Aha, I misunderstood which chart you had in mind. I thought that your link was intended to go to the data for 17 year olds, but that you were unable to link it directly because the page used Javascript to flip between the charts for different ages. I see now I’m wrong about that—one can link directly to the chart for each age, and it sounds like you were pointing to the age 9 data.
So I’ll try this again with the 9 year olds. I’ve taken the liberty of looking at the black-white gap graph instead of the scale score graph so I don’t have to do any mental arithmetic to get the gap size at each testing. Looks to me like the gap consistently narrowed from 1973 to 1986, and has fluctuated from 1986 so it’s sometimes wider, sometimes thinner, but no overall trend since then.
Regressing gap size on year like I did before gives a shrinking of .24 or .25 points per year. So the picture is more mixed than for the older kids: there’s an overall shrinking, but it’s only two-thirds what you get for 17 year olds, and the trend looks like it’s stalled since the late 80s.
Still, I am not sure that this means Nisbett is wrong. Looking at the bit of Nisbett you quote yourself downthread, Nisbett does not seem to say anything about the math scores, which means looking at the math scores would not tell us whether Nisbett is wrong or right.
It is possible that Nisbett cherry-picked by ignoring the math data, but I think a .25 point per year narrowing is still evidence against that idea. At a quarter point per year, the math gap would disappear in about a century, which isn’t much longer than the 75 years Nisbett suggests for science.
Of course there are ways to interpret the graph to argue that the gap is narrowing and on track to disappear, but if you look at it and use your common sense, it’s just not a reasonable conclusion.
The reasonable conclusion—as you allude to—is that the gap has been pretty much stable for a number of years.
Of course there are ways to interpret the graph to argue that the gap is narrowing and on track to disappear, but if you look at it and use your common sense, it’s just not a reasonable conclusion.
You put more trust in your common sense than I do. I try to avoid depending exclusively on what my common sense infers from eyeballing noisy time series—that way lies ’global warming stopped in 1998’esque error.
I find your preferred interpretation reasonable, but I don’t see why it would be unreasonable to look at the entire data and see a net narrowing. (Especially if we lacked the 2008 data, as Nisbett did.)
If the choice is between trusting your common sense and trusting someone with an agenda, I would say go with your common sense.
Here’s a thought experiment: You show the graph I linked to to 10 statisticians, except you replace the labels with something less politically charged. For example, the price of winter wheat versus the price of summer wheat. And you ask them to interpret the graph as far as long term trends go. I’m pretty confident that 10 out of 10 would interpret the graph the same way I did.
Ditto for global surface temperatures. Take the temperature label off the graph and tell people it’s the dollar to yen exchange rate. I bet 10 out of 10 statisticians will say the rate is basically flat for the last 10 years.
Ditto for global surface temperatures. Take the temperature label off the graph and tell people it’s the dollar to yen exchange rate. I bet 10 out of 10 statisticians will say the rate is basically flat for the last 10 years.
cupholder has the empirical data—which, you will note, is increasing in all cases—but do you really imagine that no-one’s tried a blind test?
cupholder has the empirical data—which, you will note, is increasing in all cases—but do you really imagine that no-one’s tried a blind test?
No I do not imagine so. But I’m a little confused. Are you saying that the absence of significant cooling is the same thing as the presence of significant warming?
PS: The empirical data is not “increasing in all cases.” Indeed, by most accounts global surface temperatures have not met or exceeded the high reached 12 years ago.
Every 10-year trendline in cupholder’s data was increasing.
If you give a statistician the 30-year or 130-year data set with the y-axis label taken off, they will tell you that there is no sign of a levelling-off.
Every 10-year trendline in cupholder’s data was increasing.
A quick clarification: for each of the data links I posted there, the trendline is calculated based on all of the data that’s shown, i.e. for the post-1998 data the trendline is based on the last twelve years, for the post-1970s data the trendline is based on all of the post-1970s data, and so on. In other words, only the data for the last 10 years of data really have a 10-year trendline.
[ETA: Unless you mean you calculated 10-year trendlines for each data set yourself, in which case feel free to disregard this.]
The linear trend is definitely decreasing for this particular plot.
If you give a statistician the 30-year or 130-year data set with the y-axis label taken off, they will tell you that there is no sign of a levelling-off.
I’m seriously skeptical of this.
P.S. Are you saying that the absence of significant cooling is the same thing as the presence of significant warming?
Note that changing the beginning data point to either 1997 or 1999 makes the regression line have a positive slope. It’s not at all surprising that there is enough variability that cherry-picking data is possible. Stuffing a positive outlier at the beginning will, of course, tend to do this.
Note that changing the beginning data point to either 1997 or 1999 makes the regression line have a positive slope.
Agreed. I cherry-picked 1998 as a starting point to counter the claim that the data was increasing “in all cases.”
Still, I would also note that as I explain on my blog post, there is some significance to the observation that global surface temperatures still have not exceeded the 1998 high. (According to the majority of leading temperature measurements.)
In a blind test, the AP gave temperature data to four independent statisticians and asked them to look for trends, without telling them what the numbers represented. The experts found no true temperature declines over time.
“If you look at the data and sort of cherry-pick a micro-trend within a bigger trend, that technique is particularly suspect,” said John Grego, a professor of statistics at the University of South Carolina.
[...]
The AP sent expert statisticians NOAA’s year-to-year ground temperature changes over 130 years and the 30 years of satellite-measured temperatures preferred by skeptics and gathered by scientists at the University of Alabama in Huntsville.
Statisticians who analyzed the data found a distinct decades-long upward trend in the numbers, but could not find a significant drop in the past 10 years in either data set. The ups and downs during the last decade repeat random variability in data as far back as 1880.
Saying there’s a downward trend since 1998 is not scientifically legitimate, said David Peterson, a retired Duke University statistics professor and one of those analyzing the numbers.
Identifying a downward trend is a case of “people coming at the data with preconceived notions,” said Peterson, author of the book “Why Did They Do That? An Introduction to Forensic Decision Analysis.”
1998 was a strong El Nino year—unusually high atmospheric temperatures that year in no way suggests that the earth has stopped heating.
I’m claiming that this one data set does not by itself support rejection of the body of theory that suggests global warming is occurring, and that it is intellectually dishonest to imply that it does.
Well answered (and I have downvoted brazil for trying to coerce you into making a stupid claim with the obvious intent of presenting a misleading dichotomy.)
I’m not sure what the claim “global warming is occuring” means so I can’t really speak to that.
