I'll be adding a new feature to my monthly world temperature
analysis, an evaluation of the confidence of nonzero correlation.
This "F ratio" inferential statistic tests whether the slope
of the correlation is zero. This procedure is well known. Even
"CO2 Scientists," use it. Consult any good statistics text for
more information.

(You may also find information on, or may already be aware of, a
"t test," which evaluates whether the slope of the correlation is
positive or negative. I would have used the "t test" to test for
a positive warming slope, but to avoid confusing some people I
chose to follow the lead of the "CO2 Scientists" and use the
"F ratio." (Actually, "F" and "t" are largely the same, both use
the Incomplete Beta Function, but with different arguments.))

I would have added this feature earlier, but the 124-year record
shows warming so very strongly that special attention is required
to evaluate the "F distribution function" correctly. In most cases,
a simple table listing "F" values for 95% and 99% confidence will
do. (For an example, see this table from the "CO2 Science" site:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

I have therefore used the "BETAI" routine from "Numerical Recipes"
by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and
William T. Vetterling in 1986. My results pass the test routines
provided by the authors, and they match the table from "CO2 Science"
as well. I've also checked my more extreme results, with their long
series of "9"s, against Wolfram Research's "Mathematica" version 3.0
for Macintosh. I used variations on these three commands:
Statistics'ContinuousDistributions'
$MaxExtraPrecision = 2000
N[CDF[FRatioDistribution[1, insertdegreesfreedomhere], Fratiogoeshere], 500]
This computation uses symbolic representations for numbers to simulate
many digits of precision, and is therefore a very slow process. A
single evaluation by "Mathematica," like the one needed to test the
case below, can take hours on my 266 MHz Mac G3 Power PC. In most
cases I tested, "Mathematica" and my implementation of "BETAI" agreed
on the number of "9"s; occasionally, they differed by a single 9 digit.


Here are the results for 124 years of GISS global land and sea data:
Rxy 0.833087 Rxy^2 0.694034
TEMP = 13.666145 + (0.004797 * (YEAR-1879))
Degrees of Freedom = 122 F = 276.73745
Confidence of nonzero correlation = approximately
0.99999999999999999999999999999999 (32 nines), which is darn close to 100%!



These globally averaged yearly temperature data come from NASA:
http://www.giss.nasa.gov/data/update...LB.Ts+dSST.txt
They represent the results of hundreds of millions of readings
taken at thousands of stations around the globe over the last
124 years. Yes, the land data are corrected for urban heat
island effect. The sea data do not need to be. There are few
urban centers in the sea.


--

"One who joyfully guards his mind
And fears his own confusion
Can not fall.
He has found his way to peace."

-- Buddha, in the "Pali Dhammapada,"
~5th century BCE


-.-. --.- Roger Coppock )


-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

"Roger Coppock" wrote in message
...
I'll be adding a new feature to my monthly world temperature
analysis, an evaluation of the confidence of nonzero correlation.
This "F ratio" inferential statistic tests whether the slope
of the correlation is zero. This procedure is well known. Even
"CO2 Scientists," use it. Consult any good statistics text for
more information.

(You may also find information on, or may already be aware of, a
"t test," which evaluates whether the slope of the correlation is
positive or negative. I would have used the "t test" to test for
a positive warming slope, but to avoid confusing some people I
chose to follow the lead of the "CO2 Scientists" and use the
"F ratio." (Actually, "F" and "t" are largely the same, both use
the Incomplete Beta Function, but with different arguments.))

