Which of the following statements is true about variables?

Concept: In research methodology, measurability is exactly what separates a variable from a concept. A concept — ‘motivation’, ‘high achiever’, ‘satisfaction’ — is a subjective impression whose meaning is not understood uniformly by different people and which, as such, cannot be measured. A variable is a property that has been given an operational definition and can therefore be observed and recorded as one of two or more values. The measurement scale used — nominal, ordinal, interval or ratio — determines how those values may be compared and which arithmetic is legitimate, and hence the degree of accuracy the measurement can claim.

Application: Take the property ‘academic achievement’. Recorded as pass/fail it sits on a nominal scale, which only classifies; recorded as a class rank it sits on an ordinal scale, which orders the cases but leaves the distance between ranks undefined; recorded as marks out of 100 it is treated as an interval-type score, whose equal units permit means and standard deviations. A property such as hours of study carries a true zero and so reaches the ratio scale, where ratios themselves are meaningful. The same kind of property is thus recorded with a different degree of accuracy according to the scale used, which is precisely the statement that variables are measurable with varying degrees of accuracy depending upon the measurement scale used.

Cross-check: Contrasting this with the other descriptions offered:

• A concept is the subjective, unmeasured impression from which research starts; turning a concept into a variable is a separate step that requires an operational definition, so identifying variables with concepts drops the very measurability that defines a variable.

• Mental images are private representations held inside an individual’s mind and their meaning varies markedly from person to person; a variable must instead be defined publicly, so that two investigators recording the same case arrive at the same value.

• Perceptions are individual interpretations of sensory input and likewise differ between observers; both mental images and perceptions describe how a concept is held, not how a property is measured.

Hence what is true of variables is their measurability, and the accuracy attainable in that measurement depends on the scale used.