In any event, as I noted in the blog post, the warmists have made specific predictions. The temperature record for the past 10 or so years contradicts some of those predictions.
ETA: Can I take it that your answer to my question is “no”?
I’m not saying the absence of a significant cooling trend is the same thing as the presence of a significant warming trend—that would be a stupid thing to say. As for the remainder: I don’t trust your judgment, but the data you provided is interesting. I will examine the composite NOAA temperature data (ocean, land, and combined) and update accordingly.
(It should be noted, however, that if anthropogenic inputs are significant, as claimed by the climate scientists whose work we are discussing, predicting the climate would require predicting all anthropogenic climate forcings—and therefore we might expect the predictions to be worse than anticipated.)
It should be noted, however, that if anthropogenic inputs are significant, as claimed by the climate scientists whose work we are discussing, predicting the climate would require predicting all anthropogenic climate forcings—and therefore we might expect the predictions to be worse than anticipated.
They can get around this by expressing their predictions as a function of future anthropogenic emissions, thus removing this source of uncertainty.
I’m not saying the absence of a significant cooling trend is the same thing as the presence of a significant warming trend—that would be a stupid thing to say
Correct. Which is why the article you linked to does not contradict the claim I made.
As for the remainder: I don’t trust your judgment, but the data you provided is interesting
Well you shouldn’t trust my judgment. What’s the motto of the British science academy? Something like “Don’t take my word for it.”
Here’s a thought experiment: You show the graph I linked to to 10 statisticians, except you replace the labels with something less politically charged. For example, the price of winter wheat versus the price of summer wheat. And you ask them to interpret the graph as far as long term trends go. I’m pretty confident that 10 out of 10 would interpret the graph the same way I did.
I am far less confident.
Ditto for global surface temperatures. Take the temperature label off the graph and tell people it’s the dollar to yen exchange rate. I bet 10 out of 10 statisticians will say the rate is basically flat for the last 10 years.
If the choice is between trusting your common sense and trusting someone with an agenda, I would say go with your common sense.
That sounds nice, but I don’t know how practical that would turn out to be, in this case or in general. In this particular case, how can I even tell with certainty whether you have ‘an agenda’ or not? And what if the key participants in a debate all have some agenda? It’s very possible that Nisbett has a ‘politically correct’ (not that I like the phrase, but I can’t think of a better way of putting it) agenda, and that Rushton and Jensen have a ‘politically incorrect’ agenda. How do I know, and what do I do if they do? And so on.
In this particular case, how can I even tell with certainty whether you have ‘an agenda’ or not?
How can you tell anything with certainty? The fact is that you can’t. Respectfully, it seems to me you are playing the “I’m such a skeptic” game.
Let me ask you this: Do you seriously doubt that Nisbett has an agenda?
Do you give them data for the past 10 years, data since 1998, the data since they started measuring temperatures with satellites as well as thermometers, or the longest-running data set, which runs from 1850 onwards
I would give them the data since the 1970s when sattelite measurement became possible.
How can you tell anything with certainty? The fact is that you can’t. Respectfully, it seems to me you are playing the “I’m such a skeptic” game.
Sorry. I was being sloppy in my earlier comment, and using ‘certainty’ as a shorthand for ‘certainty enough for me to label you as Having An Agenda, and therefore to reject your interpretation of the data as Tainted With An Agenda.’ It is of course true that you can’t tell anything inductive with cast-iron 100% certainty, but what I’m getting at is the question of how to get to what you or I would practically treat as certainty (like if I put a 95% probability on someone Having An Agenda).
Let me rephrase: in this particular case, how can I even tell whether you have ‘an agenda’ with sufficient certainty to disregard whatever you say about the data, and retreat to my own common sense gut feeling?
Let me ask you this: Do you seriously doubt that Nisbett has an agenda?
Do I doubt he has an agenda in the sense that he believes he’s right? A tiny bit, but only in the sense that I am never completely sure of another person’s motivation for stating something.
Do I doubt he has an agenda in the sense that he wants to convince other people of what he believes? Not really.
Do I doubt he has an agenda in the sense that he has an emotional investment in the argument as well as rational considerations? Only a little...but then again, who doesn’t get emotionally invested in arguments?
Do I doubt he has an agenda in the sense that he has political motivations for his article as well as self-centered emotional and rational ones? Quite a lot, actually. I don’t think I could reliably tell Nisbett’s emotional motivations apart from those that spring from his political agenda (whatever that is—Nisbett sounds like a leftist to me, but how the hell do I really know? There were rightists who crapped on The Bell Curve too.) Does it even make sense to distinguish the two? I’m not sure. (I suddenly feel that these are good questions to think about. Thank you for prodding me into thinking of them.)
Also, for whatever it’s worth, I am just as sure that Rushton and Jensen have ‘an agenda,’ however you want to define that, as Nisbett does. Do I throw all their papers out and just go with my common sense?
To clarify, this doesn’t mean I can’t get behind the idea of being alert to other people’s biases on some subject, but I’m not willing to push that to the point of a dichotomy between my common sense vs. someone with an agenda. Taking the global warming example, I’m sure many climate scientists have ‘an agenda,’ but I’d still tend to accept their consensus interpretation of the data than my own common sense where the two differ, and I think that’s reasonable if I don’t have time to dig through all of the research myself.
I would give them the data since the 1970s when sattelite measurement became possible.
In that case I think I’m roughly 90% confident that fewer than ’10 out of 10 statisticians will say the rate is basically flat for the last 10 years’. I am interpreting ‘the rate is flat here’ to mean that the net temperature trend is flat over time, as I believe we’re talking about whether global warming is continuing and not whether global warming is accelerating. (Thought process here: I reckon a randomly selected statistician has at most a 4 in 5 chance of deciding that temperatures have been ‘basically flat’ for the last 10 years’ based on the satellite data. Then the chance of 10 random statisticians all saying temperatures have been flat is 11%, so an 89% chance of at least one of them dissenting.)
Do I doubt he has an agenda in the sense that he believes he’s right?
By “having an agenda,” I mean that Nisbett is emphasizing the facts that support a particular point of view and de-emphasizing the facts which undermine that point of view in order to persuade the reader.
So defined, one can ask whether Nisbett has an agenda. Do you have any doubt that Nisbett has an agenda?
I am interpreting ‘the rate is flat here’ to mean that the net temperature trend is flat over time,
So by your definition, the temperature trend is NOT basically flat between 1995 and the present, correct?
