How much warming over the last 16 years is required for a statistically significant increase?

In general, nonparametric tests like Mann-Kendall or Spearman's rho are less sensitive to normality issues than the parametric t-test.

More importantly, you need to think about what you are really asking and if the test can give you an answer.

Every test is going to give you an answer - including tests that cannot answer the question you are asking.

Regardless of whether you use a t-test or some other test - the answer you get depends on where you start and where you stop - and that determines whether you get a Bullshlt answer or not.

If you look at global temperature through a 16-year window and run a t-test each time, the t-test will always give you either a 'significant' or 'not significant' answer - depending on where you happen to be looking - because that is what, and all that, the test does - the validity of the test and the test results are the researcher's responsibility.

As for you question, specifically: There is no finite solution because it not only depends on the slope, variance, and degrees of freedom - but also on where you set the p-value (significance level).

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Bing --

>>which have triggered debate among climate scientists<<

No it has not - and there is no reason reason that it would. It has no effect on AGW theory, and if you knew anything about science and had some math skills you would understand why.

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Sage --

>>CR: Wrong again! <<

No, Sage you are wrong again. The truth is that you do not understand one damn thing on the webpage your reference. You lack the education and knowledge to know if you are right - so there is no way you can know whether anyone else is.

Here is what you are doing: You are like someone who flips through a book in a foreign language they do not understand - and then argues with a native speaker of the language about the book's contents.

When my daughter was in the 7th grade, I tried - unsuccessfully - to teach her how to do those algebra word problems where two trains are leaving Chicago and New York, blah, blah, blah. However, one day she said, "You can think with numbers just like people think with words?" I said, "yes" and she said, "Ok, now I get it."

She, of course, did not mean she "got it" as in she "got the math." What she had figured out was that math is a language - a language she did not know. She figured out in junior high school something that adult Deniers still do not understand. She was also honest enough to live with the fact that she knew she did not understand it - and that is quality of character that adult Deniers do not have.

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phil ---

>>and even those are not worth a crap scientifically<<

How would you know? Oh, that's right, you wouldn't know - you're too stupid to know anything about scientific data.

Years ago during a discussion with a well known consultant and expert in statistical analysis, he mentioned the following to me and a few others during a difficult assessment of an unwanted variation in one of our manufacturing processes. In so many words... "At some point in your analysis you might have to take a step back and reassess. It is so easy to look at a certain set(s) of data and get caught up in the many ways to analyze it (different confidence levels bands, tests if outliers, differences of significance, etc. etc.). These are important, but far too often engineers get caught up in trying to prove what they think is right and totally disregarding an important factor(s) and what might actually be proving that they are wrong. I'm convinced, that many engineers (and presumably scientists) simply cannot do this after they have gone about something for a long time. It is human nature not to give up. But at some point, you need to take a step back, and throw it on the wall to see if it sticks against all reason, If it doesn't, you may need to restate your whole objective." These words and my own experiences have left me with a hearty skepticism that has been proposed in many field of this study of climate change.

I'm no time series analysis expert, but my opinion is that you can't use standard t-tests for comparing means of time series data because the assumption of independence is immediately violated in time series data and, no, I don't think anomaly data would follow a normal distribution (but what do I know?).

I would think that significant warming would mean that deltaT is significant in relation to time, but your method of comparing means from two different time periods seems like it should at least provide some inkling of information.

Linear regression can be use to test for significance but this violates the independence assumption the same as other parametric methods. I can run simple regression tests with a graphing software package I have if you'd like to send me the data somehow.

Across two decades and thousands of pages of reports, the world's most authoritative voice on climate science has consistently understated the rate and intensity of climate change and the danger those impacts represent, say a growing number of studies on the topic.

The GISS data is not fake. James Hansen put his career on the line to stand up to the Bush administration. People lie when the stand to profit from the lie, or if they are afraid of people knowing the consequences of the truth. If James Hansen were willing to lie for financial gain, he would have been Dubya's best buddy when the U.S. withdrew from Kyoto. And don't forget the $1 billion check which Exxon will mail to Dr. Hansen the day he recants.

Sagebrush

What is a video of a graph taped to a see-saw supposed to prove?

It's amazing how many times this same discussion keeps coming up, especially after I've posted a link repeatedly to a fairly understandable paper that addresses these sorts of questions. Liebmann et al look at EVERY trend for every time interval greater than 2 years in the HadCRUT3 data from 1850--2009. They discuss how to test for significance and do it multiple ways and show plots of significance for ALL the possible intervals. People need to start looking at this link.

http://www.esrl.noaa.gov/psd/people/brant.liebmann...

At least I know that Koshka has been paying attention, she gave the link in her answer to another question this morning.

EDIT: Sagebrush, your example of the polling data is an example of the (incorrect) reasoning that the Romney supporters used to convince themselves that Romney would win. If a poll is split 43/42 with a 3% margin of error that is not a tie. We could simulate such a thing with random numbers and make even money bets, and if you bet on 42 and we did this enough times, you would lose all your money...kind of like Romney and all his SuperPACs.

Don't use the term "statistical" if you don't know what you are talking about, and obviously you don't. One cannot do a statistical analysis without controlling for known variances. That is basic high school statistics.

You must either control for the effects of the ENSO, or state your observation accurately and honestly. You are picking 16 years ago because you wish to say there is little nominal difference in average temperatures specifically in the lower atmosphere. You are leaving the oceans out. Why? Either because you are stupid or because you are a political hack. We know the oceans have warmed because of the ongoing sea level rise. And we know the lower atmosphere temperature is affected by the ENSO because more ice cold water from the deep ocean during a La Nina causes the oceans to absorb more of the heat.

You might review the work done by statistician David Brillinger. He does no make the basic statistical errors that you do.

http://berkeleyearth.org/results-summary/

You might want to look at Tamino's blog, particularly this post (though it deals with how long a trend must be to be called 'statistically significant' rather then how much warming would be required within a 16 year time frame): http://tamino.wordpress.com/2012/07/06/how-long/

I find his blog highly informative in general so I do advice you browse it a bit.

The world stopped getting warmer almost 16 years ago, according to new data released last week.

The figures, which have triggered debate among climate scientists, reveal that from the beginning of 1997 until August 2012, there was no discernible rise in aggregate global temperatures.

This means that the ‘plateau’ or ‘pause’ in global warming has now lasted for about the same time as the previous period when temperatures rose, 1980 to 1996. Before that, temperatures had been stable or declining for about 40 years.

Just off the top of my head I would think that the measurement error bars (or measurement uncertainty) would need to be included.