USING STATISTICS: Spotting and Avoiding Them
Variation, Variability, Uncertainty
Some authors, particularly in environmental studies, make a
technical distinction between the terms "variation," "variability", and
"uncertainty." Van Belle1 describes variability
and uncertainty as two
different categories of variation,
involving different sources and kinds of randomness. As he uses the
refers to natural variation in some quantity
refers to the degree of precision with which a quantity is measured2.
The amount of a certain pollutant in the air is variable: it varies
from place to place and from time to time. However, the uncertainty in
the amount of that pollutant present in a particular place at a
particular time depends on the quality (and presence or absence) of the
instruments used to measure it.
Further thought and elaboration lead to a variety of types of
variability and uncertainty, plus complications involving, for example,
uncertainty about variability. See Cullen and Frey3
However, the distinction is sometimes useful in helping
understand some statistical mistakes, including pseudoreplication and the distinction
between confidence intervals and prediction
Global warming provides a good example of how making the distinction
variability and uncertainty can be helpful in understanding a
situation. The evidence available and careful
analysis of this evidence has steadily decreased our level of uncertainty that
are increasing. But there is still so much
variability in how an increase
in average temperature translates into
weather patterns and their consequences in different places and in
different ways, that we cannot predict with any reasonable degree of
precision just what the effects of global warming will be at any given
time and place.
1. Van Belle (2008), Statistical Rules of Thumb, Wiley, pp. 99 - 100
2. Terminology varies; some authors use the phrases "aleatory
uncertainty" and "epistemic
uncertainty" to refer to "variability" and "uncertainty"
(respectively) as defined by Van Belle. Some authors use "fuzziness" to
describe what Van Belle defines as "uncertainty."
3. A. C. Cullen and H. C. Frey (1999), Probabilistic Techniques in
Exposure Assessment, Plenum, pp. 21 - 35
Last updated July 5, 2011