By “having an agenda,” I mean that Nisbett is emphasizing the facts that support a particular point of view and de-emphasizing the facts which undermine that point of view in order to persuade the reader.
So defined, one can ask whether Nisbett has an agenda. Do you have any doubt that Nisbett has an agenda?
Not much. I think it is very likely that Nisbett suffers from confirmation bias about as much as everybody else.
So by your definition, the temperature trend is NOT basically flat between 1995 and the present, correct?
Eyeballing it I’d say it’s much more likely that temperatures rose since 1995 than that they stayed flat, so I’d say you’re pretty much correct. I wouldn’t dogmatically say it’s not flat in big capital letters, but I think the rising temperature hypothesis is a lot more likely than the flat temperature hypothesis.
I’d double check my intuition by running a regression, but that’d stack the deck because of autocorrelation, and I can’t remember from the top of my head how to fit a linear model that accounts for that.
The fact that you quote this doesn’t help your credibility
I’m not sure what your point is. My argument does not depend on my credibility.
In any event, do you agree that “journalistic malpractice” works both ways? In other words, if it’s malpractice to claim that there has been no warming since 1995, it’s also malpractice to claim that there has been no cooling since 1998?
I’m not sure what this means. Are you saying that every piece of written material has an agenda behind it as I’ve defined the term?
Not every piece of written material, but I’d bet that almost all lengthy pieces of writing intended to communicate a point to others have an agenda behind them, sure. There’s always a temptation to round the numbers to your advantage, to leave out bits of data that might conflict with your hypothesis, to neglect to mention possible problems with your statistical tests, and so on.
Even ignoring that sort of thing, cognitive biases play an important role. Nisbett presumably had a half-formed opinion of the race and IQ argument even before he started researching it in depth. And that would in turn have affected which bits of relevant evidence got stuck in his mind. And that would in turn have hardened his opinion. You get positive feedbacks that push your opinion away from others that conflict with it. So even if Nisbett were consciously being as honest as possible, he could still be
emphasizing the facts that support a particular point of view and de-emphasizing the facts which undermine that point of view in order to persuade the reader
just because his mental database of facts is going to overrepresent the 1st kind of fact and underrepresent the 2nd—and precisely because of that, he is going to be sure that his point of view is obviously correct, and precisely because of that, he is going to be writing to persuade the reader of it—even though, as far as he knows, he is being completely honest!
but I’d bet that almost all lengthy pieces of writing intended to communicate a point to others have an agenda behind them, sure
Ok, and the stronger the agenda, the more you should trust your common sense over claims made by the person with the agenda.
That’s what he said.
Ok, and presumably what he meant was that any warming which took place between 1995 and the present was less than some statistical minimum threshold. I’m not sophisticated enough to calculate such a limit, but that’s what I meant when I said that temperatures have been basically flat for the last 10 years.
Ok, and the stronger the agenda, the more you should trust your common sense over claims made by the person with the agenda.
Cool. I feel more comfortable now that you’ve expressed this in continuous terms. There’s still a catch, though: using your definition of having an agenda, I can’t really tell whether someone has an agenda without also knowing the facts (because ‘having an agenda’ here is being used to mean that someone’s making a slanted presentation of the facts), and if I know the facts already, I have little need for your has-an-agenda heuristic.
Ok, and presumably what he meant was that any warming which took place between 1995 and the present was less than some statistical minimum threshold.
Roughly speaking, I think that’s about right.
I’m not sophisticated enough to calculate such a limit, but that’s what I meant when I said that temperatures have been basically flat for the last 10 years.
I think I understand now. Alrighty...yeah, I would suspect that there’s been no statistically significant warming trend in the last 10 years. I would however avoid using phrases like ‘temperatures have been basically flat for the last 10 years’ to describe this, as I nonetheless believe that if one considers the last 10 years of records in the context of unambiguous past warming, they are consistent with an ongoing, underlying warming trend.
I can’t really tell whether someone has an agenda without also knowing the facts
I would suggest you practice. It also helps to read people who contradict eachother. It also helps if you learn some of the facts.
I would however avoid using phrases like ‘temperatures have been basically flat for the last 10 years’ to describe this, as I nonetheless believe that if one considers the last 10 years of records in the context of unambiguous past warming, they are consistent with an ongoing, underlying warming trend.
Lol, I guess that means American housing prices have been going up the last couple years too.
In any event, I think it’s fair to say that temperatures have been basically flat because it contradicts many of the predictions of the warmists.
I would suggest you practice. It also helps to read people who contradict eachother. It also helps if you learn some of the facts.
I reckon the first two things only help in as much as they help you do the third. Learning the facts is what really matters—and in my experience, once I feel I know enough about an issue to decide who has an agenda (in your sense of the phrase), I typically feel I know enough to make my own judgement of the issue without having to tie my colours to the talking head I like the most.
Lol, I guess that means American housing prices have been going up the last couple years too.
I am not familiar enough with US house prices to be sure, but I suspect that’s a poor analogy to the global warming data.
In any event, I think it’s fair to say that temperatures have been basically flat because it contradicts many of the predictions of the warmists.
Here are two better criteria for judging your statement’s fairness:
Compare the temperature data. It’s quite clear that there’s relatively a lot more noise and external forcing, which makes it harder to see a trend in the data. That’s why it’s reasonable to suppose that past upward trends in temperature are continuing, even though the most recent temperatures look flat in some of the data sets; the greater noise hurts your statistical power to detect a trend, which means that you can get the appearance of no trend whether or not the upward trend is continuing.
Hence why I see your analogy as a poor one: you’re implying that arguing for an ongoing increase in temperature is as silly as arguing for an ongoing increase in house prices, but that ignores the far greater statistical power to detect a change in trend in recent house price data.
And how do I know if the statement is liable to mislead people?
Apply your rough mental model of how other people are likely to interpret your statement to decide whether your statement is likely to direct them to a misleading impression of the data.
For example, if I show someone this graph, it’s fair to say that there’s a significant chance they’ll think it shows that US temperature increase per century has no practical significance. But that would of course be a fallacious inference: the fact that other temperature measurements can vary a lot is logically disconnected from the issue of whether the rise in US temperature has real importance. In that sense the graph is liable to mislead.
That’s why it’s reasonable to suppose that past upward trends in temperature are continuing, even though the most recent temperatures look flat in some of the data sets
It may be reasonable to suppose so, but it doesn’t change the fact that temperatures have been basically flat for the last 10 (or 15) years.
