Proof that the recent global warming slowdown is statistically significant (at the 99% confidence level)

Guest analysis by Sheldon Walker

Introduction

In this article I will present convincing evidence that the recent slowdown was statistically significant (at the 99% confidence level).

I will describe the method that I used in detail, so that other people can duplicate my results.

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 99% 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 99% 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 99% 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 99% 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. All of the calculations for this article can be found at the end of the article.

The 99% confidence level was selected in order to make this test as trustworthy and reliable as possible. This is higher than the normal confidence level used for statistical testing in science, which is 95%.

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 1.7817 degrees Celsius per century.

Results

Please look at Graph 1.

clip_image002

Graph 1

The warming rate for each 10 year trend is plotted against the final year of the trend. The red circle above the year 2017 on the X axis, represents the warming rate from 2007 to 2017 (note – when a year is specified, it always means January of that year. So 2007 to 2017 means January 2007 to January 2017.)

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 99% confidence level.

If you look at the speedups, they only occur in groups of 1 or 2. But the slowdowns occur in groups of 1, 3, and 5.

Could any reasonable person look at the group of 5 slowdowns, from 2011 to 2015, and claim that the slowdown never existed. Remember, each blue circle is a 10 year trend, and they overlap with each other. You could consider the group of 5 blue circles to represent 14 years (10 years for the first circle, and one additional year for each additional circle).

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 0.0885 degrees Celsius per century – that is less than 0.1 degrees Celsius in 100 years). A person could get VERY bored waiting for the temperature to change at this warming rate.

I don’t think that I need to say much more. It is perfectly obvious that there was a slowdown. Why didn’t the warmists just admit that there had been a small temporary slowdown. Instead, it seemed to become extremely important to them, that they deny the slowdown. So who should be called “deniers” now?

Numbers and calculations

Start Year End Year Number of Years Warming Rate Degrees of Freedom Std Error t-value t-critical
1970 1980 10 1.4278 119 0.4434 0.7981 2.6178
1971 1981 10 2.8170 119 0.4578 2.2618 2.6178
1972 1982 10 3.0701 119 0.4737 2.7201 2.6178
1973 1983 10 2.9268 119 0.4852 2.3603 2.6178
1974 1984 10 4.2394 119 0.4255 5.7766 2.6178
1975 1985 10 3.0268 119 0.4590 2.7128 2.6178
1976 1986 10 1.8915 119 0.4745 0.2315 2.6178
1977 1987 10 0.2566 119 0.4213 3.6196 2.6178
1978 1988 10 0.9869 119 0.4408 1.8032 2.6178
1979 1989 10 0.8843 119 0.4421 2.0300 2.6178
1980 1990 10 0.6998 119 0.4268 2.5350 2.6178
1981 1991 10 1.7630 119 0.4450 0.0419 2.6178
1982 1992 10 2.9008 119 0.4018 2.7854 2.6178
1983 1993 10 1.5612 119 0.4546 0.4850 2.6178
1984 1994 10 1.4235 119 0.4566 0.7844 2.6178
1985 1995 10 0.9772 119 0.4555 1.7663 2.6178
1986 1996 10 0.4927 119 0.4501 2.8637 2.6178
1987 1997 10 -0.3504 119 0.4227 5.0434 2.6178
1988 1998 10 0.3979 119 0.4480 3.0888 2.6178
1989 1999 10 2.0576 119 0.4807 0.5741 2.6178
1990 2000 10 1.4648 119 0.4907 0.6457 2.6178
1991 2001 10 1.9464 119 0.4705 0.3501 2.6178
1992 2002 10 3.0766 119 0.4498 2.8787 2.6178
1993 2003 10 3.1143 119 0.4359 3.0572 2.6178
1994 2004 10 2.6849 119 0.4225 2.1378 2.6178
1995 2005 10 1.9544 119 0.4326 0.3992 2.6178
1996 2006 10 2.4839 119 0.4169 1.6843 2.6178
1997 2007 10 1.9892 119 0.4136 0.5017 2.6178
1998 2008 10 1.5323 119 0.4250 0.5867 2.6178
1999 2009 10 1.8895 119 0.4004 0.2693 2.6178
2000 2010 10 1.3776 119 0.3864 1.0456 2.6178
2001 2011 10 0.7378 119 0.3711 2.8130 2.6178
2002 2012 10 0.0885 119 0.3721 4.5505 2.6178
2003 2013 10 0.3261 119 0.3641 3.9975 2.6178
2004 2014 10 0.5116 119 0.3627 3.5017 2.6178
2005 2015 10 0.6389 119 0.3560 3.2103 2.6178
2006 2016 10 2.2681 119 0.4066 1.1965 2.6178
2007 2017 10 3.6217 119 0.4531 4.0610 2.6178
1970 2017 47 1.7817 563

via Watts Up With That?

http://ift.tt/2DsHkm0

January 12, 2018 at 02:12PM

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