Geoscience Reference
In-Depth Information
Chapter 12
Statistics and other damned lies
The remark attributed to Disraeli
would often apply with justice and
force: 'There are three kinds of lies:
lies, damned lies, and statistics'.
Mark Twain
be achieved in one fell swoop by a large vol-
cano sampling a large volume of the same man-
tle. If the outputs of many large volcanoes are
plotted on a histogram, the spread will be much
smaller than from the rock samples, even though
the same mantle is being sampled. Midocean
ridges sample vast volumes of the mantle and
mix together a variety of components. They are
the world's largest blenders. Seamount and ocean
island volcanoes sample much smaller volumes.
This is a situation where the
central limit
theorem
(CLT) applies.
['lies, damn lies -- and statistics' (sic) --
usually attributed to Twain (a lie) -- or
to Disraeli (a damn lie), as Twain took
trouble to do; Lord Blake, Disraeli's
biographer, thinks that this is most
unlikely (statistics)].
The central limit theorem
The
central limit theorem and the law
of large numbers
state that variably sized
samples from a heterogenous population will
yield the same mean but will have variances
that decrease as
n
(the sample size) or
V
(the
volume of the sampled region) increases. Small
sample sizes are more likely to have extreme
values than samples that blend components from
a large volume [
CLT isotopes
]. One expects
that melt inclusions in a lava sample will have
greater isotopic diversity than that sampled in
whole rocks.
An amazing thing about the central limit the-
orem is that no matter what the shape of the
original distribution -- bimodal, uniform, expo-
nential, multiple peaks -- the sampling distribu-
tion of the mean approaches a normal distri-
bution. Furthermore, a normal distribution is
usually approached very quickly as
n
increases;
Overview
Semantics, rhetoric, logic and assumptions play
a large role in science but are usually relegated
to specialized topics and courses on philosophy
and paradigms. Conventional wisdom is often the
controlling factor in picking and solving prob-
lems. This chapter is a detour into issues that
may be holding up efforts to develop a
theory of
the Earth
, one that is as paradox free as possible.
A large part of petrology, geochemistry and
geophysics is about sampling the Earth.
Sam-
pling theory
isabranchofstatistics.Ifthe
mantle is blobby on a kilometer scale, then
individual rocks will exhibit large scatter -- or
variance -- but the mean of a large number of
samples will eventually settle down to the appro-
priate mean for the mantle; the same mean will
