Measurement scales are used to categorize and/or quantify variables. This lesson describes the four scales of measurement that are commonly used in statistical analysis: nominal, ordinal, interval, and ratio scales.
Properties of Measurement Scales:
Each scale of measurement satisfies one or more of the following properties of measurement.
1.Identity. Each value on the measurement scale has a unique meaning.
2.Magnitude. Values on the measurement scale have an ordered relationship to one another. That is, some values are larger and some are smaller.
3.Equal intervals. Scale units along the scale are equal to one another. This means, for example, that the difference between 1 and 2 would be equal to the difference between 19 and 20.
4.A minimum value of zero. The scale has a true zero point, below which no values exist.
Nominal Scale of Measurement
The nominal scale of measurement only satisfies the identity property of measurement. Values assigned to variables represent a descriptive category, but have no inherent numerical value with respect to magnitude.
Gender is an example of a variable that is measured on a nominal scale. Individuals may be classified as "male" or "female", but neither value represents more or less "gender" than the other. Religion and political affiliation are other examples of variables that are normally measured on a nominal scale.
Ordinal Scale of Measurement
The ordinal scale has the property of both identity and magnitude. Each value on the ordinal scale has a unique meaning, and it has an ordered relationship to every other value on the scale.
An example of an ordinal scale in action would be the results of a horse race, reported as "win", "place", and "show". We know the rank order in which horses finished the race. The horse that won finished ahead of the horse that placed, and the horse that placed finished ahead of the horse that showed. However, we cannot tell from this ordinal scale whether it was a close race or whether the winning horse won by a mile.
Interval Scale of Measurement
The interval scale of measurement has the properties of identity, magnitude, and equal intervals.
A perfect example of an interval scale is the Fahrenheit scale to measure temperature. The scale is made up of equal temperature units, so that the difference between 40 and 50 degrees Fahrenheit is equal to the difference between 50 and 60 degrees Fahrenheit.
With an interval scale, you know not only whether different values are bigger or smaller, you also know how much bigger or smaller they are. For example, suppose it is 60 degrees Fahrenheit on Monday and 70 degrees on Tuesday. You know not only that it was hotter on Tuesday, you also know that it was 10 degrees hotter.
Ratio Scale of Measurement
The ratio scale of measurement satisfies all four of the properties of measurement: identity, magnitude, equal intervals, and a minimum value of zero.
The weight of an object would be an example of a ratio scale. Each value on the weight scale has a unique meaning, weights can be rank ordered, units along the weight scale are equal to one another, and the scale has a minimum value of zero.
Weight scales have a minimum value of zero because objects at rest can be weightless, but they cannot have negative weight.
Nominal Scale Examples
diagnostic categories
sex of the participant
classification based on discrete characteristics (e.g., hair color)
group affiliation (e.g., Republican, Democrate, Boy Scout, etc.)
the town people live in
a person's name
an arbitrary identification, including identification numbers that are arbitrary
menu items selected
any yes/no distinctions
most forms of classification (species of animals or type of tree)
location of damage in the brain
Ordinal Scale Examples
any rank ordering
class ranks
social class categories
order of finish in a race
Interval Scale Examples
scores on scales that are standardized (i.e., with an arbitrary mean and standard deviation, usually designed to always give a positive score)
scores on scales that are known to not have a true zero (e.g., most temperature scales except for the Kelvin Scale)
scores on measures where it is not clear that zero means none of the trait (e.g., a math test)
scores on most personality scales based on counting the number of endorsed items
Ratio Scale Examples
time to complete a task
number of responses given in a specified time period
weight of an object
size of an object
number of objects detected
number of errors made in a specified time period
proportion of responses in a specified category
Properties of Measurement Scales:
Each scale of measurement satisfies one or more of the following properties of measurement.
1.Identity. Each value on the measurement scale has a unique meaning.
2.Magnitude. Values on the measurement scale have an ordered relationship to one another. That is, some values are larger and some are smaller.
3.Equal intervals. Scale units along the scale are equal to one another. This means, for example, that the difference between 1 and 2 would be equal to the difference between 19 and 20.
4.A minimum value of zero. The scale has a true zero point, below which no values exist.
Nominal Scale of Measurement
The nominal scale of measurement only satisfies the identity property of measurement. Values assigned to variables represent a descriptive category, but have no inherent numerical value with respect to magnitude.
Gender is an example of a variable that is measured on a nominal scale. Individuals may be classified as "male" or "female", but neither value represents more or less "gender" than the other. Religion and political affiliation are other examples of variables that are normally measured on a nominal scale.
Ordinal Scale of Measurement
The ordinal scale has the property of both identity and magnitude. Each value on the ordinal scale has a unique meaning, and it has an ordered relationship to every other value on the scale.
An example of an ordinal scale in action would be the results of a horse race, reported as "win", "place", and "show". We know the rank order in which horses finished the race. The horse that won finished ahead of the horse that placed, and the horse that placed finished ahead of the horse that showed. However, we cannot tell from this ordinal scale whether it was a close race or whether the winning horse won by a mile.
Interval Scale of Measurement
The interval scale of measurement has the properties of identity, magnitude, and equal intervals.
A perfect example of an interval scale is the Fahrenheit scale to measure temperature. The scale is made up of equal temperature units, so that the difference between 40 and 50 degrees Fahrenheit is equal to the difference between 50 and 60 degrees Fahrenheit.
With an interval scale, you know not only whether different values are bigger or smaller, you also know how much bigger or smaller they are. For example, suppose it is 60 degrees Fahrenheit on Monday and 70 degrees on Tuesday. You know not only that it was hotter on Tuesday, you also know that it was 10 degrees hotter.
Ratio Scale of Measurement
The ratio scale of measurement satisfies all four of the properties of measurement: identity, magnitude, equal intervals, and a minimum value of zero.
The weight of an object would be an example of a ratio scale. Each value on the weight scale has a unique meaning, weights can be rank ordered, units along the weight scale are equal to one another, and the scale has a minimum value of zero.
Weight scales have a minimum value of zero because objects at rest can be weightless, but they cannot have negative weight.
Nominal Scale Examples
diagnostic categories
sex of the participant
classification based on discrete characteristics (e.g., hair color)
group affiliation (e.g., Republican, Democrate, Boy Scout, etc.)
the town people live in
a person's name
an arbitrary identification, including identification numbers that are arbitrary
menu items selected
any yes/no distinctions
most forms of classification (species of animals or type of tree)
location of damage in the brain
Ordinal Scale Examples
any rank ordering
class ranks
social class categories
order of finish in a race
Interval Scale Examples
scores on scales that are standardized (i.e., with an arbitrary mean and standard deviation, usually designed to always give a positive score)
scores on scales that are known to not have a true zero (e.g., most temperature scales except for the Kelvin Scale)
scores on measures where it is not clear that zero means none of the trait (e.g., a math test)
scores on most personality scales based on counting the number of endorsed items
Ratio Scale Examples
time to complete a task
number of responses given in a specified time period
weight of an object
size of an object
number of objects detected
number of errors made in a specified time period
proportion of responses in a specified category
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