COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding Them

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Terminology:  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 terms,
variability refers to natural variation in some quantity

whereas

    uncertainty refers to the degree of precision with which a quantity is measured2.

Example: 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 for further discussion.

However, the distinction is sometimes useful in helping understand some statistical mistakes, including pseudoreplication and the distinction between confidence intervals and prediction intervals.

Global warming provides a good example of how making the distinction between 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 average global temperatures 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.
Notes:
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