There is nothing in “being” a statistician that bestows wisdom. It lies in whether the statistical analysis is done properly. If the AP story correctly presents what the “four statisticians” said, there is a great deal missing from the account.

For example, was the only statistical analysis made a simple linear regression on the entire data set? Such an analysis implicitly assumes that the slope (if any) is constant. No one denies that the trend has been generally upward since the ending of the Little Ice Age. But the hypothesis to be tested is that the slope has changed in the past ten years or so. For that, a different sort of test is required.

However, the AP is remarkably silent on what was actually done. Moreover, if the statisticians were not told what the data was, how could one of them then make a statement about temperature trends? Unless they were told afterward. Left unstated is whether they found an upward trend in the past ten years of data and, based on past data, whether such a flat 10-year period is likely.

My basic argument has been, and remains, what is really happening as opposed to what the IPCC and its cronies have predicted would happen based upon their so-called “models?” The answer is that they haven’t even been close. That is the reason for all the “cooling” talk. As George E. Smith pointed out, what is worse is that the surface temperature data that the alarmist scientists use to try to bolster their arguments is highly questionable if not unreliable.

Further, let’s face facts: all climate predictions are shams. Talk of “trends” are useless, and it is time guys like you recognize this. These guys couldn’t predict tomorrow’s weather much less predict long-term climate “trends.”

That’s an inappropriate analogy. We skeptics are consistently applauding and deriding, respectively, the proper and improper use of statistics. (And we aren’t focusing primarily on the statisticians, but on the way their methodology can be used inappropriately.)

“the decadal and interdecadal trends are still pointing up;”

Sure, because the PDO has a 30-year cycle. Now it’s turning. Hit page-up 12 times and see my post that parses and critiques the statistics and argumentation used in the AP article. In particular, here’s its key point/counterpoint:

“They say that since then, temperatures have fallen — thus, a cooling trend. But it’s not that simple.”

That’s a red herring (diversion). It IS that simple, because a short-term flattening and cooling trend falsifies the IPCC’s prediction for this decade, casting doubt on its models’ reliability; because it casts doubt on the implacability (and the urgency of the threat) of CO2’s alleged “forcing”; and because the PDO has flattened and turned negative at about the same time, which suggests that the PDO is the climate “forcer,” not CO2.

And here’s what I posted as a follow-up to it on another thread on this topic:

“If a patient has a fever and the fever “breaks,” that breakage can’t be waved aside with the diversionary argument that the temperature decline hasn’t lasted long enough to be a long-term trend. No one is claiming it is a long-term trend–-just that the fever (most likely PDO-driven) has broken.”

There you are Merrick; a direct quotation from my post ; exactly what it was I said; that evidently you completely misunderstood. I was extremely careful in the choice of words that I used; I usually am.

It is not my fault if people substitute their own words for mine.

In “other words” lies “other meaning”. So I choose to not use “other words”.

Well, George E. Smith – let’s test your “hypothesis” – A head in the oven and feet in ice water. This defines an integral or an average how? If you’re a mathematician, as you claim, why don’t you use descriptions which actually apply?

Now, by definition, an integral is a sum. An average is a sum multiplied by the inverse of the number of elements in the sum. So the difference between a sum and an average is a multiplier. We can’t get into calculus if you want, but no matter how you slice it my statement is exactly and unquestionably true.

Your image is colorful, but it’s fairly meaningless. “”

Well Merrick, I give up; you clearly didn’t read what I said; and since you didn’t read that and understand it, then you didn’t get the point of my “frairly meaningless” example.

To reiterate; I said that climatologists (in their writings) define climate as the long term average of weather. Note the two terms climate and weather. Nowhere is the word “temperature” mentioned. That is their definition not mine.

And I asserted that I believe that climate is the integral of weather. Once again no mention of the word temperature.

Weather and climate encompass a whole lot more variables than simply temperature. And the planet as a whole reacts to the continous sum of THE EFFECTS of all those variables that change during the course of what we call weather.

I’m sure there are some aspects of both weather and climate that might react to the average of temperature; but what about the many effects of both climate and weather that are a direct result in DIFFERENCES of temperature from place to place and from time to time.

It is the integral of THE EFFECTS of weather that makes its mark on the planet.

So if you believe that the integral of weather (not temperature) is just a factor times the average of weather (not temperature); what value do you presently have for that constant (or varying) factor that relates the integral to the average.

And to revisit my fairly meaningless example; I quite deliberately chose the extremes that I used so that it was quite clear that the EFFECTS of some of the “weather” items; such as the superheated steam, and the dry ice were of such a nature that they would never be cancelled out by some other extreme weather event; to yield a benign average result.

If you want to believe that we can get the climate by simply multiplying the weather (averaged in some way of course) by a factor; well you are welcome to that point of view.

I wonder what the average of a Hurricane and a Tornado is, in climate science terms of course.

And as to my “credentials” which you see fit to impugn there is more than one bio to be found out there in webland. I didn’t write any of them; so they are probably about like what typical Journalists might write from information they get from various sources. I’m sure if you contacted my alma mater, you could easily get what are the public records; they aren’t secret.

