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A variable is a characteristic that exhibits detectable changes, either regionally or temporally. Implicit in this concept of change is influence by something else: Newtonian dynamics show us that movement in itself does not imply an external force -- change in movement does. Thus scientists are seldom concerned with a single variable; more often we seek patterns among variables. This chapter focuses on one variable at a time, thereby setting the stage for considerations in the next chapter of relationships among variables.

Variables, measurements, and quantification are related components of the foundation of science. Characterizing a variable requires measurements, and measurements require prior quantification. Each variable has an associated measurement type: They differ in that only ratio scales have a true, or meaningful, zero, permitting determination of ratios between data measurements. For example, temperatures are measured with an interval scale, whereas length is a ratio scale. To refer to one temperature as twice that of another is pointless, whereas it is valid to say that one object is twice as long as another.
 * Nominal measurements classify information and count the frequency of observations within each class. An example is tabulation of the numbers of protons and neutrons in an atom.
 * Ordinal measurements specify order, or relative position. Ordinal scales may be objectively determined (e.g., the k, l, and m electron shells), subjectively determined but familiar (e.g., youth, young adult, adult, old age), or subjectively invented for a particular experiment (e.g., social science often uses scales such as this: strongly agree (+2), agree (+1), not sure (0), disagree (-1), strongly disagree (-2)).
 * Interval and ratio scales permit measurements of distance along a continuum, with determinable distance between data. The scales involve either real (fractional) or integer (counting) numbers.

The initial quantification of any variable is challenging, for we seek a scale that is both measurable and reliable. Soon, however, that quantification is taken for granted. Finding a way to quantify some variable tends to be more of a problem in the social sciences than in the physical sciences.

Statistics
Statistics are pattern recognition transformed, from a qualitative guess about what may be, into a quantitative statement about what probably is.

A decade ago, scientific statistics usually required either complex number crunching or simplifying approximations. Since then, computers have revolutionized our approach to statistics. Now standard statistical techniques are available on most personal computers by simply choosing an option, and programs for even the most sophisticated statistical techniques are available from books such as Numerical Recipes [Press et al., 1988]. With easy access comes widespread misuse; one can use various statistical routines without learning their assumptions and limitations.

Statistics help us both to solve single-variable problems (this chapter) and to accomplish multivariate pattern recognition (next chapter). Neither chapter is a substitute for a statistics course or statistics book; no proofs or derivations are given, and many subjects are skipped. Statistics books