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Storks Deliver Babies (p0.008)
KEYWORDS:
Teaching;
Correlation;
Signi¢cance;
p-values.
Robert Matthews
Aston University, Birmingham, England.
e-mail: rajm@compuserve.com
Summary
This article shows that a highly statistically
signi¢cant correlation exists between stork
populations and human birth rates across Europe.
While storks may not deliver babies, unthinking
interpretation of correlation and p-values can
certainly deliver unreliable conclusions.
^INTRODUCTION ^
Introductory statistics textbooks routinely warn
of the dangers of confusing correlation with
causation, pointing out that while a high corre-
lation coe¤cient is indicative of (linear) association,
it cannot be taken as a measure of causation. Such
warnings are typically accompanied by illustrative
examples, such as the correlation between the
reading skills of children and their shoe size, or the
apparent relationship between educational level
and unemployment (see e.g. Freedman et al. 1998).
However, such examples are often either trivially
explained via an obvious confounder (e.g. age, in
the case of reading age and shoe size) or are not
obviously cases of mere association (e.g.
educational level may indeed be at least partly
responsible for time spent unemployed). In what
follows, I give an example based on genuine data
of an association which is clearly ludicrous, but
which cannot be so easily dismissed as non-causal
via an obvious confounder.
My starting point is the familiar folk tale that
babies are delivered by storks. The origins of this
connection are believed to lie partly in the
association between storks and the concept of
women as bringers of life, and also in the bird's
feeding habits, which were once regarded as a
search for embryonic life in water (Cooper 1992).
The legend lives on to this day, with neonate-
bearing storks being a regular feature of greetings
cards celebrating births.
While it is (I trust) obvious that the legend is
complete nonsense, it is legitimate to ask precisely
how one might set about refuting it scienti¢cally. If
one were approaching the question in the same
way that many other links are investigated (e.g.
suspected links between diet and cancer risk), one
may well decide to carry out a correlational study,
to see if the number of storks in a country bears a
simple relationship to the number of human births
in that country. Although the presence of a
statistically signi¢cant degree of correlation cannot
be taken to imply causation, its absence would
certainly constitute evidence against a simple
relationship. This possibility can quickly be
investigated in the present case using standard
hypothesis testing, with the null hypothesis being
the absence of any correlation between the number
of storks and the number of live births in a
particular country. This I now proceed to do.
36 .Teaching Statistics. Volume 22, Number 2, Summer 2000
^TESTING THE STORK-BIRTH ^
RELATIONSHIP
The white stork (Ciconia ciconia) is a surprisingly
common bird in many parts of Europe, and data
on the number of breeding pairs are available for
17 European countries (Harbard 1999, pers.
comm.); the latest ¢gures, covering the period from
1980 to 1990, are given in table 1, along with
demographic data taken from Britannica
Yearbook for 1990.
Plotting the number of stork pairs against the
number of births in each of the 17 countries, one
can discern signs of a possible correlation between
the two (see ¢gure 1).
The existence of this correlation is con¢rmed by
performing a linear regression of the annual
number of births in each country (the ¢nal column
in table 1) against the number of breeding pairs
of white storks (column 3). This leads to a
correlation coe¤cient of r0:62, whose statistical
signi¢cance can be gauged using the standard
t-test, where trpnÿ2=1ÿr2 and nis the
sample size. In our case, n17 so that t3:06,
which for nÿ2 15 degrees of freedom leads to
ap-value of 0.008.
