Discrete scale definition
Discrete data, like counts, are numeric data that have a finite number of possible values and can only be whole numbers. Discrete data arise from observations that can only take certain numerical values. Fractions are meaningless. In some situations, mathematical functions or calculations are not possible either.
Discrete variables are measured across a set of fixed values, such as age in years (not microseconds). These are commonly used on arbitrary scales, such as scoring your level of happiness, although such scales can also be continuous.
Discrete data can be used as ordered categorical data in statistical analysis, but some information is lost in doing so.
Discrete scale examples
The number of children someone has: 1, 2, 3, etc. is possible, but 1.5 children are not meaningful.
Credit card number: The number is a discrete value, but cannot be used for addition or subtraction, etc.
Another classic is the spin or electric charge of a single electron. Quantum Mechanics, the field of physics which deals with the very small, is much concerned with discrete values.
Another example might be how many students were absent on a given day. Counts are usually considered exact and integer. Consider, however, if three absences make a suspension, then aren't two absences equal to 0.67 suspensions?
Other scale types
- Verbal scale - a verbal scale also referred to as a “word statement” or “scale expression”, is where the response options are presented to the respondent using words, whether spoken or written.
- Guttman scale - an ordinal scale type where statements are arranged in a hierarchical order so that someone who agrees with one item will also agree with lower-order, easier, less extreme items.
- Likert scale - Questions utilizing a Likert scale generally present the respondent with a statement and asks for his/her level of agreement with the statement by selecting a point on the scale. These points have often verbal statements or numbers attached to them. The scale should be balanced between positive and negative agreement options.
- Interval scale - An interval scale has intervals which each have the same interpretation and do not have a "true" zero point, therefore it is not possible to make statements about how many times higher one score is than another. One unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the scale.
- Continuous scale - On a continuous scale, respondents rate the objects by placing a mark at the appropriate position on a line that runs from one extreme of the variable to the other. The form of the continuous scale may vary considerably.
- Comparative scale - Comparative scales involve the direct comparison of stimulus objects. Most often, the respondent is asked to compare one brand, product or feature against another. Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties.
- Survey scale - scale is an ordered series of response options, presented verbally or numerically from which the respondents select to indicate their level of feeling about the measured attribute.
- Forced choice scale - A forced-choice scale (also known as an ipsative scale) is a rating scale that does not allow for an Undecided, Neutral, Doesn't know, or No opinion response.
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