I would have added this feature earlier, but the 124-year record
shows warming so very strongly that special attention is required
to evaluate the "F distribution function" correctly. In most cases,
a simple table listing "F" values for 95% and 99% confidence will
do. (For an example, see this table from the "CO2 Science" site:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

I have therefore used the "BETAI" routine from "Numerical Recipes"
by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and
William T. Vetterling in 1986. My results pass the test routines
provided by the authors, and they match the table from "CO2 Science"
as well. I've also checked my more extreme results, with their long
series of "9"s, against Wolfram Research's "Mathematica" version 3.0
for Macintosh. I used variations on these three commands:
Statistics'ContinuousDistributions'
$MaxExtraPrecision = 2000
N[CDF[FRatioDistribution[1, insertdegreesfreedomhere], Fratiogoeshere],
500]
This computation uses symbolic representations for numbers to simulate
many digits of precision, and is therefore a very slow process. A
single evaluation by "Mathematica," like the one needed to test the
case below, can take hours on my 266 MHz Mac G3 Power PC. In most
cases I tested, "Mathematica" and my implementation of "BETAI" agreed
on the number of "9"s; occasionally, they differed by a single 9 digit.


Here are the results for 124 years of GISS global land and sea data:
Rxy 0.833087 Rxy^2 0.694034
TEMP = 13.666145 + (0.004797 * (YEAR-1879))
Degrees of Freedom = 122 F = 276.73745
Confidence of nonzero correlation = approximately
0.99999999999999999999999999999999 (32 nines), which is darn close to
100%!



Great. Now carry out pi as far as you can.

"James" wrote in message ...
"Roger Coppock" wrote in message
...
I'll be adding a new feature to my monthly world temperature
analysis, an evaluation of the confidence of nonzero correlation.
This "F ratio" inferential statistic tests whether the slope
of the correlation is zero. This procedure is well known. Even
"CO2 Scientists," use it. Consult any good statistics text for
more information.

(You may also find information on, or may already be aware of, a
"t test," which evaluates whether the slope of the correlation is
positive or negative. I would have used the "t test" to test for
a positive warming slope, but to avoid confusing some people I
chose to follow the lead of the "CO2 Scientists" and use the
"F ratio." (Actually, "F" and "t" are largely the same, both use
the Incomplete Beta Function, but with different arguments.))

I would have added this feature earlier, but the 124-year record
shows warming so very strongly that special attention is required
to evaluate the "F distribution function" correctly. In most cases,
a simple table listing "F" values for 95% and 99% confidence will
do. (For an example, see this table from the "CO2 Science" site:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

I have therefore used the "BETAI" routine from "Numerical Recipes"
by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and
William T. Vetterling in 1986. My results pass the test routines
provided by the authors, and they match the table from "CO2 Science"
as well. I've also checked my more extreme results, with their long
series of "9"s, against Wolfram Research's "Mathematica" version 3.0
for Macintosh. I used variations on these three commands:
Statistics'ContinuousDistributions'
$MaxExtraPrecision = 2000
N[CDF[FRatioDistribution[1, insertdegreesfreedomhere], Fratiogoeshere],
500]
This computation uses symbolic representations for numbers to simulate
many digits of precision, and is therefore a very slow process. A
single evaluation by "Mathematica," like the one needed to test the
case below, can take hours on my 266 MHz Mac G3 Power PC. In most
cases I tested, "Mathematica" and my implementation of "BETAI" agreed
on the number of "9"s; occasionally, they differed by a single 9 digit.


Here are the results for 124 years of GISS global land and sea data:
Rxy 0.833087 Rxy^2 0.694034
TEMP = 13.666145 + (0.004797 * (YEAR-1879))
Degrees of Freedom = 122 F = 276.73745
Confidence of nonzero correlation = approximately
0.99999999999999999999999999999999 (32 nines), which is darn close to
100%!



Great. Now carry out pi as far as you can.

It appears that Crappock is 99.9999999999999999999999999999999%
certain of what climatologists have known for a very long time - that
the earth has been (generally) in a warming phase since records began
124 years ago. In point of fact, all reliable ( and by reliable I
don't mean Mann's tree ring nonsense) proxies put the warming trend to
have started in the 17th Century, a century before the Industrial
Revolution, and slap bang in the middle of the Maunder Minimum of
solar activity.

That the earth has warmed in the last 124 years is news to nobody.
That Crappock doesn't know the difference between a monthly variation
in mean temperature and climate we can only ascribe to a very low
cranial capacity and lots of time on his hands.

