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A lesson in statistics

September 11th, 2003

Ken Parish supply the expected quibbles for my post on global warming. He illustrates some important statistical fallacies in the process. To support my case that the weather has got no cooler relative to the “the climatic extremes of 1998-2002″, I linked to the NOAA/National Climatic Data Center which showed that during the period since Daly’s post “January-July 2003, the global average land and ocean surface temperature was 0.54¡C (0.97¡F) above the long term mean, third warmest “.

Ken’s response is to go back to the underlying data and perform comparisons between Jan-July 2003 and the corresponding period in 2002, as well as month by month comparisons between 2002 and 2003 . Since the data set consists of deviations from long-term averages, it has no seasonal pattern, and there is, therefore, no justification for this procedure, or for focusing on 2002 when my post referred to the period 1998-2002 (the warmest five-year period on record,). It does, however, mean that the base period for his comparisons includes three of the four warmest months (in deviation terms) in the entire data set, all of which were in early 2002 (you can see them in the graph below). This is a prime example of ‘cherrypicking’.

Ken’s next move is to compare the individual months of June and July 2003 with the corresponding months in 2002, finding them to be cooler by 0.09 and 0.05 degrees respectively, and says “Thus the weather has got cooler since last year, albeit only slightly so far. ” In drawing this conclusion, he ignores the problem of statistical signifiance, which is acute when making pairwise comparisons for periods as a short as a single month. It’s easy to check that, even if you suppose that the data is an average of 1000 independent observations (far too many, given that short-term weather patterns at adjacent points are highly correlated) and that the standard deviation of monthly average temperatures at a given point is 1 degree, the difference found by Ken is statistically, as well as climatically insignificant.

All this might lead you to conclude that you can prove anything with statistics. But in fact, this is one case where you don’t need elaborate statistical analysis. The graph below (taken from NOAA) makes it clear that there is a warming trend that swamps the short-run cycles associated with sunspots and El Nino events.


To end on a positive note, I broadly agree with Ken’s assessment that

If the global average temperature falls back to well below the long-term average by 2006 that would suggest Daly may be correct. On the other hand, if it continues to fall but remains above the long-term average, that will clearly demonstrate the imprint of man-made global warming.

To be more specific, I predict that the average global temperature for 2006, as measured by NOAA, will be above the average for 1971-2000 (the baseline in the chart above) and I promise a retraction if this prediction is not correct.

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  1. Ken Parish
    September 11th, 2003 at 22:25 | #1


    My post was hardly a nitpick, nor does it merit your “lesson” on statistics. My post made precisely the point you’ve just repeated about the recent temperature drop being statistically insignificant:

    Thus the weather has got cooler since last year, albeit only slightly so far. But that’s pretty much what you’d expect (whether or not Daly is correct). The recent El Ni–o only started to taper off around February, so you’d expect that temperatures would so far only have fallen slightly. It’s simply too early to tell at present …

    The point of my post was to suggest that you were playing a little fast and loose in suggesting that Daly’s prediction was already looking shaky (at the very least) merely because of the alleged failure of temperatures to exhibit a fall over the last few months, but was refusing to admit it: “Of course, Daly will find a way to ignore all this.” Would you deny that the temperature record since the El Nino started to abate in about February this year does nothing to disprove Daly’s argument?

    To avoid being misconstrued, let me stress that I agree with you that the temperature record of the last 25 years or so seems already to show a fairly clear imprint of human-induced warming (albeit there’s plenty of room for conjecture as to its magnitude). I don’t even clearly understand how Daly mounts his case to the contrary. I know he argues that the high temperatures of 1998-2002 are explained by the fact that 2 separate El Nino events and a solar maximum overlapped, but I don’t know how he seeks to explain the fact that the period 1978-1987 was also consistently above the long-term average (while the previous 30 years had been consistently below, even though computer models suggested that warming should have been taking place). Perhaps he argues that this is just too short a dataset to draw meaningful conclusions, an argument you yourself have deployed in other contexts.

