Scale is the ratio of one measurement to another. It’s used on maps, in blueprints, and when measuring ingredients for making recipes.
Participants in our survey provided valuable comments and suggestions on the types of scale that they consider most important to their work. Using these advances will lead to more accurate research findings.
Definition
The Next Generation Science Standards include the crosscutting concepts of scale, proportion, and quantity. These concepts are critical to understanding the natural world and conducting scientific investigations. For example, comparing the sizes of organisms in a habitat helps scientists understand their relationships within ecosystems.
In geometry, a scale is a graduated line that represents proportionate size. It is used to create blueprints and scale models of machinery and architecture, shrink vast lands into small pieces on maps, and help architects, machine-makers, and artists work with models that are too large to hold if they were their actual size.
In music, a scale is a set of intervals that separates musical tones (for example, C to C5 or F to F). The pattern of intervals defines what type of scale—hemitonic, diatonic, or chromatic—that scale is. Each interval in a scale has a certain ratio between its higher and lower frequency, which gives the scale its particular sound.
Examples
Using scale helps designers balance the elements of their designs. It also ensures that an element is not too big or too small relative to its surroundings. For example, a large chair would not be appropriate in a tiny room and vice versa. Scale is also important for illustrating relationships in diagrams and graphs.
Examples of scale include nominal, interval and ratio scales. The latter includes variables that can be added or subtracted from each other and therefore contains properties of both the nominal and interval scales. It can also include an absolute zero, which is a feature unique to the ratio scales.
An example of a scale is a Likert scale, which has five response categories that rank different attributes from low to high (e.g. very strongly agree to very much disagree). Another example is classifying children into groups in reading evaluations such as #0 – non-readers, #1 – beginners, #2 – grade level readers, #3 – advanced readers.
Usage
A scale is often seen as a symbol of commerce and trade. The balance scales depicted in the Book of the Dead and a traditional legal instrument used to weigh evidence are examples of such scales. A scale or balance can also refer to a mechanical device, such as a spring scale, hanging scales, triple beam balances and force gauges.
In musical situations, a scale is defined by its interval pattern and a choice of one note to be the first degree (or tonic). The other notes of the scale are then named according to their position relative to this tonic.
Scales are also widely used in physics and engineering. For example, a geometric shape can be reproduced in another size by specifying a scaling factor, which is the ratio of the new to original dimensions. When the scale is a fraction, such as a reduction, the shape becomes smaller. Scales are also used to make maps that are printed at different sizes. Scupulous geographic information specialists avoid enlarging source maps, since doing so can distort the appearance of the image.
Misconceptions
Many misconceptions surround scale types. Some of these may result in unnecessary and unhelpful restrictions on the statistical analyses one can conduct with data. For instance, the popular idea that all rating scales need to be labeled (for example, five or seven points on a disagree-to-agree scale) has little empirical support. Fully labeling a scale does not appear to increase reliability any more than using a larger number of geographic units (e.g., from a pouce to a league).
Others stem from the misinterpretation of Michell’s distinction between the operational-ish and representational-ish perspectives. For example, those who hold the realist view tend to believe that interval-level measurement is an ideal that observed measurements fall short of, which translates into recommendations to use continuous rather than ordinal scales, and to fit models only with ratio or interval-level statistics.
Such pedagogical changes would more honestly reflect statistical practice and encourage researchers to question, manipulate, and deeply understand their scale units, and thus help overcome the current state of ignorance about the necessary conditions for achieving interval-level measurement. Attempts to establish interval-level scales prior to experimentation, however, are likely to be ineffective and instill a false sense of confidence that results will be robust to future experimental manipulation.