In any event, it’s quite possible—even likely—that the upward trend in housing prices is continuing in the same sense you believe that the upward trend in temperatures may be continuing; and that the recent housing bubble is the rough equivalent of an el nino
It may be reasonable to suppose so, but it doesn’t change the fact that temperatures have been basically flat for the last 10 (or 15) years.
I don’t believe it is true that ‘temperatures have been basically flat’ for the last 15 years: I see a net gain of 0.1 to 0.2 Kelvin, depending on the data set (HadCRUT3 v. GISTEMP v. UAH v. RSS). And it looks to me like temperatures have only been ‘flat’ for the last 10 years in the sense that a short enough snippet of a noisy time series will always look ‘flat.’
In any event, it’s quite possible—even likely—that the upward trend in housing prices is continuing in the same sense you believe that the upward trend in temperatures may be continuing; and that the recent housing bubble is the rough equivalent of an el nino
And the accompanying crash would be a La Niña? I think the house price boom & crash is a little too big to characterize like that.
I don’t believe it is true that ‘temperatures have been basically flat’ for the last 15 years: I see a net gain of 0.1 to 0.2 Kelvin, depending on the data set (HadCRUT3 v. GISTEMP v. UAH v. RSS).
So the standard is “net gain,” and a net gain greater than (or less than) 0.1 Kelvin means not basically flat?
And it looks to me like temperatures have only been ‘flat’ for the last 10 years in the sense that a short enough snippet of a noisy time series will always look ‘flat.’
That may be true, but so what? characterization of evidence != interpretation of evidence. Agreed?
I think the house price boom & crash is a little too big to characterize like that.
Why not? It’s a short term detour in a larger overall trend. If you happened to buy a house at the top of the market, there is still an excellent chance that some day the market price will exceed your purchase price.
So the standard is “net gain,” and a net gain greater than (or less than) 0.1 Kelvin means not basically flat?
Any net gain (or net loss), however small, means not flat, if you are confident enough that it’s not an artefact or noise. (Adding the adverb ‘basically’ muddies things a bit, because it implies that you’re not interested in small deviations from flatness.) So: am I quite confident that there has been a deviation from flatness since 1995, and that the deviation is neither artefact nor noise? Yes. But you knew that already, so I’ll go deeper.
You earlier referred to the Phil Jones interview where he stated that the warming since 1995 is ‘only just’ statistically insignificant. I don’t know enough about testing autocorrelated time series to check that, but I’m willing to pretty much trust him on this point.
OK, so every so often on Less Wrong you see a snippet of Jaynes or a popular science article presented in the context of a frequentism vs. Bayesianism comparison. I’ve gone to bat before (see that first link’s discussion) to explain why pitting the two against each other seems wrong-minded to me. I’ve yet to see an example where frequentist methods necessarily have to give a different result to Bayesian methods, just by virtue of being frequentist rather than Bayesian. I see the two as two sides of the same coin.
Still, there are certain techniques that are more associated with the frequentist school than the Bayesian. One of them is statistical significance testing. That particular technique gets a lot of heat from statisticians of all sorts (not just Bayesians!), and arguably rightly so. People are liable to equate statistical significance with practical significance, which is simply wrong, and to dogmatically reject any null hypothesis that doesn’t clear a particular p-value bar. On this point, I have to agree with the critics. Far as I can tell, there are too many people who fundamentally misunderstand significance tests, and as someone who does understand them (or I think I do—maybe that’s just the Dunning-Kruger effect talking) and finds them useful, that disappoints me.
In the end, you have to exercise judgment in interpreting significance tests, like any other tool. Just because a test limps over the magic significance level with a p-value of 0.049 doesn’t mean you should immediately shitcan your null hypothesis, and just because your test falls a hair short with an 0.051 p-value doesn’t mean there’s nothing there.
To get more specific, that net warming since 1995 has been ‘just’ statistically insignificant does not mean no warming. It means that under a particular model, the null hypothesis of no overall trend cannot be rejected. It could be because there really is no trend. Or there might be a true trend, but your data are too noisy and too few. Or the test could be cherrypicked. You have to exercise judgment and decide which is most likely. I believe the last two possibilities are most likely: I can see the noise with my own eyes, and apparently 1995 is the earliest year where warming since that year is statistically insignificant, which would be consistent with cherry-picking the year 1995.
Which is why I reject the null hypothesis of no net temperature change since 1995, even though the p-value of Phil Jones’ test is presumably a bit higher than 0.05.
That may be true, but so what? characterization of evidence != interpretation of evidence. Agreed?
They are distinct concepts.
I get the feeling that you think calling the last decade of temperatures ‘flat’ is characterization and not interpretation, and I would disagree. When I say temperatures have risen overall, that’s an interpretation. When you say they have not, that’s an interpretation. Either interpretation is defensible, though I believe mine is more accurate (but of course I would believe that).
Why not? It’s a short term detour in a larger overall trend.
Right, but if you compare the housing price detour to the noise in the house price data, it’s relatively way way bigger than the El Niño deviation compared to the noise in the temperature data.
I pulled the temperature data behind this plot and regressed temperature on year. Then I calculated the standard deviation of the residuals from the start of the time series up to 1998 (when the EN kicked in). The peak in the data (at ‘year’ 1998.08, with a value of 0.6595 degrees) is then 3.9 sigmas above the regression line.
Look back at the home price graph—maybe that particular graph’s been massively smoothed, but the post-peak drop looks like way more than a 4 sigma decline: I’d eyeball it as on the order of 10-20 sigmas—and that’s a big underestimate because the standard deviation is going to be inflated by what looks like a seasonal fluctuation (the yearly-looking spikes). The El Niño is big and bold, no doubt about it, but it’s a puppy compared to the housing pricing crash.
Adding the adverb ‘basically’ muddies things a bit, because it implies that you’re not interested in small deviations from flatness.
Of course it muddies things and we should not be interested in small deviations. That’s the basic point of your argument. The only question is how small is small.
When I say temperatures have risen overall, that’s an interpretation. When you say they have not, that’s an interpretation
Well can you give me an example of a statement about temperature in the last 10 years which is not an “interpretation”?
Right, but if you compare the housing price detour to the noise in the house price data, it’s relatively way way bigger than the El Niño deviation compared to the noise in the temperature data.
The El Niño is big and bold, no doubt about it, but it’s a puppy compared to the housing pricing crash.
So what? In 1998, would it have been wrong to say that global surface temperatures had risen (relatively) rapidly over the previous few years?
Of course it muddies things and we should not be interested in small deviations. That’s the basic point of your argument.
