A Better Explanation of Tamino’s Folly
Posted by Jeff Id on October 23, 2008
Ok, I can’t blame the posters from my last article. It is clearly my fault for not explaining what I did well enough. Fortunately for me, others have a better gift for this than I. I have referred to the Digital Diatribes blog repeatedly for trend analysis, simply because he does the best job on the internet of describing the measured trends of several key values. He posted this comment on Watts Up With That.
This is how he described my methods using a more beter vucabilary than me.

Diatribical Idiot
Here’s my attempt at a clarifying point, as I understand it:
There is a difference between the standard deviation of the data itself that calculates a confidence around a mean value and the confidence interval of the observed trend line. The ARMA analysis originally done proves the point that actual observed data showing a negative trend can occur within a longer range set of data that has a positive trend. It does not prove that the current observations fall into that increasing trend model, only that it is possible, and a reasonable hypothesis. It doesn’t negate the hypothesis at all that the observed trend is a correct reflection of the actual trend.
The statement Tamino seems to dispute is a statement of observed fact. The observed fact is that trend lines (I’m assuming the author meant 2001current as “this decade”) show that there has been cooling. This is not the same as saying that global warming has stopped, nor is it a statement that says this could be one of those aberrations that occur with fluctuating data. It says that, given the observed data, the trends are negative.
Tamino used a valid statistical process to make an invalid claim: that the author made an incorrect statement about the cooling trend lines. Whatever one’s thoughts about the statistical validity of a low rsquared of the trend line or high standard deviation of the observed data, the best that Tamino should have done with his point is to refer back to his ARMA presentation and remind the readers that the observed negative trend may well be the effect of what he refers to as “noise” and leave it at that.
What Jeff has done is to show that the calculated trend line, which is the best fit regardless of your comfort level with the best fit, is properly calculated – given the observed data – to a high degree of certainty. The only uncertainty with the observed data that would impact the certainty of the trend calculation then, is the measurement error in the observations.
A proxy to test this is consistency of the different sets of temperature measurements. By determining that the significance of these differences are not enough to change the trend line significantly enough to turn a negative trend into a positive trend, the conclusion is that we can be reasonably certain that the best fit trend line of temperature measurements are, in fact, negative.
The argument is simply that making such a statement is a true statement, based on observed data, and is in no way some kind of manipulation of fact by a “denialist.” It does not argue that other considerations as to why it is negative shouldn’t be considered through techniques such as an ARMA analysis.
Only one point of difference which I believe was wording. Tamino’s statisical process was valid for another type of analysis NOT for this one. Still I believe that is what our Random friend meant.
3 Responses to “A Better Explanation of Tamino’s Folly”

October 23, 2008 at 9:06 am
@Jeff
Sorry, but after rereading everything (inc. a couple of Tamino’s post), I still think that you & Tamino are trying to prove different things (i.e. talking at crosspurposes). Where you & he part company is when you say:“The first thing you notice from this graph is that the 3 measurements track each other pretty well. The signal is therefore not completely noise.”
After this point you & he are talking about completely different things, and therefore you cannot claim to have disproven his point (since you haven’t actually addressed it at all, but rather have proven SOMETHING ELSE – something unrelated to what he discusses).
If you don’t like calling shortterm variations “noise” then don’t. Call it (say) “weather variations” instead. But that does not stop ARMA from modelling “weather variations” in a convincing fashion – see here:
http://tamino.wordpress.com/2008/09/12/dontgetfooledagain/Just to repeat once more (before I giveup this particular discussion), your objection seems to be based on a particular (and highly specific) interpretation of the word “noise”. Whereas I (and seemingly Tamino) are taking a more practical view – if “weather variations” can be accurately modelled as ARMA, then it seems reasonable to label it “noise”. Just don’t get hungup on that particular label when trying to extract it from real temperature data.
I have also posted this reply on your priorup blog item:
http://noconsensus.wordpress.com/2008/10/21/taminosfollytemperaturesdiddrop/#comment789 
October 23, 2008 at 9:20 am
P.S. Another way to look at it is that Tamino classes ANY variation from the (overall) linear trend as “noise”. Again, if you dislike that word then use something else. His point is that these variations from the linear trend easily hide the actual linear trend over short periods.
Sure, I perfectly agree that we have seen a downward trend in the last 10 years, but the point Tamino was trying to make is that this is meaningless when trying to disprove longterm Global Warming (which I personally believe is NOT manmade).
Chris H said