Statiscal significance of 150 years of data over 4.5 billion years

The subject line is close to a recent search query that lead someone here, and echoes a comment that's not unusual in blog comment sections. The thing about it is, it's not a very strong question.

One part of the question's failure is that it isn't really a proper statistical question. Given limits of search strings, that's no surprise. But it does show up in comments (usually in the vein of assertion "150 years is too small a statistical sample of 4.5 billion years of climate.") where such limits don't apply.

The basis of any good question is to try to understand something. If what you are trying to understand is not statistical, then pursuing statistics is not going to help you. "What is your height?" is marginally statistical. If you measure the length of a short metal bar many times, which I did in freshman physics lab, you'll get slightly differing answers. So you may well answer statistically with your mean and a sample standard deviation. This is only marginally statistical, in that it is purely descriptive statistics and no hypothesis testing is involved.

Your question, however, could be non-statistical: Did it rain in my back yard last night? How much rain did my rain gauge capture? If so, you will be wasting your time if you chase after statistical tables. More at hand, someone raising statistics in a blog debate about a non-statistical question is wasting your time.

But suppose that what you're trying to understand truly does require statistical considerations beyond minor description. What would such a question look like? One could be "Given the population of voters in the USA, how many randomly selected voters would I need to ask a yes/no question in order to have a standard error in my sample of 3% or less as compared to asking the everybody?" or, for more climate-related flavor "How many satellite observations with a (known) standard error of measurement would I need to find an average sea surface temperature whose standard error would be less than 0.1 K?"

Required is a description of the 'population' -- all possible observations (the population of voters in the USA, satellite observations) -- of your 'sample' (ask some number, which we want to determine, of voters, or satellite observations -- and what statistic you are trying to estimate (% of voters who like your candidate, mean sea surface temperature).

So, back to the original question. Does it describe the population? No. 'data' certainly doesn't limit us to anything in particular. I'll guess that it is global mean temperature, of the earth (maybe it's Mars -- I've read interesting papers about Martian climatology), that is the point of interest. But we shouldn't have to guess, a good question is clear on what it is asking about. Does it describe a sampling method? Not really. 150 years, well, I'll guess that this means 'take the most recent 150 years'. Most importantly, however, does it describe what statistic one is trying to estimate? No. Again, I'll guess: that it is "Global mean temperature over the entire history of the earth."

Putting it all together, the statistical question more reasonably posed is something like "Does the last 150 years of global mean air temperatures provide a good estimate of the global mean air temperature through the history of the earth?" (better would be to define 'good', say 'standard error within 0.2 K')

That's the statistical side. But since we're not interested solely in statistical questions regarding climate, at least not most of us, we also have to ask, "Is this a physically meaningful question?" The person who did the search, I don't know what they have in mind. They could indeed have in mind a question for which the mean temperature of the planet throughout its history is exactly the right number to answer.

Usually, though, comments about the 150 years vs. 4.5 billion surface in debates about modern climate and modern climate change. I'll have to invite contributions on what relevance the planetary mean temperature from 4.5 billion years ago to ... oh, let's say 30 million years ago ... has to questions of current climate and climate change. Certainly one wants to know how climate has changed through all of time, and why. I'm one such person. But at hand is those who argue that the global mean over that entire period matters.

What's important regarding human responses to climate change is the climate on human time scales. The last 150 years handily covers me back through my great-grandparents. The next 150 years will cover my children, grandchildren, and possibly great-grandchildren. Even a 'mere' million years ago, much less 4.5 billion, there weren't any humans around to think about climate change at all. So the 4.5 billion years is, for 'what do we do now' questions, a spectacularly large red herring.

Human society infrastructure also dictates a much shorter term (than 4.5 billion years) concern. Almost every mile of paved road in the world is less than 150 years old. Almost every mile of railroad. Almost all port structures. Absolutely all air transport terminals are less than 150 years old. Absolutely all electrical distribution structure, all phone lines, and even more so all cell phone towers are less than 150 years old. Coal, oil, natural gas distribution networks, again, are almost entirely or entirely less than 150 years old. Many of the world's major cities are less than 150 years old (I'll count Chicago here, as the great fire in 1871 erased so much of the city).