Now, by definition, an integral is a sum. An average is a sum multiplied by the inverse of the number of elements in the sum. So the difference between a sum and an average is a multiplier. We can’t get into calculus if you want, but no matter how you slice it my statement is exactly and unquestionably true.

Your image is colorful, but it’s fairly meaningless.

Your complaint is that the (min+max)/2 definition of average temperature is at best inadequate and at worst ludicrous. I coudn’t agree more. Your argument was still poorly made, your counter to criticism was equally so. You immediately assumed I disagree with you, and I don’t. What I was criticizing was what I saw and still see as poor arguments.

An integral is a sum. An average is a weighted sum. Talking about heads in ovens and feet in ice water doesn’t change that.

When we translate from Statisticalese into plain Engish, there’s not always a one-to-one correspondence. Take the word “no”. When a statistician says “no recent cooling trend”, what does he mean? Here’s my educated guess about the meaning of the word “no” in this context:

Null hypothesis: Global temperatures in recent years have not changed appreciably. Given the paucity of global temperature data over the last 11 years, and given the high noise level within that data set, we cannot reject the null hypothesis at the 95% confidence level.

If the statisticians in the AP story had been able to reject the null hypothesis with even 90% confidence, that would still not pass muster; 95% is the magic number. In other words, “no” does not always mean no.

That’s pretty much what I said: the extremal average is unbiased under strict conditions not likely met by the distribution of temperatures during the day, and even if it were, it is extremely sensitive to outliers in the data. A proper daily average needs to take samples at multiple times during the day.

“Funny how a group of uninvolved statisticians all arrived at the same conclusions, yet are vilified here. I can’t for the life of me understand how people can’t look at the data objectively, and continue to entrench themselves further with confirmation bias (in this case, ignoring substantive findings that conflict with their belief system).

Amazing what the human psyche will go through to maintain it’s version of reality…”

We have seen the actual data, do we need unnamed “uninvolved statisticians” to tell us what we see? We see temperatures not following the predictions of the vaunted climate models. Skeptics favour the null hypothesis in the face of what could charitably be called insufficient evidence for AGW. One only has to look at the statistical atrocities committed by “confirmation bias” prone scientists their pathetic attempts to get rid of the medieval warming period. Appeals to authority get no traction here, skeptics have seem too many authorities disgrace themselves over the so called “settled science”.

@George Smith

The extremal average (M+m)/2 may not be an unbiased estimator if the distribution of values within the day is not symmetric. Even if it is, and even if it is approximately Gaussian*, it is still an inefficient estimator. If there are outliers in the daily data, due to measurement system error or actual +/- spikes, those outliers will be one or the other or both of the extreme values, and so will affect the extremal average, making the estimator subject to considerable variation.

If it is impractical to “integrate” over the entire series of daily temperatures — perhaps temperatures are not taken continuously — it would make more sense to take samples at random times of the day and compute a sample average and sample standard deviation. (Of course, there is the problem of serial correlation…) “”"

Well Mike, the simplest situation would be if the daily temperature cycle at a single loaction were a pure sine wave. (M+m)/2 ; to use your terminology, would in fact be the correct average, and moreover would meet the Nyquist criterion for two samples per cycle of the highest signal frquency (in this case only one frequency). But in general exactly two samples per cycle (not M and m) is not sufficient to reconstruct the signal; it’s a degenerate case. For a non sinusoidal but periodic signal, there must be at least a second harmonic component or higher frequency present, so at least four samples per day would be required to at least get the average correct, although once again not to reconstruct the signal. Bear in mind that at exactly two samples per cycle, the samples would be phase locked to the waveform, and would never reveal the waveform; but a slightly higher sample frequency, would slue the sampling, and eventually capture the complete waveform.

But the real daily cycle is not sinusoidal so two samples per day even M and m cannot give a correct average. More importantly the radiated thermal emission, that is a consequence of the temperature, varies more as the 4th power of the temperature, so the daily integrated radiation is always greater than what is calculated from the average temperature; even if you do have the correct average temperature. It’s a small but not zero effect for the daily cycles; but is quite significant for the annual cycle.

No you don’t have to take the temperature every second or minute; but more often that twice daily M and m is worse than crude; and as I have said in the past; that completely ignores the effect of random cloud changes. Gaia does NOT ignore the effect of cloud changes on even the average temperature; let alone on the weather and climate.

George E. Smith – the only difference between and integral and an average is a multiplier – but what do I know, I’m only a chemist and a physicist. “”"

Well Merrick, let’s test your thesis with the often cited absurdity. Shall we place your legs in Dry ice at -80 deg C, and simultaneously put your head in superheated steam at 120 deg C. On average you are at a very comfortanble +20 deg C; but if we integrate (add up) the effects of the “weather events”, the results are quite uncomfortable; fatally so. So what multiplier would you suggest to equate the two situations.

Climate is the sum total of ALL of the weather events that have ever occurred.

Under the average conditions; there would be no weather at all.

http://www.amazon.com/How-Lie-Statistics-Darrell-Huff/dp/0393310728/ref=sr_1_1?ie=UTF8&s=books&qid=1256832335&sr=1-1