?!
The point I was making in the first 550 words of the grandparent comment is that one shouldn’t automatically disregard a small deviation from flatness merely because it’s (barely) statistically insignificant. I am not sure how you interpreted it to mean that ‘we should not be interested in small deviations.’
Well can you give me an example of a statement about temperature in the last 10 years which is not an “interpretation”?
A statement that’s a few written words or sentences? I doubt it. Trying to summarize a complicated time series in a few words is inevitably going to mean not mentioning some features of the time series, and your editorial judgment of which features not to mention means you’re interpreting it.
So what?
You should know, you asked me ‘Why not?’ in the first place.
In 1998, would it have been wrong to say that global surface temperatures had risen (relatively) rapidly over the previous few years?
Practically, yes, because that claim carries the implication that the El Niño spike is representative of the warming ‘over the previous few years.’
So the standard is “net gain,” and a net gain greater than (or less than) 0.1 Kelvin means not basically flat?
My linear regressions based on NOAA data (I was stupid and lost the citation for where I downloaded it) have 0.005-0.007 K/year since 1880; 0.1 to 0.2 K in a decade is beating the trend.
I took the liberty of downloading the GISTEMP data, which I suspect are very similar to the NOAA data (because the GISTEMP series also starts at 1880, and I dimly remember reading somewhere that the GISS gets land-based temperature data from the NOAA). Regressing anomaly on year I get an 0.00577 K/year increase since 1880, consistent with Robin’s estimate. R tells me the standard error on that estimate is 0.00011 K/year.
However, that standard error estimate should be taken with a pinch of salt for two reasons: the regression’s residuals are correlated, and it is unlikely that a linear model is wholly appropriate because global warming was reduced mid-century by sulphate emissions. Caveat calculator!
(ETA: I just noticed you wrote ‘these,’ so I thought you might be interested in the trend for the past decade as well. Regressing anomaly on year for the past 120 monthly GISTEMP temperature anomalies has a trend of 0.0167 ± 0.0023 K/year, but the same warning about that standard error applies.)
I have no idea. Varying the starting point from ten to thirty years ago with Feb 2010 as the endpoint puts the slope anywhere in the range [-0.0001,0.2], so it must be fairly large on the scale of a decade.
Aha, I misunderstood which chart you had in mind. I thought that your link was intended to go to the data for 17 year olds, but that you were unable to link it directly because the page used Javascript to flip between the charts for different ages. I see now I’m wrong about that—one can link directly to the chart for each age, and it sounds like you were pointing to the age 9 data.
So I’ll try this again with the 9 year olds. I’ve taken the liberty of looking at the black-white gap graph instead of the scale score graph so I don’t have to do any mental arithmetic to get the gap size at each testing. Looks to me like the gap consistently narrowed from 1973 to 1986, and has fluctuated from 1986 so it’s sometimes wider, sometimes thinner, but no overall trend since then.
Regressing gap size on year like I did before gives a shrinking of .24 or .25 points per year. So the picture is more mixed than for the older kids: there’s an overall shrinking, but it’s only two-thirds what you get for 17 year olds, and the trend looks like it’s stalled since the late 80s.
Still, I am not sure that this means Nisbett is wrong. Looking at the bit of Nisbett you quote yourself downthread, Nisbett does not seem to say anything about the math scores, which means looking at the math scores would not tell us whether Nisbett is wrong or right.
It is possible that Nisbett cherry-picked by ignoring the math data, but I think a .25 point per year narrowing is still evidence against that idea. At a quarter point per year, the math gap would disappear in about a century, which isn’t much longer than the 75 years Nisbett suggests for science.
Of course there are ways to interpret the graph to argue that the gap is narrowing and on track to disappear, but if you look at it and use your common sense, it’s just not a reasonable conclusion.
The reasonable conclusion—as you allude to—is that the gap has been pretty much stable for a number of years.
You put more trust in your common sense than I do. I try to avoid depending exclusively on what my common sense infers from eyeballing noisy time series—that way lies ’global warming stopped in 1998’esque error.
I find your preferred interpretation reasonable, but I don’t see why it would be unreasonable to look at the entire data and see a net narrowing. (Especially if we lacked the 2008 data, as Nisbett did.)
If the choice is between trusting your common sense and trusting someone with an agenda, I would say go with your common sense.
Here’s a thought experiment: You show the graph I linked to to 10 statisticians, except you replace the labels with something less politically charged. For example, the price of winter wheat versus the price of summer wheat. And you ask them to interpret the graph as far as long term trends go. I’m pretty confident that 10 out of 10 would interpret the graph the same way I did.
Ditto for global surface temperatures. Take the temperature label off the graph and tell people it’s the dollar to yen exchange rate. I bet 10 out of 10 statisticians will say the rate is basically flat for the last 10 years.
cupholder has the empirical data—which, you will note, is increasing in all cases—but do you really imagine that no-one’s tried a blind test?
No I do not imagine so. But I’m a little confused. Are you saying that the absence of significant cooling is the same thing as the presence of significant warming?
PS: The empirical data is not “increasing in all cases.” Indeed, by most accounts global surface temperatures have not met or exceeded the high reached 12 years ago.
Every 10-year trendline in cupholder’s data was increasing.
If you give a statistician the 30-year or 130-year data set with the y-axis label taken off, they will tell you that there is no sign of a levelling-off.
A quick clarification: for each of the data links I posted there, the trendline is calculated based on all of the data that’s shown, i.e. for the post-1998 data the trendline is based on the last twelve years, for the post-1970s data the trendline is based on all of the post-1970s data, and so on. In other words, only the data for the last 10 years of data really have a 10-year trendline.
[ETA: Unless you mean you calculated 10-year trendlines for each data set yourself, in which case feel free to disregard this.]
Here’s a plot of the UAH index from 1998 to 2009.
http://www.woodfortrees.org/plot/uah/from:1998/to:2009/plot/uah/from:1998/to:2009/trend
The linear trend is definitely decreasing for this particular plot.
I’m seriously skeptical of this.
P.S. Are you saying that the absence of significant cooling is the same thing as the presence of significant warming?
Note that changing the beginning data point to either 1997 or 1999 makes the regression line have a positive slope. It’s not at all surprising that there is enough variability that cherry-picking data is possible. Stuffing a positive outlier at the beginning will, of course, tend to do this.
Agreed. I cherry-picked 1998 as a starting point to counter the claim that the data was increasing “in all cases.”
