hiatus” used a confidence level of 90%, and warmists did not object to that. Warmists would be hypocrites if they tried to apply a double standard.
The GISTEMP monthly global temperature series was used for all temperature data. The Excel linear regression tool was used to calculate all regressions. This is part of the Data Analysis Toolpak. If anybody wants to repeat my calculations using Excel, then you may need to install the Data Analysis Toolpak. To check if it is installed, click Data from the Excel menu. If you can see the Data Analysis command in the Analysis group (far right), then the Data Analysis Toolpak is already installed. If the Data Analysis Toolpak is NOT already installed, then you can find instructions on how to install it, on the internet.
Please note that I like to work in degrees Celsius per century, but the Excel regression results are in degrees Celsius per year. I multiplied some values by 100 to get them into the form that I like to use. This does not change the results of the statistical testing, and if people want to, they can repeat the statistical testing using the raw Excel numbers.
The average warming rate is defined as the slope of the linear regression line fitted to the GISTEMP monthly global temperature series from January 1970 to January 2017. This is an interval that is 47 years in length. The value of the average warming rate is calculated to be 0.6642 degrees Celsius per century, after correcting for autocorrelation. It is interesting that this warming rate is considerably less than the average warming rate without correcting for autocorrelation (1.7817 degrees Celsius per century). It appears that we are warming at a much slower rate than we thought we were.
Graph 1 is the graph from the last article. This graph has now been replaced by Graph 2.
The warming rate for each 10 year trend is plotted against the final year of the trend. The red circle above the year 1992 on the X axis, represents the warming rate from 1982 to 1992 (note – when a year is specified, it always means January of that year. So 1982 to 1992 means January 1982 to January 1992.)
A note for people who think that the date range from January 1982 to January 1992 is 10 years and 1 month in length (it is actually 10 years in length). The date range from January 1992 to January 1992 is an interval of length zero months. The date range from January 1992 to Febraury 1992 is an interval of length one month. If you keep adding months, one at a time, you will eventually get to January 1992 to January 1993, which is an interval of length one year (NOT one year and one month).
The graph is easy to understand.
· The green line shows the average warming rate from 1970 to 2017.
· The grey circles show the 10 year warming rates which are statistically the same as the average warming rate – these are called Midways.
· The red circles show the 10 year warming rates which are statistically significantly greater than the average warming rate – these are called Speedups.
· The blue circles show the 10 year warming rates which are statistically significantly less than the average warming rate – these are called Slowdowns.
· Note – statistical significance is at the 90% confidence level.
On Graph 2 there are 2 speedups (at 1984 and 1992), and 2 slowdowns (at 1997 and 2012). These speedups and slowdowns are each a trend 10 years long, and they are statistically significant at the 90% confidence level.
The blue circle above 2012 represents the trend from 2002 to 2012, an interval of 10 years. It had a warming rate of nearly zero (it was actually -0.0016 degrees Celsius per century – that is a very small cooling trend). Since this is a very small cooling trend (when corrected for autocorrelation), it would be more correct to call this a TOTAL PAUSE, rather than just a slowdown.
I don’t think that I need to say much more. It is perfectly obvious that there was a recent TOTAL PAUSE, or slowdown. Why don’t the warmists just accept that there was a recent slowdown. Refusing to accept the slowdown, in the face of evidence like this article, makes them look like foolish deniers. Some advice for foolish deniers, when you find that you are in a hole, stop digging.
via Watts Up With That? http://ift.tt/1Viafi3