    Whatever Daly’s detailed argument about the immediate past, once you accept that he’s now made a testable prediction you can only in all fairness allow a reasonable time to observe what actually happens. Your post was unfair in suggesting wrongly (albeit obliquely) that Daly’s prediction was already looking shaky from weather over the last few months. There simply hasn’t been time for the prediction to be assessed against reality, and temperatures to dat are entirely consistent with his prediction. As I said, the proof will be how low the global average temperature dips by comparison with the long-term mean by around 2005-6. In that respect at least, it appears we both agree.

  2. John
    September 12th, 2003 at 06:26 | #2

    Ken, I’ll just point out that Daly explicitly made his prediction for “the months and years ahead”. I was going to emphasise this, and obviously should have done so.

  3. Ken Parish
    September 12th, 2003 at 11:03 | #3


    On any reasonable, fair-minded basis using the expression “the months and years ahead” does not bear the interpretation/conclusion that Daly’s prediction has failed because the measured temperature drop in the 4 months since El Nino began to recede is below statistically significant levels. The speed with which the global mean temperature reacts is dictated by the speed with which the El Nino oscillation reverts to neutral, and may also be influenced by one-off large scale weather events in a single month, such as the large blocking high pressure system that caused the recent heatwave right across Europe. Daly knows this at least as well as you or I, and he clearly didn’t mean by the use of “months and years” that we could necessarily expect a precipitous drop instantaneously. In fact, any reasonable interpretation would assume he used the expression to connote the fact that you can’t be too precise about the exact timing of events i.e. almost the exact opposite of the interpretation you want the words to bear.

  4. Brian Bahnisch
    September 13th, 2003 at 11:41 | #4

    In my limited understanding of these things, there are four major systems affecting Australia’s weather.

    1. The seasonal monsoons
    2. The polar and Southern Ocean circulation patterns
    3. The Pacific Ocean (El Nino, La Ninja, waters temperatures, wind and current direction)
    4. The Indian Ocean (not a lot is known as the Yanks have just recently devoted a satellite to monitoring it, but it is clearly significant for us)

    There was also a Southern Ocean warm wave effect – a giant warm wave or waves circulating the globe. I understand this has broken down in recent years.

    To the north, Indonesia is one of the biggest lower/upper atmosphere interchange regions on the planet.

    In recent years, there has been an unusual pattern of anti-cyclones (high pressure systems) moving across the Southern part of the continent.

    It seems that the southern systems are staying further south (Catalyst on ABCTV next Thursday is doing an item on this – it seems the polar convection systems are pulling in tighter). At the same time the Monsoons seem to be staying further north. Where I sit in Brisbane it means we are drier and hotter.

    Re El Ninos, I thought the significant thing is that they are happening more frequently and the interesting thing is why.

    To what degree changes in these systems are caused by human activity is, I think, still a bit moot, but I believe in the precautionary principle. My brother, who grows beef around Rockhampton, tells me they have done core samples of the Reef going back 300 years. From memory, he said there were periods in that time when there was no rain at all to make the rivers run in Central Queensland for 10 years or more. These events preceded any increased carbon outputs attributable to the human race.

    I must stress I have only a lay interest in these matters, so please treat the above accordingly.

  5. September 13th, 2003 at 12:42 | #5

    It’s interesting to note that on that chart the coolest period noted is in the mid 1970s, which is when the ‘climate change’ experts were telling us that man made pollution was going to trigger a new Ice Age.

    The “End of the World” syndrome sells a lot of books but it’s been used quite a bit in the last 50 years, which is why some of us are a wee bit sceptical.

    There has, of course, always been climate change. The weather system of the globe has always been a dynamic thing- something I’ve noted reading European history over the last 1,000 years. There seems to be a notion going around that nature is static. It’s not, and never was.

  6. September 13th, 2003 at 15:45 | #6

    Scott, there is a massive difference between global warming, and the ice age scare of the 70′s. There wasn’t a single scientific paper which predicted a human induced ice age published. Whereas, global warming is backed up with hundreds, if not thousands, of scientific papers.

  7. PK
    September 15th, 2003 at 21:51 | #7

    Which long-term average are you talking about? That of the past 100 years? If you’re talking about weather patterns, 100 years is insignificant.

    Geological history shows temperatures have varied a lot over the life of the planet, often changing quite suddenly.

    So while the temperature may be rising (or may not), there is no proof that this phenomenon is man-made.