Still, I would also note that as I explain on my blog post, there is some significance to the observation that global surface temperatures still have not exceeded the 1998 high. (According to the majority of leading temperature measurements.)
Did you read the linked article?
[...]
1998 was a strong El Nino year—unusually high atmospheric temperatures that year in no way suggests that the earth has stopped heating.
Yes, and I’m not sure what your point is.
Are you claiming that the absence of a significant cooling trend is the same thing as the presence of a significant warming trend?
It’s a very simple question. Why won’t you answer it?
Incidentally, I wrote a blog post about the article in question which touches on these issues.
http://brazil84.wordpress.com/2009/10/27/more-on-global-cooling/
I’m claiming that this one data set does not by itself support rejection of the body of theory that suggests global warming is occurring, and that it is intellectually dishonest to imply that it does.
Well answered (and I have downvoted brazil for trying to coerce you into making a stupid claim with the obvious intent of presenting a misleading dichotomy.)
In light of the spelling thread, dichotomy? This immediately jumped out at me in the manner that a few others describe for spelling mistakes.
Thankyou. It jumped out at me too upon rereading. I wonder why my browser has stopped spell checking for me.
I’m not sure what the claim “global warming is occuring” means so I can’t really speak to that.
In any event, as I noted in the blog post, the warmists have made specific predictions. The temperature record for the past 10 or so years contradicts some of those predictions.
ETA: Can I take it that your answer to my question is “no”?
I’m not saying the absence of a significant cooling trend is the same thing as the presence of a significant warming trend—that would be a stupid thing to say. As for the remainder: I don’t trust your judgment, but the data you provided is interesting. I will examine the composite NOAA temperature data (ocean, land, and combined) and update accordingly.
(It should be noted, however, that if anthropogenic inputs are significant, as claimed by the climate scientists whose work we are discussing, predicting the climate would require predicting all anthropogenic climate forcings—and therefore we might expect the predictions to be worse than anticipated.)
They can get around this by expressing their predictions as a function of future anthropogenic emissions, thus removing this source of uncertainty.
From the papers I looked at today, a major problem appears to be measuring the forcings that go into the model.
I imagine they do—do we have a climatologist in the house?
I imagine they do too; the question is whether they claim the right to (retroactively) “massage” their predictions, which would invalidate this test.
Correct. Which is why the article you linked to does not contradict the claim I made.
Well you shouldn’t trust my judgment. What’s the motto of the British science academy? Something like “Don’t take my word for it.”
I am far less confident.
I bet it would depend on exactly which data set you gave them. Do you give them data for the past 10 years, data since 1998, the data since they started measuring temperatures with satellites as well as thermometers, or the longest-running data set, which runs from 1850 onwards? If you just give them the last decade of data, they might well just write it off as flat and noisy, but if you let them judge the recent numbers in the context of the entire time series, they might recognize them as flat-looking fuzz obscuring an ongoing linear trend.
That sounds nice, but I don’t know how practical that would turn out to be, in this case or in general. In this particular case, how can I even tell with certainty whether you have ‘an agenda’ or not? And what if the key participants in a debate all have some agenda? It’s very possible that Nisbett has a ‘politically correct’ (not that I like the phrase, but I can’t think of a better way of putting it) agenda, and that Rushton and Jensen have a ‘politically incorrect’ agenda. How do I know, and what do I do if they do? And so on.
How can you tell anything with certainty? The fact is that you can’t. Respectfully, it seems to me you are playing the “I’m such a skeptic” game.
Let me ask you this: Do you seriously doubt that Nisbett has an agenda?
I would give them the data since the 1970s when sattelite measurement became possible.
Sorry. I was being sloppy in my earlier comment, and using ‘certainty’ as a shorthand for ‘certainty enough for me to label you as Having An Agenda, and therefore to reject your interpretation of the data as Tainted With An Agenda.’ It is of course true that you can’t tell anything inductive with cast-iron 100% certainty, but what I’m getting at is the question of how to get to what you or I would practically treat as certainty (like if I put a 95% probability on someone Having An Agenda).
Let me rephrase: in this particular case, how can I even tell whether you have ‘an agenda’ with sufficient certainty to disregard whatever you say about the data, and retreat to my own common sense gut feeling?
Do I doubt he has an agenda in the sense that he believes he’s right? A tiny bit, but only in the sense that I am never completely sure of another person’s motivation for stating something.
Do I doubt he has an agenda in the sense that he wants to convince other people of what he believes? Not really.
Do I doubt he has an agenda in the sense that he has an emotional investment in the argument as well as rational considerations? Only a little...but then again, who doesn’t get emotionally invested in arguments?
Do I doubt he has an agenda in the sense that he has political motivations for his article as well as self-centered emotional and rational ones? Quite a lot, actually. I don’t think I could reliably tell Nisbett’s emotional motivations apart from those that spring from his political agenda (whatever that is—Nisbett sounds like a leftist to me, but how the hell do I really know? There were rightists who crapped on The Bell Curve too.) Does it even make sense to distinguish the two? I’m not sure. (I suddenly feel that these are good questions to think about. Thank you for prodding me into thinking of them.)
Also, for whatever it’s worth, I am just as sure that Rushton and Jensen have ‘an agenda,’ however you want to define that, as Nisbett does. Do I throw all their papers out and just go with my common sense?
To clarify, this doesn’t mean I can’t get behind the idea of being alert to other people’s biases on some subject, but I’m not willing to push that to the point of a dichotomy between my common sense vs. someone with an agenda. Taking the global warming example, I’m sure many climate scientists have ‘an agenda,’ but I’d still tend to accept their consensus interpretation of the data than my own common sense where the two differ, and I think that’s reasonable if I don’t have time to dig through all of the research myself.
In that case I think I’m roughly 90% confident that fewer than ’10 out of 10 statisticians will say the rate is basically flat for the last 10 years’. I am interpreting ‘the rate is flat here’ to mean that the net temperature trend is flat over time, as I believe we’re talking about whether global warming is continuing and not whether global warming is accelerating. (Thought process here: I reckon a randomly selected statistician has at most a 4 in 5 chance of deciding that temperatures have been ‘basically flat’ for the last 10 years’ based on the satellite data. Then the chance of 10 random statisticians all saying temperatures have been flat is 11%, so an 89% chance of at least one of them dissenting.)
By “having an agenda,” I mean that Nisbett is emphasizing the facts that support a particular point of view and de-emphasizing the facts which undermine that point of view in order to persuade the reader.