Roger Coppock wrote in message ...
[snip]
I would have added this feature earlier, but the 124-year record
shows warming so very strongly that special attention is required
to evaluate the "F distribution function" correctly. In most cases,
a simple table listing "F" values for 95% and 99% confidence will
do. (For an example, see this table from the "CO2 Science" site:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

I have therefore used the "BETAI" routine from "Numerical Recipes"
by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and
William T. Vetterling in 1986. My results pass the test routines
provided by the authors, and they match the table from "CO2 Science"
as well. I've also checked my more extreme results, with their long
series of "9"s, against Wolfram Research's "Mathematica" version 3.0
for Macintosh. I used variations on these three commands:
Statistics'ContinuousDistributions'
$MaxExtraPrecision = 2000
N[CDF[FRatioDistribution[1, insertdegreesfreedomhere], Fratiogoeshere], 500]
This computation uses symbolic representations for numbers to simulate
many digits of precision, and is therefore a very slow process. A
single evaluation by "Mathematica," like the one needed to test the
case below, can take hours on my 266 MHz Mac G3 Power PC. In most
cases I tested, "Mathematica" and my implementation of "BETAI" agreed
on the number of "9"s; occasionally, they differed by a single 9 digit.


Here are the results for 124 years of GISS global land and sea data:
Rxy 0.833087 Rxy^2 0.694034
TEMP = 13.666145 + (0.004797 * (YEAR-1879))
Degrees of Freedom = 122 F = 276.73745
Confidence of nonzero correlation = approximately
0.99999999999999999999999999999999 (32 nines), which is darn close to 100%!
[snip]

I can save you hours of computing time. Use the calculator at
http://members.aol.com/iandjmsmith/FEX.HTM

Set it to calculate 1 - F distribution. With X = 75.92 and Denominator
df = 73 you get
Cumulative probability = 6.429602941527236e-13, so the F value is
1-6.429602941527236e-13

With X = 276.73745 and Denominator df = 122 you get
Cumulative probability = 3.644936641931845e-33, so the F value is
1-3.644936641931845e-33

I think you'll find lots of calculators can do the calculation this
accurately if they can work with the complement of (i.e. 1 minus) the
F distribution.

Alternatively, if you set the calculator to calculate F distribution,
then enter X = 1/276.73745, Numerator df = 122, Denominator df = 1 and
you'll get the same answer.

Now you can use a most F distribution calculators - even EXCEL gets it
right! It calculates the complement of the F distribution in the first
place so =FDIST(276.73745,1,122) gives 3.644936641694430E-33, a
relative error of approx 6.5e-11.

Ian Smith

"Titan Point" wrote in message
om...
It appears that Crappock is 99.9999999999999999999999999999999%
certain of what climatologists have known for a very long time - that
the earth has been (generally) in a warming phase since records began
124 years ago.

Is this the same Titan Point who just a few years ago was claiming that
there were warnings that the earth was in a cooling phase in the 70's?

Now which is it Titan. Are you lying now, or were you lying then?

Now that is pretty much confidence.
And the oil,aviation and automobile industry is working hard on the missing bit.

(Ian Smith) wrote in message . com...
Roger Coppock wrote in message ...
[snip]
I would have added this feature earlier, but the 124-year record
shows warming so very strongly that special attention is required
to evaluate the "F distribution function" correctly. In most cases,
a simple table listing "F" values for 95% and 99% confidence will
do. (For an example, see this table from the "CO2 Science" site:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

I have therefore used the "BETAI" routine from "Numerical Recipes"
by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and
William T. Vetterling in 1986. My results pass the test routines
provided by the authors, and they match the table from "CO2 Science"
as well. I've also checked my more extreme results, with their long
series of "9"s, against Wolfram Research's "Mathematica" version 3.0
for Macintosh. I used variations on these three commands:
Statistics'ContinuousDistributions'
$MaxExtraPrecision = 2000
N[CDF[FRatioDistribution[1, insertdegreesfreedomhere], Fratiogoeshere], 500]
This computation uses symbolic representations for numbers to simulate
many digits of precision, and is therefore a very slow process. A
single evaluation by "Mathematica," like the one needed to test the
case below, can take hours on my 266 MHz Mac G3 Power PC. In most
cases I tested, "Mathematica" and my implementation of "BETAI" agreed
on the number of "9"s; occasionally, they differed by a single 9 digit.


