Let me give you two examples. Let's say that I gave some American, English-speaking students a true-or false test in Swahili, and told them to fill it in. Their results, in other words, would be random, and you would expect (with a large enough sample size) that the average score would be right around 50%.
That doesn't mean, of course, that everyone got 50%. Again, with a large enough population of test-takers, the scores would very likely fall on a normal distribution (also known as a "bell curve"). So far, nothing surprising here.
But suppose you took the top 5% of the test-takers -- the ones who scored well above the mean score of 50% -- and asked them to take a second test, this one written in Latvian. What would happen to their scores?
The answer, of course, is that virtually all of them would fall -- not because they suddenly got stupider, but because their first scores were so far outside the norm that their second is extremely likely not to be. If you gave all of the original students the test in Latvian, there would once again be that 5% who got anomalously high scores -- but it almost certainly wouldn't be the same students.
It doesn't need to be a random process to generate a regression to the mean. I see this happening all the time with my students, who (I hope) aren't simply guessing answers randomly. As a second example, let's say we have a kid who usually scores around 85%, and then she scores a 65% on a twenty-point quiz. Her next score is pretty likely to rise -- even assuming that she studied the same amount on both of them. The 65% was simply an anomalous low score. Bouncing back up to 85% could just be a regression to the mean, especially given (1) how many factors can be involved in missing questions on quizzes, and (2) the fact that the difference between a 65% and an 85% on a twenty-point quiz is only four additional questions correct.
It's the reason why so many people expect "lucky streaks" (or unlucky ones) to keep going -- and they almost never do. You're much more likely to see a regression to the mean sooner rather than later (or a "correction," as they call it in the stock market.)
So, the question I'm sure you're all asking by this point is: how does this relate to climate change?
Some of you may have seen recent articles, mostly in conservative media outlets, that have headlines like this one from The Daily Caller: "Global Warming? Satellite Data Shows Arctic Sea Ice Coverage Up 50%!" The author, Michael Bastasch, writes:
The North Pole is still there, and growing. BBC News reports that data from Europe’s Cryosat spacecraft shows that Arctic sea ice coverage was nearly 9,000 cubic kilometers (2,100 cubic miles) by the end of this year’s melting season, up from about 6,000 cubic kilometers (1,400 cubic miles) during the same time last year...Oh, those poor scientists, always "struggling to explain away" stuff. Well, sorry, Mr. Bastasch, but no climate scientist I've ever heard of has trouble understanding regression to the mean -- which is what you and your climate-denier friends, in your apparent ignorance, are referring to as a "pause."
This is good news for the Arctic, but presents somewhat of a tough problem for environmentalists and some climate scientists who have been pummeled with evidence this year contradicting the theory of man-made global warming.
Scientists have been struggling to explain away the 15-year pause in rising global temperatures. Some have turned to solar activity or natural climate cycles to explain the hiatus in warming.
Amusing, too, that The Daily Caller chose to illustrate their article on Arctic sea ice with a photograph of ice... that includes a penguin:
Be that as it may, let's see what an actual climate scientist has to say about this year's miraculous rebound, okay? Here's what Andrew Shepherd, climatologist at University College London, has to say about the situation (quoted in an article in The Independent):
"The 9,000 cubic kilometres we measured in October is still very much smaller than the 20,000 cubic kilometres we estimate for the same time in the early 1980s. So today's minimum still ranks among the lowest for the past 30 years," Professor Shepherd said. "The October figure is still a significant result and it's not to be underestimated, but it's not an unexpected result. We do see year-to-year variations in the sea ice due to changes in weather patterns."Oh, and then there's this quote, from David Kennedy, deputy undersecretary for operations at the National Oceanic and Atmospheric Administration: "The Arctic caught a bit of break in 2013 from the recent string of record-breaking warmth and ice melts of the last decade. But the relatively cool year in some parts of the Arctic does little to offset the long-term trend of the last 30 years: the Arctic is warming rapidly."
In other words: the previous years' ice coverage was so low that sooner or later, there was bound to be a cooler year. It's just regression to the mean, even if the overall trend is still obvious to anyone who is not willfully blind.
Scientists look at patterns, not at cherry-picked data points that happen to support their favorite biases -- unlike the agenda-driven climate deniers who are (with luck) decreasing in number as the data piles up. And the data is piling up. NOAA's National Climatic Data Center just released November's Global Climate Report, and reported that the globally-averaged sea and land temperatures for November were the highest for that month since record keeping began in 1880. "Aha," the deniers might say. "Couldn't this just be an anomalously high number, just like our kid who got a 90% on a Swahili test that he couldn't read? Aren't you committing just what you said was a statistical fallacy, in your opening paragraphs?"
Sure, could be. Until you add the second thing that this month's report announced; that this is the 37th consecutive November, and 345th consecutive month, with an average temperature higher than the 20th century mean.
That, my friend, is a trend. Show me a kid who can score higher than the mean on a test in Swahili 345 times in a row, and I'll show you a kid who is lying about the fact that he can actually read Swahili.
So, yeah. Slam dunk. Not that I expect that this will change the minds of the climate change deniers, any more than the retraction of the Seralini study will change the minds of the anti-GMO crowd, or the retraction of the Wakefield study will change the minds of the anti-vaxxers. But it is becoming clearer and clearer that the people who are denying the existence of anthropogenic climate change are deliberately misinterpreting the data, or else ignoring it entirely. The scientists, however they are portrayed as "struggling," seem to have a pretty good consensus about what is happening.
But unfortunately, nobody much seems to be explaining all of this to the layperson, leading lots of them to believe what the media is claiming -- that the climate is yo-yoing all over the place, and no one knows why, not even the scientists. But what started out as legitimate questioning, back in the 1980s when the alarm bells on climate change first began to sound, has now turned into nothing more than "la-la-la-la-la-la-la, not listening." Agenda-driven political organizations like the Heartland Institute are, at this point, no longer simply pointing out uncertainties in the data and analysis; they are lying outright.
To buy that this regression to the mean in the Arctic pack ice coverage is significant, and means that climate change isn't happening, requires you simultaneously to ignore a mountain of other data. Meaning that you are coming to that conclusion for some other reason than science. But the deniers don't want you to know that -- because a confused populace, who thinks that no one can know what's causing climate shifts and that (anyway) we couldn't do anything about it even if we did, is much more likely to vote to keep doing what we've always done.
Convenient for the powers-that-be, isn't it?