Monday, 27 April 2015


Introductory books on statistics usually start by noting some ways in which they can
used to mislead.  A popular textbook possibly still in use was called "How to lie with
statistics",  Three elementary fallacies were usually noted:  the selection of base dates
for a time series;  possible misuse or misunderstanding of averages;  and the
fact that correlation does not imply causation.  All three are widely evident in the
debate about global warming.
(1)  Selective use of base dates:  Long-run series of temperature statistics usually start
about 1850,  However this was towards the end of the Little Ice Age  (in fact, I think
the cold era could be regarded as continuing until about 1900) so that this starting
point shows figures for subsequent years rising more than they would is based on
a presumably "more normal"  one.  Even more importantly, the two or three decades
leading up to 1970 (in some cases, 1976)  were much colder than the preceding five,
so that an annual series starting then shows a much higher rise since. What would be
a "normal" year ro series of years to use as a base date?  The answer is that there
isn t one, and all that can be done is to give the raw figures for as many years as
possible and allow the reader to form a judgement.
                                  The practice, adopted by all sides in the global warming
debate, of giving annual figures as "anomolies"  also presupposes that the base date(s)
are in some sense normal.  Using a fairly long period of time as the base helps to
remedy this; for example the most recent World Bank Development Report, for 2014,
shows (Table 9, p.316)  global temperatures relative to 1951-1980.  This seems at
first sight a fairly fool-proof  procedure, but it includes three probably cold decades and only one warm one, 1970-1980.
                                  The anti-warmists, in arguing that global temperatures have not
risen since about 1997, fall into the same fallacy.  It is fairly universally agreed that
the decade of the 1990s was exceptionally warm  (there were three El Ninos, which
usually come at intervals of up to five years)  and a stable statistical series starting from
a high base date is compatible with a long-run rising trend.  (In any case, it does not seem
to be true that global temperatures have not risen since ca. 1997.  The World Bank
table just quoted shows an anomaly of 0.59 for 2001-2010, compared wirth 0.37 for
(2)  The dangers of averages  The elementary statistical textbooks often quote the
example of the non-swimmer told that a river is on average 3 feet deep, walks in and
gets drowned.  The point of course is that an river could be much deeper than three feet
in some parts if it is shallower than that in others.  .Foe many (most) purposes, differences
in temperature-  polar, temperate zones and tropics; day and night;  summer and winter,
ground level and atmosphere (lower and upper)- \are more important in tryng to elucidate
causal relationships than is the global average.  In addition it seems that there is a causal
link between opposing trends in different regions.  This may be more apparent in
rainfall than in temperature trends. For example there seems to be a link between wet
weather caused by El Nino in the Southern Hemisphere and drought in California  (though,
one of many cases where assumptions and prediction are unrelaible, the expected severe
El Nino in 2014 did not materialise, and California is suffering one of its worst droughts
on record).
(3)  Correlation does not imply causation  The textbooks in the 1950s used to quote the
example of the birth rate and the number of storks in Sweden in the 1930s- both were
falling at about the same rate. Many discussions of the link between atmospheric carbon
dioxide and global temperatures consist of little more than a juxtaposition of two
series of statistics, with little attempt to set out the physics, chemistry and meterology
of the presumed link  (this is true for example of Unit 1, "Global Warming", in an
otherwise admirable Open University course "Exploring Science",  S104 and, even more
a very close examination of  alternative  explanations.


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