So defined, one can ask whether Nisbett has an agenda. Do you have any doubt that Nisbett has an agenda?
So by your definition, the temperature trend is NOT basically flat between 1995 and the present, correct?
Not much. I think it is very likely that Nisbett suffers from confirmation bias about as much as everybody else.
Eyeballing it I’d say it’s much more likely that temperatures rose since 1995 than that they stayed flat, so I’d say you’re pretty much correct. I wouldn’t dogmatically say it’s not flat in big capital letters, but I think the rising temperature hypothesis is a lot more likely than the flat temperature hypothesis.
I’d double check my intuition by running a regression, but that’d stack the deck because of autocorrelation, and I can’t remember from the top of my head how to fit a linear model that accounts for that.
I’m not sure what this means. Are you saying that every piece of written material has an agenda behind it as I’ve defined the term?
And do you agree that according to Phil Jones, there has been no statistically significant warming between 1995 and the present?
The fact that you quote this doesn’t help your credibility. The Economist: Journalistic malpractice on global warming
I’m not sure what your point is. My argument does not depend on my credibility.
In any event, do you agree that “journalistic malpractice” works both ways? In other words, if it’s malpractice to claim that there has been no warming since 1995, it’s also malpractice to claim that there has been no cooling since 1998?
Not every piece of written material, but I’d bet that almost all lengthy pieces of writing intended to communicate a point to others have an agenda behind them, sure. There’s always a temptation to round the numbers to your advantage, to leave out bits of data that might conflict with your hypothesis, to neglect to mention possible problems with your statistical tests, and so on.
Even ignoring that sort of thing, cognitive biases play an important role. Nisbett presumably had a half-formed opinion of the race and IQ argument even before he started researching it in depth. And that would in turn have affected which bits of relevant evidence got stuck in his mind. And that would in turn have hardened his opinion. You get positive feedbacks that push your opinion away from others that conflict with it. So even if Nisbett were consciously being as honest as possible, he could still be
just because his mental database of facts is going to overrepresent the 1st kind of fact and underrepresent the 2nd—and precisely because of that, he is going to be sure that his point of view is obviously correct, and precisely because of that, he is going to be writing to persuade the reader of it—even though, as far as he knows, he is being completely honest!
(Tangent: it’s somehow amusing and fitting that the person we’re using to argue this point is the person whose most cited article is “Telling more than we can know: Verbal reports on mental processes.”)
That’s what he said.
Ok, and the stronger the agenda, the more you should trust your common sense over claims made by the person with the agenda.
Ok, and presumably what he meant was that any warming which took place between 1995 and the present was less than some statistical minimum threshold. I’m not sophisticated enough to calculate such a limit, but that’s what I meant when I said that temperatures have been basically flat for the last 10 years.
Cool. I feel more comfortable now that you’ve expressed this in continuous terms. There’s still a catch, though: using your definition of having an agenda, I can’t really tell whether someone has an agenda without also knowing the facts (because ‘having an agenda’ here is being used to mean that someone’s making a slanted presentation of the facts), and if I know the facts already, I have little need for your has-an-agenda heuristic.
Roughly speaking, I think that’s about right.
I think I understand now. Alrighty...yeah, I would suspect that there’s been no statistically significant warming trend in the last 10 years. I would however avoid using phrases like ‘temperatures have been basically flat for the last 10 years’ to describe this, as I nonetheless believe that if one considers the last 10 years of records in the context of unambiguous past warming, they are consistent with an ongoing, underlying warming trend.
I would suggest you practice. It also helps to read people who contradict eachother. It also helps if you learn some of the facts.
Lol, I guess that means American housing prices have been going up the last couple years too.
In any event, I think it’s fair to say that temperatures have been basically flat because it contradicts many of the predictions of the warmists.
I reckon the first two things only help in as much as they help you do the third. Learning the facts is what really matters—and in my experience, once I feel I know enough about an issue to decide who has an agenda (in your sense of the phrase), I typically feel I know enough to make my own judgement of the issue without having to tie my colours to the talking head I like the most.
I am not familiar enough with US house prices to be sure, but I suspect that’s a poor analogy to the global warming data.
Here are two better criteria for judging your statement’s fairness:
is the statement true?
is the statement liable to mislead people?
How is it a poor analogy? The general for the last 50 years is upwards, but the trend over the last couple years is flat or downwards.
And how do I know if the statement is liable to mislead people?
A quick Google for house price data led me to this graph of US house prices from 1970 up until what looks like last year. It is immediately clear to me that there is far less noise obscuring the changes in trends than in the global temperature data. The recent house price crash looks about an order of magnitude larger than the seasonal(?) fuzz, so it’s easy to distinguish it from the earlier upward trend.
Compare the temperature data. It’s quite clear that there’s relatively a lot more noise and external forcing, which makes it harder to see a trend in the data. That’s why it’s reasonable to suppose that past upward trends in temperature are continuing, even though the most recent temperatures look flat in some of the data sets; the greater noise hurts your statistical power to detect a trend, which means that you can get the appearance of no trend whether or not the upward trend is continuing.
Hence why I see your analogy as a poor one: you’re implying that arguing for an ongoing increase in temperature is as silly as arguing for an ongoing increase in house prices, but that ignores the far greater statistical power to detect a change in trend in recent house price data.
Apply your rough mental model of how other people are likely to interpret your statement to decide whether your statement is likely to direct them to a misleading impression of the data.
For example, if I show someone this graph, it’s fair to say that there’s a significant chance they’ll think it shows that US temperature increase per century has no practical significance. But that would of course be a fallacious inference: the fact that other temperature measurements can vary a lot is logically disconnected from the issue of whether the rise in US temperature has real importance. In that sense the graph is liable to mislead.
It may be reasonable to suppose so, but it doesn’t change the fact that temperatures have been basically flat for the last 10 (or 15) years.
In any event, it’s quite possible—even likely—that the upward trend in housing prices is continuing in the same sense you believe that the upward trend in temperatures may be continuing; and that the recent housing bubble is the rough equivalent of an el nino
I don’t believe it is true that ‘temperatures have been basically flat’ for the last 15 years: I see a net gain of 0.1 to 0.2 Kelvin, depending on the data set (HadCRUT3 v. GISTEMP v. UAH v. RSS). And it looks to me like temperatures have only been ‘flat’ for the last 10 years in the sense that a short enough snippet of a noisy time series will always look ‘flat.’
And the accompanying crash would be a La Niña? I think the house price boom & crash is a little too big to characterize like that.
