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**Levels of Measurement**

In statistics and quantitative research methodology various attempts have been made to classify variables (or types of data) and thereby develop a taxonomy of levels of measurement or scales of measure. The best known are those developed by the psychologist **Stanley Smith Stevens.**

He proposed four types –

- Nominal
- Interval
- Ordinal
- Ratio

## Properties of Measurement Scales

Each scale of measurement satisfies one or more of the following properties of measurement-

**Identity-**Each values on the measurement scale has a unique meaning.-
**Magnitude-**Values on the measurement scale have an ordered relationship to one another i.e. some values are large and some are smaller. -
**Equal intervals-**Scale units along the scale are equal to one another. This mean that the difference between 1 and 2 would be equal to the difference between 19 and 20. -
**A minimum value of zero-**The scale has a true zero point, below which no value exits.

## Scales/Levels of Measurement

There are four ways of quantifying variables and there are four corresponding scales-

**Nominal or classificatory scales.****Ordinal or Ranking scales.****Interval scales.****Ratio scales.**

**Nominal or Classificatory scales**

Nominal measurement involves classification of an item into two more categories which are qualitatively rather than quantitatively different. This measurement requires, only to be able to distinguish two or more relevant categories and should be able to place the individual or objects into one or the other category. There is no particular order assigned to them. The required empirical operation just requires recognizing a particular individual or object to belong to a given mutually exclusive category. The only difference is that they differ in quality only.

Therefore, the number or other symbols used simply to classify an object, person or characteristics or to identify the groups to which various objects belong, then there numbers or symbols constitute a nominal or classificatory scale.

Some examples are classifying individuals according to gender, colour, state where they reside or nationality.

A very good example of the nominal scale is the number of the license plates of automobiles because they are classified into various sub-classes showing the state, district and the period to which it belongs.

This scale is also used frequently in schools for ranking in academics, sports, cultural activities etc.

**In Short-**

**This is the simplest level of measurement. Data at this level are categorized or named without any quantitative significance. Examples include categories like gender, race, or marital status. The only operations that can be performed on nominal data are counting and categorizing.**

**Ordinal Ranking Scales**

This scale indicates the relative position of the individuals or objects with respect to certain attributes. No value is assigned to the distance between positions of ranking. The scale assigns observations to categories by number and arranges them in logical order. The essential requirement for measurement is an empirical criterion for ordering individuals or objects or events with respect to the attribute.

The basic requirement for this scale is that the objects of a set can be rank- ordered on an operationally defined characteristics or property.

The variables categorized into groups have some kind of relationship. Some of the common relationship among classes are greater, more preferred, more difficult, more mature, etc.

When we discuss the social class in the country i.e. lower, lower-middle, middle, upper-middle and upper-constitute an Ordinal Scale.

When a teacher assigns ranks to his students on certain characteristics e.g. their social maturity, spelling ability, singing ability, leadership ability, etc. then the ordinal or ranking scale measurement occurs.

If fifteen children are made to stand in a line and are arranged from the shortest to the tallest then this also constitute an ordinal scale. The numbers used in identifying the observations are called ranks.

In this scale when the numbers are assigned to every person or an object then only the order of the object is considered. Over here the number or the rank shows only the order. It does not portray their differences or the ratios. Therefore the ordinal numbers do not indicate absolute quantities, nor they shows that the intervals between the numbers are equal e.g. if the first, second and third rank or position is arranged there is no information about the empirical distance between the first and the second rank or second and the third rank.

Since in this scale, the ranks or successive intervals or distance between classes are not equal so statistical operation are limited. The ordinal scale cannot be subjected to arithmetic calculation. The allotted ranks are explicit that one observation represents more or less of the variable than another but they do not specify as to how much more or less..

The major statistical operations that can be calculated in this scale are the Median, Percentiles and Rank Difference Correlation.

**In Short-**

**Data at this level can be ordered or ranked, but the intervals between the categories are not uniform. In other words, ordinal data can be ranked in a meaningful order, but the differences between the ranks are not consistent. Examples include rankings such as movie ratings (1 star, 2 stars, 3 stars, etc.) or educational levels (elementary, high school, college). Operations like ranking, ordering, or comparing the data can be performed, but arithmetic operations like addition or subtraction are not meaningful.**

### Interval Scale

The interval scale of measurement has the properties of identity, magnitude and equal intervals. It is more precise and refined than the above two scales. In this scale, distances or intervals between any two number of known size i.e. we know how large are the distance or interval between all objects on the scale.

An interval scale is one that provides equal interval from arbitrary origin. It is characterized by a common and constant unit of measurement which assigns a real number to all pairs of objects in the ordered set.

The interval scale not only orders the individuals, objects or events according to the amount of attribute they represent but also establishes equal intervals between the units of measurement. A linear relationship is established in the equal interval scale.

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 60° Fahrenheit is equal to the difference between 50° and 60° Fahrenheit.

This scale has a greater use in the teaching learning situation, educational administration, educational guidance and counseling and educational research.

The effectiveness of any instructional procedure can be evaluated precisely by collecting the data on the scale.

With an interval scale you know not only whether different values are bigger or smaller but you also know how much bigger or smaller they are.

**In Short-**

**Data at this level can be ordered, and the intervals between the values are equal and meaningful, but there is no true zero point. Examples include temperature in Celsius or Fahrenheit. In interval data, addition and subtraction can be performed, but multiplication and division are not meaningful because there is no true zero.**

### Ratio Scale

The ratio scale of measurement satisfies all the four properties of measurement- identity, magnitude, equal intervals and a minimum value of zero.

In a ratio scale, the ratio of any two scale points is independent of the unit of measurement.

This scale is used in physical science and less frequently in behavioural science.

The weight of an object is an example of ratio scale. Each value on the weight scale has a unique meaning. The weights can be rank ordered, units along the weight scale are equal to one another and the scale has 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.

The data in this scale can be subjected to arithmetic operations. Such operations are possible as the numerical values assigned to the objects in the data as well as on the intervals between numbers.

**In Short-**

**This is the highest level of measurement. Data at this level have all the properties of interval data, plus a true zero point, meaning that zero represents the absence of the measured attribute. Therefore, all arithmetic operations can be performed on ratio data. Examples include height, weight, and income.**

## Examples of Each Scale of Measurement

### Nominal Scale

- diagnostic categories
- sex of the participant
- classification based on discrete characterization (e.g. hair colour)
- group affiliation (e.g. Republican, Democrat, Boy Scouts, Girl Guide, etc).
- the town where people live in
- a person’s name
- an arbitrary identification
- menu items selected
- any yes/no distinction
- most form of classification (species of animals or type of tree)
- location of damage in the brain

### Ordinal Scale

- any rank ordering
- class ranks
- social class categories
- order of finish in a race

### Interval Scale

- Scores on scales that are standardized (e.g. with an arbitrary) mean and standard deviation, usually designed to always give a positive score.
- Scores on scales that are known to 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 maths test)
- Scores on most personality scales based on counting the number of endorsed items.

### Ratio Scales

- time to complete tasks.
- 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.
- proportions of responses in a specified category.