Climate data is a large ensemble by any reasonable definition. We provided the explicit relationship regardless of the size of the sample.

We just wanted to correct the misimpression that it was not possible to combine data from many sources in order to garner a more precise estimate, even if some of the data has large error bars. We discussed standard statistical methods, but there are much better tools for large ensembles, such as a Monte Carlo or kriging approach.

]]>So we have much more precision,with more data and better instrumentation today than we had years ago, and we can improve on how hot it was at Wichita airport ever since it was an airport. I am not sure what that tells you about the weather in Dodge City or Harper.

What I would like to know is whether you can take tree-ring data from a hundred years ago, and derive any meaningful information from them at all that can be further refined with statistics. Are the trees all pin oaks? Or are they apple trees and orange trees (mixing apples and oranges)? How do you control the many other variables, including whether the pin oak was growing five feet away from another tree?

These data are speculative at best, and should not be used for any argument about the global temperature and the trend over the past hundred years. One can improve one's data by getting more thermometer data from more places.

For that reason we Deniers do not argue at all that it has warmed about a half a degree in the last century, or that the climate changes. That is the straw man that alarmists use to discredit critics. Rather, Deniers argue there is some debate about where we are going, and when the IPCC puts out a forecast to a tenth of a degree, it is fair to ask why they do not use a less precise number.

The proper response to that question is not that 99 percent agree with us, so shut up and get with the program, nor is it to digress into particle physics theory. Rather, one needs to understand and explain one's limitations.

]]>Good example. A gun will not fire exactly the same every time. Let's say we want to determine the true center of a gun's firing pattern, and we've noticed that at a certain distance the shot ranges a centimeter or so around the bulls eye.

To test this, we fire a single shot from a fixed rifle. It may be on the bulls eye, or a centimeter or two away. We really can't say whether this is the true sight of the rifle or not. However, if we fire many shots, they will form a pattern around a fixed point. The pattern of shots will provide a high confidence of the exact center of the rifle pattern (the mean), and the spread (the standard deviation). So even though each measurement may be ±1 centimeter, after many shots, our estimate can be very precise.

Absent biasing, measurements form a standard deviation around the true value. Because of this, we can make a number of important claims about measurement. We can combine measurements with differing accuracy to obtain a standard error which is less than any single measurement.

**Harry**: *And what is a large ensemble? Has it occurred to you that it may be an elusive word loosely defined? *

Standard deviation is *precisely* defined in statistics. And yes, it does depend on N, the number of measurements.

http://www.zachriel.com/blog/standard-deviation-formula.gif

This is critical to understanding any science that relies upon quantitative measurement (which is nearly all of science).

]]>If a sportsman/statistician were to fire a rifle from point A to point B, he goes to the range and sights his rifle. Depending on how steady he is, it may take ten or a thousand times to know where he should aim at a known distance to hit the bulls eye. If he wants to, he can derive an equation that will tell him with great precision where that bullet is, theoretically, along its path, thanks to Newton. All the while, his practical experience improves his aim and confirmation that Newton was right about how things work.

When he goes home, he pulls out a book on the trajectories of blunderbusses, hoping to improve on what he learned at the range, and discovers a large ensemble of data just in volume 23. So he puts all that data into his computer to find out precisely where to aim a blunderbuss as well as he aims his deer rifle.

Please do not refer me to any statistics textbook to argue that one can refine the blunderbuss data, and don't say we do not have enough data to refine. Talk about tree rings and what you do to make sense of them, and how you avoid the post hoc ergo propter hoc fallacy. If the latter problem is unfamiliar to you , I might explain it further and not refer you to a logic textbook.

What I suspect is that you are not what people refer to as a skeptic.

And what is a large ensemble? Has it occurred to you that it may be an elusive word loosely defined? I would like to know what it means to you. If you woke up in the hospital in a body cast and the doctor said, what we have here is a large ensemble of data about you, and therefore we know exactly what your ten problems are, would you ask him to explain himself further?

]]>Statistics informs all measurement, from astronomy to zoology.

**Harry**: *So when presenting the historical record for thousands of locations on land and sea, you have to use thermometers that were precise to tenths of a degree. *

No, you don't. As explained above, the standard error decreasing by the square root of the number of measurements.

]]>Oh gee whiz. Statistics underlies all measurements, from astronomy to zoology.

**Harry**: *So when presenting the historical record for thousands of locations on land and sea, you have to use thermometers that were precise to tenths of a degree. *

No. As we have pointed out many times, the standard error decreases by the square root of the number of measurements, and it is quite possible to combine records with differing degrees of accuracy and precision.

**Harry**: *But I am not going to argue that all inferences are unreasonable, and am pleased to discover you agree that one's data have to be rounded to the least significant integer. *

That is not correct. Pick up a standard text in statistics and look up standard error.

]]>What you cannot do is use a proxy like tree rings, whose size depends on several variables, including temperature and available water and soil fertility, to arrive at how hot it was that year, plus or minus a tenth of a degree, just because no better data are available. You have to account for all of that, including the precision of your instrumentation. As Dirty Harry said, a man has to know his limitations.

By the way, you have not explained what an ensemble is to statisticians. Is it a short-sleeved shirt with a white pocket protector combined with Levi's and Chucks with no socks and a pearl necklace?

]]>The ironic thing about Feline's comment is that there are fewer climate related deaths today as a result of man's activity.

]]>There are three types of lies: lies, damned and statistics.

]]>It's usual to report in tenths of a degree with an uncertainty of ±0.5.

**Harry**: *you cannot infer from your data that it was somewhere halfway in between. *

Yes, actually you can. Even when reporting rounded figures, the mean will be some value in the middle, and the standard error will decrease with increasing numbers of measurements. So even though each measurement is reporting ±0.5, multiple measurements will decrease that uncertainty.

http://en.wikipedia.org/wiki/Standard_error