This article throws light upon the four main types of scales used for measurement. The types are:- 1. Nominal or Classificatory Scales 2. Ordinal or Ranking Scales 3. Interval Scales 4. Ratio Scales.
Type # 1. Nominal or Classificatory Scales:
When numbers or other symbols are used simply to classify an object, person or characteristic, or to identify the groups to which various objects belong, these numbers or symbols constitute a nominal or classificatory scale.
Lowest level of measurement:
Nominal scale is so primitive that some experts do not recognize it as measurement. It is the least precise or crude among the four basic scales of measurement. It simply implies the classification of an item into two or more categories without any extent or magnitude. There is no particular order assigned to them.
We assign roll numbers 1, 2, 3, 4, 5, 6,…….. 50 to different students in a class in order to identify them easily.
Numerical names only:
The numbers assigned to objects or places are just labels without having any number meaning. They cannot be ordered or added. The numbers used are merely names.
In this type of scales the values are arbitrary in nature and the number assigned are not bound by any rule. In other words, these values or numbers are simply numerical notations without any logical considerations.
When we assign symbols to different parts of a city as Bhubaneswar- 4, Rourkela-14, Kolkata-5, Kolkata-8 etc. or when we assign pin code numbers in postal addresses we just do so to identify a locality or a house.
Nominal level is sometimes called classification level and each class is represented by a letter, a name, a number or even geometrical design. Each number or symbol is like a category name, it has no quantitative significance.
Job classification such as; teacher, counselor, administrator, principal, minister, carpenter etc.
Numbers of the license plates of automobiles also constitute a nominal scale, because automobiles are classified into various sub-classes, each showing a district or region and a serial number.
Statistics used with nominal data:
a. Simple statistics are used with nominal data.
b. Proportion or percentage can be determined with nominal data.
c. We can calculate mode as measure of central tendency.
d. Chi-square test can be employed.
e. Contingency coefficient can be worked out.
Type # 2. Ordinal or Ranking Scales:
It is known as a ranking level. This level is one step above of the nominal level. It has the characteristics of equivalence and order. In this scale a set of objects is assigned a value on the basis of some rule, i.e. they are arranged or ordered according to some rule.
It means that categories on the ordinal scale are arranged according to the amount of trait or characteristic that each category represents. In this scale, there is a quantitative difference from category to category, and these categories are arranged according to some order.
The example of such scale is that we arrange the students of a class according to their ranking in class result like 1st, 2nd, 3rd and so on. Similarly we categorize the students as superior, above average, average, below average and inferior or may arrange them as 1, 2, 3, 4 and 5 respectively.
In ordinal scale the objects or events are ranked or ordered from lowest to highest or from highest to lowest according to the characteristic we wish to measure. Thus ordinal scale corresponds to quantitative classification of a set of objects with reference to some attribute. In the educational institutions or hierarchy we find professional as well as administrative classifications on ordinal level.
As for example, we can mention the classification as professor, the associate professor and the assistant professor in academic side. The administrative classification can be cited as principal, administrative officer, section officer etc.
Social classes in a country—lower, lower-middle, middle, upper middle and upper—constitute an ordinal scale, because in such a classification each class is higher than the classes below it and lower than the classes above it in prestige or social status.
All members of the upper class are higher to all members of the U-M; of upper-middle in turn are higher to Lower-Middle, and so on. The scale can be represented as A < B < C. If ten individuals are lined up against a wall, and arranged in order from tallest to shortest, it will constitute an “Ordinal Scale”. The numbers used in identifying our observations are called Ranks.
The fundamental difference between a nominal and an ordinal scale is that the Nominal scale incorporates the relation of ‘equivalence’ only while ordinal scale incorporates the relation of ‘equivalence’ as well as of ‘greater than’. This relation is ‘irreflexive’ i.e., it is not true that A = A.
In ordinal scaling a transformation which does not change the order of the classes is completely admissible, because it does not involve any loss of information, e.g., if a student getting a first class is given 5 books in prizes and another one getting a first class as well as distinction gets 8 books, it shows that a student with a first division and distinction is better than a student with only a first division.
This relation will be equally well expressed if a student with 1st class + distinction get 9 books and with 1st class only gets 6 books in prize.
Statistics used with ordinal data:
For ordinal data we can use the following statistics:
a. To measure the central tendency we can compute the median.
b. To measure the dispersion we can compute quartile or percentile measure.
c. Correlation can be computed by rank-difference method.
d. For tests of statistical significance non-parametric methods can be used.
