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.

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 |

Superforest,Climate Change

via Watts Up With That? http://ift.tt/1Viafi3