So the standard is “net gain,” and a net gain greater than (or less than) 0.1 Kelvin means not basically flat?
That may be true, but so what? characterization of evidence != interpretation of evidence. Agreed?
Why not? It’s a short term detour in a larger overall trend. If you happened to buy a house at the top of the market, there is still an excellent chance that some day the market price will exceed your purchase price.
Any net gain (or net loss), however small, means not flat, if you are confident enough that it’s not an artefact or noise. (Adding the adverb ‘basically’ muddies things a bit, because it implies that you’re not interested in small deviations from flatness.) So: am I quite confident that there has been a deviation from flatness since 1995, and that the deviation is neither artefact nor noise? Yes. But you knew that already, so I’ll go deeper.
You earlier referred to the Phil Jones interview where he stated that the warming since 1995 is ‘only just’ statistically insignificant. I don’t know enough about testing autocorrelated time series to check that, but I’m willing to pretty much trust him on this point.
OK, so every so often on Less Wrong you see a snippet of Jaynes or a popular science article presented in the context of a frequentism vs. Bayesianism comparison. I’ve gone to bat before (see that first link’s discussion) to explain why pitting the two against each other seems wrong-minded to me. I’ve yet to see an example where frequentist methods necessarily have to give a different result to Bayesian methods, just by virtue of being frequentist rather than Bayesian. I see the two as two sides of the same coin.
Still, there are certain techniques that are more associated with the frequentist school than the Bayesian. One of them is statistical significance testing. That particular technique gets a lot of heat from statisticians of all sorts (not just Bayesians!), and arguably rightly so. People are liable to equate statistical significance with practical significance, which is simply wrong, and to dogmatically reject any null hypothesis that doesn’t clear a particular p-value bar. On this point, I have to agree with the critics. Far as I can tell, there are too many people who fundamentally misunderstand significance tests, and as someone who does understand them (or I think I do—maybe that’s just the Dunning-Kruger effect talking) and finds them useful, that disappoints me.
In the end, you have to exercise judgment in interpreting significance tests, like any other tool. Just because a test limps over the magic significance level with a p-value of 0.049 doesn’t mean you should immediately shitcan your null hypothesis, and just because your test falls a hair short with an 0.051 p-value doesn’t mean there’s nothing there.
To get more specific, that net warming since 1995 has been ‘just’ statistically insignificant does not mean no warming. It means that under a particular model, the null hypothesis of no overall trend cannot be rejected. It could be because there really is no trend. Or there might be a true trend, but your data are too noisy and too few. Or the test could be cherrypicked. You have to exercise judgment and decide which is most likely. I believe the last two possibilities are most likely: I can see the noise with my own eyes, and apparently 1995 is the earliest year where warming since that year is statistically insignificant, which would be consistent with cherry-picking the year 1995.
Which is why I reject the null hypothesis of no net temperature change since 1995, even though the p-value of Phil Jones’ test is presumably a bit higher than 0.05.
They are distinct concepts.
I get the feeling that you think calling the last decade of temperatures ‘flat’ is characterization and not interpretation, and I would disagree. When I say temperatures have risen overall, that’s an interpretation. When you say they have not, that’s an interpretation. Either interpretation is defensible, though I believe mine is more accurate (but of course I would believe that).
Right, but if you compare the housing price detour to the noise in the house price data, it’s relatively way way bigger than the El Niño deviation compared to the noise in the temperature data.
I pulled the temperature data behind this plot and regressed temperature on year. Then I calculated the standard deviation of the residuals from the start of the time series up to 1998 (when the EN kicked in). The peak in the data (at ‘year’ 1998.08, with a value of 0.6595 degrees) is then 3.9 sigmas above the regression line.
Look back at the home price graph—maybe that particular graph’s been massively smoothed, but the post-peak drop looks like way more than a 4 sigma decline: I’d eyeball it as on the order of 10-20 sigmas—and that’s a big underestimate because the standard deviation is going to be inflated by what looks like a seasonal fluctuation (the yearly-looking spikes). The El Niño is big and bold, no doubt about it, but it’s a puppy compared to the housing pricing crash.
Of course it muddies things and we should not be interested in small deviations. That’s the basic point of your argument. The only question is how small is small.
Well can you give me an example of a statement about temperature in the last 10 years which is not an “interpretation”?
So what? In 1998, would it have been wrong to say that global surface temperatures had risen (relatively) rapidly over the previous few years?
?!
The point I was making in the first 550 words of the grandparent comment is that one shouldn’t automatically disregard a small deviation from flatness merely because it’s (barely) statistically insignificant. I am not sure how you interpreted it to mean that ‘we should not be interested in small deviations.’
A statement that’s a few written words or sentences? I doubt it. Trying to summarize a complicated time series in a few words is inevitably going to mean not mentioning some features of the time series, and your editorial judgment of which features not to mention means you’re interpreting it.
You should know, you asked me ‘Why not?’ in the first place.
Practically, yes, because that claim carries the implication that the El Niño spike is representative of the warming ‘over the previous few years.’
My linear regressions based on NOAA data (I was stupid and lost the citation for where I downloaded it) have 0.005-0.007 K/year since 1880; 0.1 to 0.2 K in a decade is beating the trend.
What are the uncertainties on each of these?
I took the liberty of downloading the GISTEMP data, which I suspect are very similar to the NOAA data (because the GISTEMP series also starts at 1880, and I dimly remember reading somewhere that the GISS gets land-based temperature data from the NOAA). Regressing anomaly on year I get an 0.00577 K/year increase since 1880, consistent with Robin’s estimate. R tells me the standard error on that estimate is 0.00011 K/year.
However, that standard error estimate should be taken with a pinch of salt for two reasons: the regression’s residuals are correlated, and it is unlikely that a linear model is wholly appropriate because global warming was reduced mid-century by sulphate emissions. Caveat calculator!
(ETA: I just noticed you wrote ‘these,’ so I thought you might be interested in the trend for the past decade as well. Regressing anomaly on year for the past 120 monthly GISTEMP temperature anomalies has a trend of 0.0167 ± 0.0023 K/year, but the same warning about that standard error applies.)
I have no idea. Varying the starting point from ten to thirty years ago with Feb 2010 as the endpoint puts the slope anywhere in the range [-0.0001,0.2], so it must be fairly large on the scale of a decade.
Your regression package doesn’t report uncertainties? (Ideally this would be in the form of a covariance matrix.)
My regression package is a tab-deliminated data file, a copy of MATLAB, and least-squares.