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Scale Types

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Nominal scale

• The lowest measurement level you can use, from a statistical point of view, is a nominal scale.

• A nominal scale, as the name implies, is simply some placing of data into categories, without any order or structure.

• A physical example of a nominal scale is the terms we use for colors. The underlying spectrum is ordered but the names are nominal.

• In research activities a YES/NO scale is nominal. It has no order and there is no distance between YES and NO.

• The nominal type, sometimes also called the qualitative type, differentiates between items or subjects based only on their names or (meta-) categories and other qualitative classifications they belong to.

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Nominal scale

• Examples:– include gender, nationality, ethnicity, language,

genre, style, biological species, and form.• Central tendency– The mode, i.e. the most common item, is allowed

as the measure of central tendency for the nominal type.

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An example of a nominal scale

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Ordinal scale

• An ordinal scale is next up the list in terms of power of measurement.

• The simplest ordinal scale is a ranking.• When a market researcher asks you to rank 5 types

of beer from most flavorful to least flavorful, he/she is asking you to create an ordinal scale of preference.

• The ordinal type allows for rank order (1st, 2nd, 3rd, etc.) by which data can be sorted, but still does not allow for relative degree of difference between them.

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Ordinal scale

• There is no objective distance between any two points on your subjective scale.

• For you the top beer may be far superior to the second preferred beer but, to another respondent with the same top and second beer, the distance may be subjectively small.

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Ordinal scale

• Examples include, on one hand, dichotomous data with dichotomous values such as ‘sick’ vs. ‘healthy’ when measuring health, 'guilty' vs. 'innocent' when making judgments in courts, 'wrong/false' vs. 'right/true' when measuring truth value,

• On the other hand, non-dichotomous data consisting of a spectrum of values, such as 'completely agree', 'mostly agree', 'mostly disagree', 'completely disagree' when measuring opinion.

• Central tendency– the median and mode– the mean (or average) as the measure of central tendency is not

allowed.

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Example of Ordinal Scales (1)

• Suppose our set of entities is a set of software modules, and the attribute we wish to capture quantitatively is “complexity.”

• Initially, we may define five distict classes of module complexity:– “trivial”– “simple”– “moderate”– “complex”– “incomprehensible”

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Example of Ordinal Scales (2)

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Semantic and semantic differential scales

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Interval scale

• The interval type allows for the degree of difference between items, but not the ratio between them.

• The standard survey rating scale is an interval scale.– When you are asked to rate your satisfaction with

a piece of software on a 7 point scale, from Dissatisfied to Satisfied, you are using an interval scale.

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Interval scale

• Interval scales are also scales which are defined by metrics such as logarithms.

• In these cases, the distances are note equal but they are strictly definable based on the metric used.

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Interval scale

• Examples include temperature with the Celsius scale, which has an arbitrarily-defined zero point (the freezing point of a particular substance under particular conditions), and date when measured from an arbitrary epoch (such as AD).

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Example of interval scales

• An example of an Interval scale is the Celsius scale of temperature.

• In the Celsius temperature scale, the distance between 20 degrees and 40 degrees is the same as the distance between 75 degrees and 95 degrees.

• With Interval scales, there is no absolute zero point.

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SW complexity example ofinterval scales

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Examples of interval scales in numeric and semantic formats

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Interval scale

• Central tendency• Interval scale data would use parametric

statistical techniques:– Mean and standard deviation– Correlation – r– Regression– Analysis of variance– Factor analysis

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Ratio scale

• A ratio scale is the top level of measurement and is not often available in social research.

• The factor which clearly defines a ratio scale is that it has a true zero point.

• The ratio type takes its name from the fact that measurement is the estimation of the ratio between a magnitude of a continuous quantity and a unit magnitude of the same kind.

• A ratio scale possesses a meaningful (unique and non-arbitrary) zero value.

• Most measurement in the physical sciences and engineering is done on ratio scales.

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Ratio scale

• Examples include mass, length, duration, plane angle, energy and electric charge.

• Ratios are allowed because having a non-arbitrary zero point makes it meaningful to say, for example, that one object has “twice the length” of another.

• Very informally, many ratio scales can be described as specifying “how much” of something (i.e. an amount or magnitude) or “how many” (a count).

• The Kelvin temperature scale is a ratio scale because it has a unique, non-arbitrary zero point called absolute zero. The zero point of the Celsius scale is at 273.15 Kelvin's, so Celsius is not a ratio scale.

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Ratio scale

• Ratio scales, do have a fixed zero point.• Not only are numbers or units on the scale equal over all

levels of the scale, but there is also a meaningful zero point which allows for the interpretation of ratio comparisons.

• Time is an example of a ratio measurement scale.• Not only can we say that difference between three hours

and five hours is the same as the difference between eight hours and ten hours (equal intervals), but we can also say that ten hours is twice as long as five hours (a ratio comparison)

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Ratio scale

• Central tendency• Interval scale data would use parametric

statistical techniques:– Mean and standard deviation– Correlation – r– Regression– Analysis of variance– Factor analysis

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