On July 15, Katharine Hayhoe – an “Associate Professor in the Public Administration program at Texas Tech University and Director of the Climate Science Center at Texas Tech,” one of the most well-known climate scientists (her Twitter account states she is one of the “2014 TIME100”), and a “lead author for the 2014 Third U.S. National Climate Assessment” – sent out the following tweet.

So what Hayhoe has provided are the NASA-GISS global land-ocean temperature index anomalies (in degrees Celsius) between 1997 and 2013 (i.e., the last 17 years).  You can download the raw data here to follow along and “plot it yourself,” as Hayhoe suggests.

Hayhoe states in no uncertain terms that it is a lie to claim that “it hasn't warmed in 17 years.”  Well then, apparently those practicing rigorous science are lying, because that data Hayhoe provided shows that “it hasn't warmed in 17 years.”  It's a telling statement of how far academia has fallen that anyone within the academy would send out such unscientific nonsense.

Anyone can take a dataset, as Hayhoe has done; hit the proverbial right-click button on the mouse; and insert a linear regression trendline.  But does that mean you obtain anything useful?  Most certainly not. Just because the trendline has a positive (as shown in the plot Hayhoe sent out) or negative slope does not in any way mean that that slope is statistically significant.  And if the slope is not statistically significant, you cannot – with any reasonable degree of confidence – reject the null hypothesis that the slope is equal to zero and that any patterns are due to random chance.

Many without a statistical background may be asking, how this is possible?  How can you possibly end up generating a positive or negative correlation using linear regression out of a random sequence?  Here is their opportunity for a demonstration.  If I go to a website that will generate 17 random numbers for me, such as this one, and then plot the 17 random numbers in the sequence they were generated, won't I always get a slope perfectly equal to zero (aka a flat line)?

Nope.  In fact, the odds of getting a perfectly zero slope from a sequence of 17 random numbers is infinitesimal.  Thus, if you generate 17 random numbers and plot their sequence, you will essentially always get a non-zero slope (either positive or negative).

And this is exactly why those practicing rigorous science don't just mindlessly insert linear regression trendlines on time series datasets (e.g., global temperatures) without also providing the readers with information as to whether or not the regression is statistically significant.  If the regression isn't statistically significant, your positive or negative correlation could be entirely due to chance.

I went to my random number generating website and generated three separate sequences of 17 random numbers each with values between 1 and 100. Here they are, along with a linear regression fit on each dataseries.

Well, look at that.  On my very first trial of random number generation, I obtained a sequence of random numbers giving a negative correlation with near statistical significance (p=0.10; a p-value of less than 0.05 is the typical criterion for statistical significance in science).  With my second random number generation trial, I got a series of random numbers yielding a modest positive correlation (not statistically significant), and with the third random number trial there was a shallow negative correlation.

In short, this experiment demonstrates exactly why we demand that rigorous science use some agreed upon measure of statistical significance when examining for trends.  In science, that measure is typically a p-value of less than 0.05 (essentially a 95% probability of the trend not being due to chance), although it could be argued for such important policy issues as climate change (whereby action would necessitate a near-complete alteration to our entire socio-economic and political structures and relationships) that we should be demanding even higher statistical significance (i.e., a p-value of 0.01 or lower, or a 99% probability of the trend not being a result of chance).

Perform the experiments yourself to test my claims, and if you need free spreadsheet programs to generate graphs and add linear regression trendlines, see here and here.  Let's call it a citizen science project, something the environmental activists are fond of.

The plot Hayhoe provided is absolutely useless for the simple reason she failed to discuss the statistical significance of the trendline – or lack thereof.  So I did what Hayhoe should have done before tweeting a statement that those practicing rigorous science are peddling lies, I examined whether the data she provided shows any statistically significant trend in global temperatures since 1997.  And it unequivocally does not, regardless of whether you employ parametric or non-parametric methods of analysis.  Actually, my first random number sequence was closer to having a statistically significant trend than is Hayhoe's global temperature dataset.

Thus, using rigorous science, we would say there is no statistically significant trend in global temperatures since at least 1997, which is generally stated more simply as there has been no trend in global temperatures for at least the past 17 years – since if a trend obtained using statistical tools isn't statistically significant, by definition there is no trend.

Hayhoe is wrong.  The conclusion from a rigorous examination of the data she provided is, in fact, that “it hasn't warmed in 17 years.”  End of story.  The climate activists can call me back with their hysteria once the recent trend reaches generally agreed upon statistical significance.  And note to the activists – especially those in academia and government: stop your war on science and start using statistical tests when you are discussing data in public.  Otherwise, you are not conducting rigorous science and are simply contributing to a poor understanding of science by your public audience.