# Scales of Measurement

Learn the basics of Scales of Measurement including Nominal, Ordinal, Interval, and Ratio Scale

## Scales of Measurement

Measurement is the foundation of research study, everything a researcher undertakes starts with measurement. The mathematical properties of the variables we analyze are important because they determine which mathematical operations are allowed. This, in turn, determines which statistics we can use with those numbers. Statistical tests are applied depending on what scale the variable measures on.

Scales of measurement are rules that describe the properties of numbers. Variables have different numerical strength, based on their numerical strength a suitable scale of measurement is assigned to the variables under study. In all, scales of measurement are characterized by four properties:

**Identity**means that each number has a particular meaning.**Magnitude**means that numbers have an inherent order from smaller to larger.**Equal intervals**means that the differences between numbers (units) anywhere on the scale are the same (e.g., the difference between 4 and 5 is the same as the difference between 76 and 77).**Absolute/true zero**means that the zero point represents the absence of the property being measured (e.g., no money, no behavior, none correct).

## Scales of Measurement

Figure provide a diagrammatic view of the scales of measurement. It shows that scales of measurement work like a ladder, with properties being added as you move up the stairs, for instance for the variable to be on Ratio scale has to have all the properties of the scales below it.

## Nominal Scale

It is the lowest scale of measurement. Values in the variable depict different categories. Numbers are assigned to different categories while subjects are divided into various categories. Nominal scales are most often for qualitative variables in which observations are classified into discrete groups.

Mathematical operation for nominal scale is **Mode**, since we can only count the number of observations.

For instance respondents of the study would be divided into the male or female category where the researcher could represent male by number 1 and female category by number 2. Here the assignment of number is for mere identification of the categories for the variable gender.

Data collected by a researcher shows that they had 50 male represented by category number **1** and 35 female represented by category number 2, Changing the number assigned to “male” and “female” **does not have any impact on the data,** we still have the same number of men and women in the data set.

Which number is assigned to which category is completely arbitrary. Therefore, the only number property of the nominal scale of measurement is **identity**. The number gives us the identity of the category assigned.

## Ordinal Scale

Next on the ladder is ordinal scale. An **ordinal scale **of measurement is one that conveys order alone. An added property apart from identification is that variables in ordinal scale have magnitude. This scale indicates that some value is greater or less than another value. There is an inherent ascending and descending order in the probable values a variable could hold. Suitable mathematical operation for ordinal scale is **Median** since the variable in this category have the property of order.

Examples of ordinal scales include finishing order in a competition, education level, and rankings. These scales only indicate that one value is greater or less than another, so differences between ranks do not have meaning. A researcher would like to collect data on Education Level of its respondents, where variable education level can be Matriculation, Intermediate, Bachelors and Masters represented by 1, 2, 3 and 4 respectively.

Changing the number assigned to different education level will disrupt the inherent order and will have serious impact on the data.

## Interval Scale

An **interval scale **measurement has the properties of identification, magnitude, and equal interval/ equidistant scales and no true zero. An **equidistant scale **is a scale distributed in units that are equidistant from one another. The equal distance between scale points allows us to know how many units greater than, or less than, one case is from another on the measured characteristic. So, we can always be confident that the **meaning** of the distance between 25 and 35 **is the same** as the distance between 65 and 75. Interval scales **DO NOT** have a **true zero point**; the number “0” is **arbitrary. **

A good example of an interval scale is the measurement of temperature on Fahrenheit or Celsius scales. The units on a thermometer represent equal volumes of mercury between each interval on the scale. The thermometer identifies for us how many units of mercury correspond to the temperature measured. We know that 60° is hotter than 30° and that there is the same 10-degree difference in temperature between 20° and 30° as between 50° and 60°. Zero degrees on either scales is an arbitrary number and not a “true” zero. The zero point does not indicate an absence of temperature; it is an arbitrary point on the scale.

Other examples of interval scale include Age or Likert scales such as Agreement Scale (1: Strongly Disagree, 2: Disagree, 3: Neutral, 4: Agree 5: Strongly Agree) or Satisfaction Scale (1: Strongly Dissatisfied, 2: Dissatisfied, 3: Neutral, 4: Satisfied, 5: Strongly Satisfied) are measured on interval scale.

## Ratio Scale

**Ratio scales **are similar to interval scales in that scores are distributed in equal units. Yet, unlike interval scales, a distribution of scores on a ratio scale has a true zero. They have all the properties of an abstract number system i-e Identity, Magnitude, Equal interval and True/Absolute zero. These properties allow us to apply all of the possible mathematical operations (addition, subtraction, multiplication, and division) in data analysis.

The **absolute/true zero** allows us to know how many times greater one case is than another. For variables on a ratio scale, order is informative. This is an ideal scale in behavioral research because any mathematical operation can be performed on the values that are measured. Common examples of ratio scales include money in the bank, return on investment, number of children, and years of education.

For example, a person earning 20000 and another earning 40000, so we could easily say that second person is earning twice as much as the first person.