Here are the results for 124 years of GISS global land and sea data:
Rxy 0.833087 Rxy^2 0.694034
TEMP = 13.666145 + (0.004797 * (YEAR-1879))
Degrees of Freedom = 122 F = 276.73745
Confidence of nonzero correlation = approximately
0.99999999999999999999999999999999 (32 nines), which is darn close to 100%!
[snip]

I can save you hours of computing time. Use the calculator at
http://members.aol.com/iandjmsmith/FEX.HTM

Set it to calculate 1 - F distribution. With X = 75.92 and Denominator
df = 73 you get
Cumulative probability = 6.429602941527236e-13, so the F value is
1-6.429602941527236e-13

With X = 276.73745 and Denominator df = 122 you get
Cumulative probability = 3.644936641931845e-33, so the F value is
1-3.644936641931845e-33

I think you'll find lots of calculators can do the calculation this
accurately if they can work with the complement of (i.e. 1 minus) the
F distribution.

Alternatively, if you set the calculator to calculate F distribution,
then enter X = 1/276.73745, Numerator df = 122, Denominator df = 1 and
you'll get the same answer.

Now you can use a most F distribution calculators - even EXCEL gets it
right! It calculates the complement of the F distribution in the first
place so =FDIST(276.73745,1,122) gives 3.644936641694430E-33, a
relative error of approx 6.5e-11.

Ian Smith

Nicolas S wrote:

Now that is pretty much confidence.
And the oil,aviation and automobile industry is working hard on the missing bit.

The tricksters hired by the fossil fuel industry
will just ignore this, and very many other truths.



(Ian Smith) wrote in message . com...
Roger Coppock wrote in message ...
[snip]
I would have added this feature earlier, but the 124-year record
shows warming so very strongly that special attention is required
to evaluate the "F distribution function" correctly. In most cases,
a simple table listing "F" values for 95% and 99% confidence will
do. (For an example, see this table from the "CO2 Science" site:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

I have therefore used the "BETAI" routine from "Numerical Recipes"
by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and
William T. Vetterling in 1986. My results pass the test routines
provided by the authors, and they match the table from "CO2 Science"
as well. I've also checked my more extreme results, with their long
series of "9"s, against Wolfram Research's "Mathematica" version 3.0
for Macintosh. I used variations on these three commands:
Statistics'ContinuousDistributions'
$MaxExtraPrecision = 2000
N[CDF[FRatioDistribution[1, insertdegreesfreedomhere], Fratiogoeshere], 500]
This computation uses symbolic representations for numbers to simulate
many digits of precision, and is therefore a very slow process. A
single evaluation by "Mathematica," like the one needed to test the
case below, can take hours on my 266 MHz Mac G3 Power PC. In most
cases I tested, "Mathematica" and my implementation of "BETAI" agreed
on the number of "9"s; occasionally, they differed by a single 9 digit.


Here are the results for 124 years of GISS global land and sea data:
Rxy 0.833087 Rxy^2 0.694034
TEMP = 13.666145 + (0.004797 * (YEAR-1879))
Degrees of Freedom = 122 F = 276.73745
Confidence of nonzero correlation = approximately
0.99999999999999999999999999999999 (32 nines), which is darn close to 100%!
[snip]

I can save you hours of computing time. Use the calculator at
http://members.aol.com/iandjmsmith/FEX.HTM

Set it to calculate 1 - F distribution. With X = 75.92 and Denominator
df = 73 you get
Cumulative probability = 6.429602941527236e-13, so the F value is
1-6.429602941527236e-13

.. . . or better than 12 nines, which is what my software reports.



With X = 276.73745 and Denominator df = 122 you get
Cumulative probability = 3.644936641931845e-33, so the F value is
1-3.644936641931845e-33

I think you'll find lots of calculators can do the calculation this
accurately if they can work with the complement of (i.e. 1 minus) the
F distribution.