The climate-related concern here is that all these things were constructed based on what climate was like around the time of their construction. That climate drove what the standards would be for, say, tolerance to flooding, tolerance to drought, high winds, high rain rates, high and low temperatures, and so on. If climate changes outside the range that the infrastructure was built for -- almost all of it globally being much less than 150 years old -- then there is a serious risk that the structure will fail when it encounters brand new climate conditions.

In this vein, then, comments about the 'we did fine in the medieval warm period' are a different flavor of red herring. Chicago, Sao Paulo, Melbourne, Johannesburg, ... didn't exist back then. They did not 'do fine' in the medieval warm period, they never encountered it. Even cities that did, such as London, Rome, Xi'an, did so with far smaller populations than today's. London, ca. 1100, had a population around 18,000, and is about 1000 times larger today (taking the metro area). Rome was about 20,000 around 1100 AD, vs. 200 times as large now. Xi'an was among the largest of cities in the world then, and may have been about 500,000 around 1100 AD. But almost 20 times that today. (mostly Wikipedia figures). While a Rome or London of 10-20,000 survived a medieval warm period ok, Rome and London of many millions have never see it before.

As usual, we can get far by asking two questions: "Is this question statistically meaningful?" "Is the question physically meaningful?" After looking at the former, regarding the original search string, and not infrequent comment, we see that it isn't a meaningful statistical question. After rephrasing it to something that is statistically good, we check to see whether it makes physical sense. Turns out, for the sort of thing I'm concerned about and others use it, that even the rephrased question isn't physically meaningful. Knowing that global mean temperature for the last 4.5 billion years was 20 C (I make up a number) as opposed to 15 C still doesn't tell us whether major modern cities, and their millions of residents, will be able to manage likely climate changes. Nor does it tell us what adaptations to take, much less how expensive it would be to make those adaptations. And it doesn't tell us what the costs, both dollars and lives, would be if there were no adaptation.

Introverted Scientists?

I'll throw this out for discussion: Are scientists in general introverted? Certainly that's the stereotype in the US. And my experiences have supported that general view. Compared to the US norm, I'm in the middle between quiet/retiring and loud/outgoing, but at a scientific meeting, I'm well towards the outgoing end of the spectrum.

Since a fair number of non-US readers are here, additional questions are
a) Is that same stereotype common in your country (and what country is it)?
b) Do the scientists in general follow it?

This was brought to mind by some recent meetings I've been at which included non-US scientists, or a meeting that was just US folks, but not just scientists. It looked like the non-US scientists weren't nearly as quiet/retiring as the US norm.

If anyone knows of some research on the subject, that'll be even better than anecdotes!

First ARCUS summary of 2009

The first sea ice outlook from ARCUS is now out. Have a look at the full report at the link. You'll see my name there, with what turned out to be a boringly typical guess. Actually, we all seem to have been pretty much of the same mind as to amounts, and to distributions around those amounts -- somewhere about 4.9 million km^2, with error ranges of about 0.5 million km^2.

The interesting part being that we arrive at such similar estimates for both value and variation around it by such different means. Do look at the descriptions of how groups arrived at their predictions. I'll spend more time here on my method later. The only particularly different guess (3.2 million km^2) was from a group (Arbetter et al.) that provided 2, and labelled the other one (4.7) their outlook prediction.

Nominations

Rather like John Wilkins, I'm loath to nominate my own writing, but not about asking y'all to enter some nominations (including for my articles :-)

I've entered a link to the submission form on the right hand side of the blog, and here it is again:
http://openlab.wufoo.com/forms/submission-form/.

All articles since 1 December 2008 are eligible. You can see the current (as I write) listing of nominated articles at Block Around the Clock, and updates will appear there routinely.

I'll also take this chance to invite comments here on which articles you've thought were the best, or worst, what you'd like to see more of, or less of, and so on.

Connolley-Grumbine sea ice bet

William Connolley and I (both people who have worked professionally on sea ice) are arranging our bet regarding this year's minimum sea ice cover. I've already mentioned a bit about my prediction, which is for this year's average sea ice extent for September, in the Arctic, as computed by the NSIDC, to be about 4.92 million km^2. To the extent that my working model is good, the standard error of that estimate is about 0.5 million km^2.