^ANALYSIS ^
What are we to make of this result, which points
to a highly statistically signi¢cant degree of
correlation between stork populations and birth
rates? The correlation coe¤cient is not particularly
high, but according to its p-value, there is only a
1 in 125 chance of obtaining at least as impressive
a value assuming the null hypothesis of no
correlation were true. Yet as with any p-value (and
contrary to what unwary users of them believe),
Country Area
(km2)
Storks
(pairs)
Humans
(106)
Birth rate
(103/yr)
Albania 28,750 100 3.2 83
Austria 83,860 300 7.6 87
Belgium 30,520 1 9.9 118
Bulgaria 111,000 5000 9.0 117
Denmark 43,100 9 5.1 59
France 544,000 140 56 774
Germany 357,000 3300 78 901
Greece 132,000 2500 10 106
Holland 41,900 4 15 188
Hungary 93,000 5000 11 124
Italy 301,280 5 57 551
Poland 312,680 30,000 38 610
Portugal 92,390 1500 10 120
Romania 237,500 5000 23 367
Spain 504,750 8000 39 439
Switzerland 41,290 150 6.7 82
Turkey 779,450 25,000 56 1576
Table 1. Geographic, human and stork data for 17
European countries
Fig 1. How the number of human births varies with stork populations in 17 European countries.
Teaching Statistics. Volume 22, Number 2, Summer 2000 .37
this does not imply that the probability that mere
£uke really is the correct explanation is just 1 in
125; still less does it imply a 124=125 99:2%
probability that storks really do deliver babies.
Such apparent nit-picking distinctions are fre-
quently overlooked by consumers of p-values. In
the case of the correlation between storks and
human births, however, they no longer seem so
pedantic: indeed, they provide the very welcome
`escape route' by which to avoid a patently
ludicrous inference. The most plausible explan-
ation of the observed correlation is, of course,
the existence of a confounding variable: some
factor common to both birth rates and the
number of breeding pairs of storks which ^ like
age in the reading skill/shoe-size correlation ^ can
lead to a statistical correlation between two
variables which are not directly linked themselves.
One candidate for a potential confounding variable
is land area: readers are invited to investigate this
possibility using the data in table 1.
^CONCLUSION ^
Standard statistical texts routinely warn of the
fallacy of mistaking correlation for causation, but
the examples they provide are usually either trivial,
with obvious confounders, or lack clear non-
causality. The empirical relationship between the
number of stork breeding pairs and human birth
rates in 17 European countries provides a non-trivial
example of a correlation which is highly statistically
signi¢cant, not immediately explicable and yet
causally nonsensical. Indeed, its sheer absurdity has
pedagogic value beyond the correlation/causation
fallacy alone, as it compels greater attention to be
paid to the precise meaning of p-values, and
promotes greater recognition of the fact that
rejection of the null hypothesis does not imply the
correctness of the substantive hypothesis.
Acknowledgements
The author is very grateful to Chris Harbard of
the Royal Society for the Protection of Birds for
supplying the stork data, and to Professor Dennis
Lindley for valuable discussions.
References
Cooper, J.C. (ed.) (1992). Brewer's Myth and
Legend. London: Cassell.
Freedman, D., Pisani, R. and Purves, R.
(1998). Statistics (3rd edn). New York:
W.W. Norton.
The Big Ticket: How Not to Design a Game Show
KEYWORDS:
Teaching;
Probability.
David Burghes
University of Exeter, England.
e-mail: d.n.burghes@exeter.ac.uk
Summary
This article analyses a television game show and
suggests improvements.
^INTRODUCTION ^
You may have seen this game show, which
was broadcast for 8^9 weeks on Saturdays
on television in the United Kingdom in the spring/
summer of 1998 as an extended National Lottery
show. I only saw parts of some of the shows, while
waiting for something else, or by mistake! I was
amazed that such an unappealing programme was
broadcast at all.
At the end of each show there was ridiculous
over-promotion of a game in which the ¢nal
contestants were certain to win substantial sums of
money. Just in case you missed the shows, I
summarize in ¢gure 1 the way this game worked.
The game seemed incredibly predictable as it was
impossible not to win a substantial amount, with a
low ceiling on the maximum that could be won,
compared with the guaranteed minimum winning
amount.
38 .Teaching Statistics. Volume 22, Number 2, Summer 2000