Alternatively, if you set the calculator to calculate F distribution,
then enter X = 1/276.73745, Numerator df = 122, Denominator df = 1 and
you'll get the same answer.

Now you can use a most F distribution calculators - even EXCEL gets it
right! It calculates the complement of the F distribution in the first
place so =FDIST(276.73745,1,122) gives 3.644936641694430E-33, a
relative error of approx 6.5e-11.

. . . or better than 32 nines as my software reports.

Thank you Ian! I never thought to use either a
page on the Internet, or a calculator. It looks
like everybody is in agreement. At these extremes,
where we are so close to 100% certain, I'll just
report the number of nines. The Incomplete Beta
function is so nonlinear that it amplifies the
smallest change in its inputs, so reporting any
significant figures would be misleading. The folks
at Heartland, Cato, CO2 'Science,' and other PR
firms hired by the industry are already making more
than enough misleading statements on this issue.
I don't plan to add to the confusion.



Ian Smith

--

"One who joyfully guards his mind
And fears his own confusion
Can not fall.
He has found his way to peace."

-- Buddha, in the "Pali Dhammapada,"
~5th century BCE


-.-. --.- Roger Coppock )


-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

Roger Coppock wrote:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

The above numbers assume that the values for successive years may be
considered independent. The actual number of degrees of freedom should
be estimated from the lag-one autocorrelation of the data set (that
auto-correlation is almost certainly 0).

Second, while the trend in the data set itself might be highly certain,
there remains some controversy over whether the data set accurately
reflects the actual trend in global temperature, or whether the trend is
an artifact of the measurements themselves (e.g. heat island effect, etc.)

I say this as one who believes that the globe is probably getting
warmer. But I want any claims to have *proven* this to be able to
withstand close scrutiny.

Grant wrote:

Roger Coppock wrote:
http://co2science.org/ushcn/ftable.htm) However, the positive
slope regression lines of global warming in temperature data series
have been more than 99% certain for over a half-century now.
(The positive correlation from 1880 to 1954 in the GISS land and
sea data set is about 99.9999999999% certain, with 73 degrees of
freedom and F = 75.92.)

The above numbers assume that the values for successive years may be
considered independent. The actual number of degrees of freedom should
be estimated from the lag-one autocorrelation of the data set (that
auto-correlation is almost certainly 0).

Then please take us step-by-step through the lag-one auto-correlation
of the data set and produce your estimate of the number of degrees of
freedom. The URL to the data set was listed in my original post, the
part you snipped.



Second, while the trend in the data set itself might be highly certain,
there remains some controversy over whether the data set accurately
reflects the actual trend in global temperature, or whether the trend is
an artifact of the measurements themselves (e.g. heat island effect, etc.)

As the snipped part of my original post said, the land data used were
corrected for the Urban Heat Island effect; the sea data did not need
to be.



I say this as one who believes that the globe is probably getting
warmer. But I want any claims to have *proven* this to be able to
withstand close scrutiny.

--

"One who joyfully guards his mind
And fears his own confusion
Can not fall.
He has found his way to peace."

-- Buddha, in the "Pali Dhammapada,"
~5th century BCE


-.-. --.- Roger Coppock )


-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

Roger Coppock wrote:
Then please take us step-by-step through the lag-one auto-correlation
of the data set and produce your estimate of the number of degrees of
freedom. The URL to the data set was listed in my original post, the
part you snipped.

Why me? I'm not the one asserting that global warming is
99.999999999999999999999999999999% Certain!

Personally, I don't think it should make much difference to reasonable
people whether it's 99.999999999999999999999999999999% certain or merely
99% certain. And the latter claim will be far easier to prove without
the help of questionable assumptions.


As the snipped part of my original post said, the land data used were
corrected for the Urban Heat Island effect; the sea data did not need
to be.

Fair enough. Not sure how accurately the magnitude of the heat island
effect is even known, though. I'm 99.9999% certain, however, that it's
not known with 99.999999999999999999999999999999% confidence.