In making that prediction, I'm taking the approach that the last two years' dramatic low covers were part of a continuing process of decline in the ice pack, though a fair portion of it still being peculiar circumstances of Arctic weather in summer/fall 2007 and 2008. This is not the usual view in the field, where the most common take is that 2007 represents a step change in the system -- one sort of thing going on before 2007, massive change in 2007, and things should continue more or less similarly for a number of years. (Until the next step change.)

William is taking the view that 2007 and 2008 were just bizarre years, not a fundamental change as most are taking it. The reasonable prediction in his view is to take the years 1979-2006, run a straight line through them, and use that as your basis. I've finally done the math for it (not at all difficult in the spreadsheet but I've been running around), and his prediction for 2009 is 5.84 million km^2 (also with about 0.5 million km^2 standard error -- but I'm rounding down for his figure, and rounding up for mine. That is, my scheme makes a better fit than his.).

So William, how about even quatloos over/under 5.38 million km^2? If it's under, you pay me 50, if over, I pay you 50? If your approach is right, 84% of the time you'll win this. If mine is, it's 84% of the time that I'll win. So, as you advised, it's a wager we each think is biased in our favor.

Fathering scientists

It's really a matter of parenting scientists, but this will appear on Father's Day. That is, suppose you're a parent and would like your child (children) to appreciate science. Not that they should become scientists -- I don't believe that this is the only career to pursue even though I did do so. (I also had my time pursuing engineering and computer science. I ended up going with the science, but it was a real question up through completing my undergraduate degree and receiving an engineering job offer.)

In this, I'll largely be drawing from examples my mother set. A good parent learns from all good parents, not just those of their own gender.

As a parent, perhaps the greatest thing you can support in your kids is the idea "The universe is a very interesting place." You don't need to know all the science yourself. It might even be a benefit if you don't. In any case, it's a family article of faith that children are born scientists -- investigators of the universe around them. When they start asking about why the sky is blue, grass green, ants are going that way, clouds are puffy rather than stringy ... cheer. You don't need to know the answers yourself. It doesn't take many years before your kids are asking questions that nobody knows the answer to. So, maybe answer where you know the answer. Where you don't, one or more of: "That's interesting. I don't know the answer. What do you think it is? How could we figure it out? Where would we search on the net?" is wonderful. The universe is incredibly interesting. If you're no great fan of insects, and find yourself parent (or, in my case, uncle) to a child who thinks they're incredibly interesting, cheer their interest. Insects are very interesting, at least to folks who study them, or maybe found fireflies pretty, and so on. In any case, I learned from my mother that you don't need to share the exact interest, and certainly don't need to know a lot about that particular thing*. The universe is interesting. That includes the parts you're not enthusiastic about yourself.

Second major thing is -- not all ideas will work out, and that's ok. "You'll think of more ideas later, and they'll be even better." Abandoning ideas that don't work out, I mentioned earlier, is one of the central skills of a scientist. If the idea doesn't work, don't spend your time 'reassuring' your child that it's 'ok that you failed'. They didn't fail, period. They successfully carried out one of the most important things a scientist can do -- test an idea and realize it doesn't work. Another better response is "Ok, since this doesn't quite work, what do you think might work instead?" Almost every idea that a scientist has, doesn't work. I doubt this is unique to science, so whether your child goes anywhere near science it's a good skill to have -- to have your idea not work, and to take it in stride and move on to the next idea.

I didn't even remember the example myself, but in my 20s or so, mom mentioned my 'blood theory of life'. I was 4 at the time, she said. The theory was, "We all have a finite amount of blood. When it runs out, say because of a trauma like a car accident or a blood disease like leukemia destroying healthy blood cells, you die." (I did know about leukemia at that age.) I don't exactly remember the responses (hey, I was 4, and 4 was ... several ... years ago), but I'm positive it wasn't "my what a wonderful idea". It was, I'm sure, in the vein of "That doesn't work because bone marrow makes more blood cells, so the supply isn't limited." Far better answer. Told me the idea didn't work, and told me something new that I could then think about more. Wow. There's even more to learn about the universe! And, it is possible for me to learn it!

