Geography Reference
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how what you've discovered relates to all the other stored objects as yet unlit. Our ability
to observe the wild is so limited that, even equipped with satellite radio collars and high-
powered computers, we are proverbial blind men encountering elephants. We would be
unwise to put too much stock in what we have observed. We must consider our inevitably
small samples of data in light of the existing literature, well-established theory, and of
course, the laws of probability.
Alas, having gone to all the trouble of getting to a difficult field site and putting up
with snow, wind, mud, insects, poor food, and any number of other unpleasant realities of
field life, it is difficult to bear in mind the trivial nature of what one has actually learned.
If, despite the most valiant of efforts, one has collected very little data, it is tempting to
proceed with an analysis anyway and sweep under the rug violations of critical assump-
tions or the size of a resulting confidence interval, rather than acknowledging that one
really still has no good idea of what is going on. But only the second of these options
would constitute good science. And even with valiant efforts, sample sizes obtained from
field work on free-ranging wildlife in western China are inevitably small. While this is
unfortunate, the problem lies not in small sample sizes per se, but in the all-too-frequent
failure to place into proper context the utility of inference based on them.
Distance sampling is currently a favored method of estimating the abundance of wild-
life in China, and for good reason. The statistical theory underlying distance sampling
is well explored: some kind of sampling is obviously called for in the huge expanses of
western China (where any claim to a complete count would be out of the question), and
most animals are, relatively speaking, easy to see in these open, treeless habitats. Dis-
tance sampling was one of the featured methods suggested in the guidelines established
by the State Forestry Administration (SFA) in its (approximately) year 2000 national
wildlife “census.” 3 But distance sampling is not magic, and it works well only when
assumptions are not grossly violated, and only when sample sizes are adequate to sup-
port a model of detection (which accounts for animals never seen). There is no clearly
demarcated threshold above which sample sizes are adequate and below which they are
not, but commonly used rules of thumb suggest sixty, or better yet, eighty independent
observations of animals. Most density estimates produced under the SFA's guidelines
were made based on less than a dozen observations, and quite a few were made based
on a sample size of only one. 4
But—at least if handled correctly—the problem of small sample size is self-correcting:
one of the roles of statistics is to correct any possible misapprehension that we know more
than we actually do by appending indices of certainty and reliability to our estimates.
Calculated and interpreted correctly, a density estimate—associated with a standard error
or confidence limits—based on very little data simply tells us that we know only that the
density is somewhere between very low and very high. Far more insidious is the problem
of extrapolating results from biased sampling.
I first encountered the biased sampling problem in a 1988 county agricultural year-
book that had seemingly documented an astounding 80,060 white-lipped deer in Qinghai
Province's Nangqian County alone. This seemed odd given that estimates in the Chinese
wildlife literature (which rarely err on the low side) had pegged the population of the
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