Scales of Measurement
Scales of measurement is a classification that describes the nature of information within the values assigned to variables.
It is an important characteristic of data. It determines what types of descriptive, graphical and inferential statistical analysis can be used.
Psychologist S.S. Stevens developed the best-known classification with four levels or scales of measurement, i.e., nominal, ordinal, interval and ratio.
Although this framework originated in psychology, it is widely criticized by scholars in other disciplines.
These four scales or levels at which researchers measure and collect their data may found to reflect a unique hierarchy in their level of functioning. The lowest lead is nominal and the highest is ratio.
These four levels can be defined in detail as following -
Nominal Scales
(Data in the form of naming or categories)
It is the lowest level of measurement.
It classify, categorize and identify objects, individuals or events related to their data collection task.
It is also called as classification level.
Nominal data do not provide quantitative information.
It cannot be used to compute any statistics like mean, median, Standard Deviation, Correlation etc.
At this level, the measuring process is simply partitioning a group into mutually exclusive sub-classes. The members of a sub-class are equal in the property measured.
E.g.- Classification of -
People as married, unmarried, divorced, widowed etc.
Gender as male and female
Schools as government, aided, self-financed, rural, urban etc.
Attitudes as positive, negative or favourable, unfavourable etc.
Its single rule -
Different numbers must mean different things.
e.g.- 1 might be assigned to female gender and 2 to male gender.
Ordinal Scales
(Data in order of rank)
It arranges data in the hierarchical order.
In addition to the property of equivalence, categories can be assigned a meaningful order and greater than or less than relationships can be identified.
Here, we can infer that one participant is higher or lower in his performance than another.
Ranks do not indicate the amount by which participants differ.
It doesnot reflect the property of equal interval between the well classified and ranked categories.
Mathematical operations like addition, multiplication and statistics like mean, median, standard deviation etc. can be applied but not at par with the case of interval or ratio scales.
e.g.- Classification of measurement outcomes in the form of income subcategories like above average, average, below average etc.
It follows two rules -
Different numbers must mean different things.
Things being measured can be ranked or ordered along some dimension.
Interval Scales
(Equal interval have no absolute zero)
Equal intervals between objects/events represent equal differences.
It do not possess absolute zero point.
Here, a scale of zero is simply another point on the scale. It does not mean an absence of the quantity being measured.
Zero marks scored in a test doesnot means that the student has no knowledge of the subject. It shows the accurate difference between two objects or peoples with the help of numbers or scales.
This scale is subject to mathematical and statistical operation like addition, subtraction, division, finding mean, median, standard deviation, correlation etc.
E.g.- Standardized and calibrated psychological, academic and performance tests. Here difference between scores 70 and 90 is same as between 50 and 60.
It follows three rules -
Different numbers must mean different things.
Things being measured can be ranked or ordered along some dimension.
Difference between adjacent levels on the scale are equal.
Ratio Scales
(Equal intervals having absolute zero point)
It is the highest level of measurement.
It possess an absolute or true zero point.
A score of zero means the complete absence of the attribute being measured.
An error score of zero, attained by a rat running a maze, means the absence of any wrong turns.
It shows the measurements in a relative or ratio format.
A measure taken on this scale can be expressed in teams of multiples, division, percentage, fractions of any other measure taken on the same scale.
This scale is subject to mathematical and statistical operation like addition, subtraction, division, finding mean, median, standard deviation, correlation etc.
E.g.- measurement of weight, height of objects, distance travelled in a journey, time spent on studying etc.
It follows four rules -
Different numbers must mean different things.
Things being measured can be ranked or ordered along some dimension.
Difference between adjacent levels on the scale are equal.
It has an absolute zero point.