This is another major skill to encourage in your children. "You may not know or understand something now, but you can learn it." Maybe they have to devote some time or effort, but it can be done. Things are possible, and regardless of where you are today, in time you can get where you'd like. Again, nothing unique to science about this. And, for that reason, a good reason to encourage it with respect to science. The skill, learning more stuff, is needed for almost everything. In science, finding out more about the universe -- that your child finds interesting -- the rewards follow more immediately from the effort than might be in other areas. In sports, if your child loves any healthy sport, support that. Skills can transfer, most especially the skill of training to do their sport well. Later, when some other sport becomes the greater interest, this overarching skill of training to do better will transfer. Same for study, practice, learn in science transferring to any other academic area. And, though I haven't seen it as often, between the sports and academics.

*I'll embarrass mom a little. She knew, and knows, far more than she has ever laid claim to. But, the key is regardless of how much she knew, she could never have hoped to answer all questions I asked. Same way that regardless of how much I know, I could never hope to answer all the questions my daughter has asked. As a parent, for us both, the key was, help your child learn more. Encourage that desire to learn more. Support the skills to learn more.

Additional support doesn't need to be expensive. Go for walks, look at the sky (works both day and night), visit the library, tour the internet with your child (perhaps at the library). An inexpensive telescope or microscope, or rock kit, or bug collecting kit, and so on can all be nice additions. But they're not necessary. If you do get things like this, it's a good idea to match them up to your child. A child interested in the stars will be thrilled with a reasonable telescope, while a child interested in insects ... not so much. Go with the flow here, a matter of good parenting anyhow.

Chances are that your child won't become a scientist. That's fine. What they're very likely to do, however, is become interested, informed people. And that's not only fine, but vital. And you'll get to spend time with them, and hear them being enthusiastic about their latest discovery for years while they grow up.

A few more comments

I'm still in 'run around' mode, but did catch up with some good comments to the blog. New comments in:

• Semi-open thread (and I can't answer the CO2 one offhand -- too many different things showing up in the literature. I'll have to do some focused reading.)
• The Central Skill of a Scientist
• Sea Ice Odds
• Results on deciding trends

Worth a look.

Scientific Specificity

Reading science is a bit different from what we're accustomed to in the rest of our lives. No, not that scientists use inscrutable jargon or math; plenty of other groups have their own jargons and uses or abuses of math. The challenge is that scientists, in writing and speaking science, are usually much more precise in what they say.

I was reminded of this in the comments to my note about the correlation between CO2 and temperature. Still thinking about how to write so as to avoid the problem. Since, even if I do complete the rewriting, there are many other scientists who won't be revising, I figure it's not a bad thing to write this general note.

Over in that note, I documented that there is indeed a correlation between CO2 levels and temperature. Quite a surprisingly large one, in fact. I also noted that merely running this correlation is not how the science is being done. (In fact, the science on temperature rising because of CO2 increase, if there were enough of one, predated there being observations of the CO2 increase or temperature rising. Conservation of energy is a powerful law.) Still, where there are people saying that there's no correlation between CO2 and temperature, there's the elementary disproof.

A catchphrase that I'd thought was very widely known (and correct, which is rarer) is "correlation is not causation". But that's particular to correlation. The more general point is, if you've supported a particular claim (CO2 correlates with temperature), that's all that has been supported. One thing we try to do in science is to find things which are true to work with. Some things that are true aren't very useful. But you can't reach a good scientific conclusion with things that are not true. These elementary truths are the building blocks for constructing larger true structures.

This is why the difference in reading for science vs. many other things. In many other areas, you can predict an entire argument from a short part of it (not least, because the author is arguing rather than trying to understand -- see my note discussion vs. debate for why this is such a difference). To read science, you need to keep this in mind. Examine that one tiny building block that's being presented at the moment very carefully, by all means. But avoid rejecting the whole thing because you think it might be used to build something that you don't like. If the block holds up to scrutiny, then it holds up and work with it.

Bouncing around

Turns out that I didn't have as ready access to the 'net while I was travelling last week as I'd expected to. Oh well. I was able to pass through some comments and have noted them to come back to. A couple will likely wind up in bit bucket on grounds of being content-free. (If nothing else, a comment should betray that the author has read the post commented upon.)

This week and next include more bouncing around, so it may be a while before I get fully caught up and back to normal flow.

On the other hand, once I do get caught up, you'll have a chance to see a Sequoia picture or two, and some posts that have been percolating in the back of my mind.