Type # 3. Interval Scale:
The third level of measurement is known as interval level. It has the characteristics of both nominal and ordinal level of scales. The additional characteristic it possesses is quality of interval. It means the distance or difference between any adjacent class on the scale can be known numerically. The intervals on the scale are the same; it is a constant unit of measurement.
This consistency of intervals is lacking in two previous level of scale. In other words, the intervals of the scale i.e. the difference between two consecutive points on the scale are equal over the entire scale. For example, the difference between 6 cm. and 7 cm. is equal to the difference between 11 cm. and 12 cm. Thus interval scale is also known as equal-interval scale.
Interval scales have an arbitrary zero. That is, there is no absolute zero-point or unique origin. With interval scales the measurement units are equal. Interval scales show that a person or item is so many units larger or smaller, heavier or lighter, brighter or duller etc. from the other.
No absolute zero. In physical sciences the concept of absolute zero is well conceived. For example, zero inch means absence of length, zero pound means absence of weight. But in psychology, education and other social sciences it is difficult to visualise a true zero in any scale used. For example a student who scores 0 (zero) in mathematics does not imply that he knows nothing in mathematics.
In this case, concept of zero is meaningless. In a similar way an I.Q. of 0 (zero) conveys no meaning. Due to the absence of a true zero-point we cannot say that a child with an I.Q. of 120 is twice as bright as a child with an I.Q. of 60.
Similarly, we cannot say that a child who scores 100 in a test of Mathematics knows twice as much as a child who scores 50 in that test. In psychological and educational measurements, although there are not true zero points of reference, yet, it is assumed that the interval between two consecutive points is equal.
Essential properties of an interval scale remain unchanged: The essential properties of an interval scale remain unchanged by any linear transformation.
In case of centigrade and Fahrenheit scale, such a linear transformation can be expressed by the formula:
F = 32 + 9/5 x C°
in which F = Number of degrees in Fahrenheit scale, and
C = Number of degrees in Centigrade
The following table gives some of the equivalent temperature difference in both scales:
If we look into the scale, we find that ratio of the differences between temperature readings on one scale is equal to the other scale but they are independent of the limit of measurement and of zero point.
For instance, in the centigrade scale freezing and boiling points are 0° and 100°C, while in Fahrenheit scale, they are 32°F and 212°F respectively.
Statistics used with Interval Scale:
Interval scales can be subjected to arithmetic operation. With interval scales, we can take ratios with respect to the interval or distance between two values. We can calculate the mean, standard deviation and product-moment correlation. For tests of significance we can employ t-tests and F-tests.
Type # 4. Ratio Scale:
It is the most refined among the four basic scales. It has all the characteristics of an interval scale. In addition to that, it has an absolute zero point as its origin representing complete absence of the property being measured.
“When a scale has all the characteristics of an interval scale and in addition has a true zero-point as its origin, it is called a ratio scale” (Seigel).
Ratio of numbers correspond to the ratios of attributes. As it has an absolute zero point we can speak that 10 kg. is twice of 5 kg. In this scale the difference between 15 and 10 is equal to the difference between 83 and 78.
The numbers used in ratio scales can be expressed in ratio relationship. For example, 20 feet is one- half of 40 feet and 20 cms is four times of 5 cms. In ratio scales there is true zero point. Here a true-zero point means complete absence of an attribute.
For example, a zero point in a centimeter scale indicates complete absence of length or height. A zero point in the ratio scale means that the object has none of the properties being measured.
Uses of Ratio Scales:
a. It is the highest level of measurement.
b. All mathematical operations—addition, subtraction, multiplication and division—can be used with ratio scales.
c. All statistical techniques are permissible with such scales.
d. In physical sciences and in all physical measurements we use ratio scales.
e. Measurement of physical dimensions such as height, weight, distance, age, years of experience etc. are the examples of ratio scale.
f. When we measure reaction time (in psychophysical measurement).
Ratio scales are almost non-existent in psychological and educational measurement. We cannot say that Amit whose I.Q. is 100 is twice as intelligent as Rohit whose I.Q. is 50. The concept of zero intelligence or zero achievement is meaningless.
When Mr. John has secured 0 (zero) in a test of general science we cannot say that he has no knowledge of science.
The properties of four scales of measurement in comparison table illustrated below:
- Scale of Measurement in Statistics
- Scale of Measurement in Statistics: Nature and Types