A couple weeks ago, Seth Borenstein from the Associated Press published an astonishingly bad piece of climate science journalism on The Big Story board entitled "US hottest spots of warming: Northeast, Southwest."

I debunked this AP story here soon after it was released.  In short, the AP had claimed to use "the least squares regression method" to analyze National Climatic Data Center temperature trends in the lower 48 states, 192 cities, and 344 smaller regions within the states between 1984 and 2013.  The AP then reported that "all but one of the lower 48 states have warmed since 1984" and that "92 percent of the more than 500 cities and smaller regions within states have warmed" since 1984.

As I noted in my previous article:

Here is what happened. The AP used 'the least squares regression method' to calculate the annual temperature trend for all these regions, but then proceeded to ignore entirely whether the regression method indicated if the trend was statistically significant (the typical criteria would be a p-value<0.05).

This is first-year statistics level stuff. Quite simply, if your statistical test ('least squares regression method') tells you the trend isn't significant, you cannot claim there is a trend, since the null hypothesis (i.e., no trend) cannot be rejected with any reasonable degree of confidence.

When I reanalyzed the data using the same approach the AP did – except I didn't ignore the statistical significance of the results, or lack thereof – I found that the AP should have reported that only 18 of the lower 48 states have statistically significant warming trends since 1984, and that only 31 percent of the cities and smaller regions within states have significant warming trends over this period, not the absurdly high 92 percent that the AP claimed.

It has also been noted by other critics that the AP should not necessarily have used parametric linear regression when analyzing the U.S. temperature trend data, because this type of statistical analysis makes a number of assumptions that the climate data may not meet.  This is a valid point, although the use of parametric linear regression to analyze for climate trends – as the AP employed – is common in the scientific literature.

It can be best to employ both parametric and non-parametric methods to analyze many types of climate data, and then compare the results to see if they tell the same story.  The non-parametric approaches do not make the same assumptions regarding the data, and are often more robust for time trend analyses.

So, just to close the loop on this fatally flawed AP article, I reanalyzed the temperature dataset using the non-parametric Mann-Kendall trend test – an approach very commonly used in the scientific literature for analyzing climate data.

With the Mann-Kendall test, only 16 of 48 (i.e., 33 percent) of the states have significant warming trends since 1984, down slightly from 37 percent using parametric regression (Connecticut and Oklahoma move from significant to non-significant).

Among the nine climate regions in the contiguous USA, the same three (the Northeast, South, and Southwest) have significant warming trends using both parametric and non-parametric methods.  The other two-thirds of the climate regions have no significant warming trends, no matter how you want to look at the data.

Using parametric regression, 99 of 338 individual climate subdivisions (29 percent) have significant warming trends.  With non-parametric analysis, this drops to 89 (26 percent).  Among the cities with complete datasets, the number (out of 86) having significant warming trends drops to 31 (36 percent) from 32 (37 percent) when we move to a non-parametric analysis.

Overall, the AP claimed that "92 percent of the more than 500 cities and smaller regions within states have warmed" since 1984.  Parametric analysis yields only 31 percent with a significant warming trend.  Non-parametric analysis gives only 28 percent.  Effectively, the same results are obtained regardless of the statistical approach – providing it is done correctly, which the AP failed to do.

Whatever way you want to tackle the problem, the results are equivalent.  Only a small number of regions within the United States have warmed over the past three decades.  Readers of the AP article would be left thinking that somewhere between 92 and 98 percent of the United States has warmed since 1984, when the true answer is around 28 to 37 percent.

The AP article in question is a disaster from all statistical perspectives when it comes to communicating rigorous climate science to the public.  On key policy issues such as climate change, the bar for science journalism at the AP needs to be set much higher.