  8. September 15th, 2003 at 22:21 | #8

    PK, your mistaken, 100 years is a significant period of time climatology.

    On different time scales, different effects predominant, so while on a multi-million year scale; continental drift, the position of the solar system in the galaxy etc all play significant roles in determining climate variability.

    Meanwhile, on a multi-decade scale, climate variability is predominately determined by solar activity, volcanos, and greenhouse gases. The increase in concentrations of the latter being virtually all man-made.

  9. Greg
    September 19th, 2003 at 10:18 | #9

    PK is quite right if we disallow John Quiggin and John Daly (quoted by Quiggin at his post on ‘Kyoto and error‘) their implicit assumption of ‘other things equal’. Either will turn out to be right in 2006 only if some long-term weather influence doesn’t intervene to rapidly shift the current long-term (120-year) mean. Any such intervention would render the sample size over which they are arguing ‘too small’. Possibilities include:

    processes whose operation is not well understood (eg, the ‘Thermohaline Circulation’ system [Ref 1]);
    an outbreak of large-scale volcanism or lava flows;
    asteroid impact (it’s a matter of when, not if, and there hasn’t been enough funding to date to complete the mapping of them);
    catastrophic nuclear detonations; and, of course,
    as-yet-unknown processes in the categories listed at [Ref 2] (Brian Bahnisch’s surmised causes are probably covered by the diagram).

    Ken Miles is right once we let the processes underlying the current global long-term mean continue uninterrupted. The sample size becomes valid and Quiggin is then supported by most of the evidence I’ve been able to find:

    140 or so years of formal record keeping [Ref 3, Ref 4]; and Palaeoclimatological data going back
    One thousand years [Ref 5, Ref 6] (northern hemisphere only); and
    240 thousand years [Ref 7].

    The 414 thousand-year data [Ref 8] is intriguing but I’ll leave comment on it to others. A lot of data covering these other periods is available for downloading and spreadsheet processing at [Ref 9] and there are some instructions on how to do it at [Ref 10] (requires careful thought and application – I may be able to help a bit).

    They’re all interesting and the shorter-term data, at least, support pretty strongly the global warming hypothesis. In the [Ref 7] 240-thousand-year graph, three feaures stand out. Firstly, the contrast between the sharp peaks and troughs over most of the range and the ‘plateau’ of just the last 8-10,000 years comprising tiny oscillations close to the modern mean. Global temps appear to have been struggling vainly back downwards for most of the period. What’s been keeping them up? Secondly, for most of the last 240 thousand years, global temperatures – and therefore almost any 120-year mean you may care to take – have been at least 3-6 degrees C. below those of the present era. Thirdly, there’s an overall impression of a ‘bouncing’ sort of effect, with relatively quick ‘ups’ followed by more leisurely returns to lower equilibria. The last big rise, from around 15,000 to 10,000 years ago, represents the end of the last ice age I guess. This chart, if reliable, really makes it look like we are well overdue for a return to more ‘normal’ temperatures – ie, 3 to 6 degrees C. lower. On this basis, perhaps the long-term determinants of global mean temperature are trying to get temperatures lower but are being held up for some reason. It hardly seems likely that they will suddenly succeed in the next couple of years, having apparently been stymied for at least the last 8,000 years.

    Until those long term determinants succeed, whatever they may be, the issue of whether humans are the main cause of the clear global warming trend is probably not as important as another issue. That’s the issue of whether we are able as a species to utilize our knowledge of the greenhouse mechanism – and take the first steps towards teaching ourselves terraforming. It’s a skill that I think the long-term data suggests we could profitably learn, and to acquire it would be as revolutionary in effect as Gregor Mendel’s formulation of the rules of heredity. All that now stands between us and our undoubted ability to lower the level of atmospheric carbon dioxide is short-sighted political leadership.* Once we have proved to ourselves that we are able to overrule our frequently unrepresentative political leaders to achieve downwards flexibility in atmospheric CO2 volumes, we can always do a bit more terraforming and kick the carbon dioxide emissions back up again if things start getting too cold for us. We know how to do that.

    *It has consistently let us down on a range of issues, of course: obtuse creation of terrorist/freedom fighter movements; depletion of environmental capital assets; premature spread of GMO products; media promotion of violent values, etc.

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