**Statistics **is an essential branch of mathematics that deals with large numerical data. In statistics, we gather, organize, manage, observe, calculate, interpret the given data. There are different types of variables used in statistics.

These are dependent variables and independent variables. Statistical variables may be qualitative or quantitative. While conducting some statistical analysis, it is required to measure the dependent variables used in the research. The exact method of measuring variables depends upon the types of variables utilized in the analysis. The different types
of variables are measured in different manner.**For Example:** If someone wishes to measure time taken in responding to a stimulus, one may use a stop watch. But if they require to measure attitude or views about a political situation, then the stop watch is of
no use.

In statistics, there are few **scales of measurement** which are used in order to measure the statistical variables. Each of these measurement scales does measure a certain type of variable. The measurement scales share some fundamental properties by which they can be classified, even though measurement procedures may differ in many
ways. In this section, the definition of scales of measurement and their different categories are discussed. Let us go ahead and learn.

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In statistics, while performing quantitative researches, the researcher has to attempt to classify the variables or data. Thus, he needs to develop some taxonomy for the measurement levels which are known as **scales of measurement**. There are number of ways available of measuring variables in statistics. These dependent variables are to be classified on the basis of scales of measurement. The measurement is the foundation for any type of scientific or statistical investigation. In a research or survey, everything we perform, does begin with its measurement. So, it is necessary to understand the difference between the type of variables and the scales according to which these would be measured. It is important to be able to
identify a scale which would be appropriate in order to analyze the data.

Therefore, we can say that the scales of measurement may be defined as the ways by which variables or numbers are classified into categories. Each scale of measurement possesses certain properties. These properties determine the appropriate use of certain statistical scale of measurement.

Every scale of measurement has few or all of the following properties explained below :

**1)** Each and every value on a measurement scale does have a unique identity or meaning.

**2)** These values usually have some magnitude or an ordered relationship with one another. We may say that some of the value are smaller, while some are bigger.

**3)** The intervals of the values on scales are equal to one another.

**4)** Absolute zero is included.
The scales of measurement are the categories used to quantify the variables.
There used be different classifications of measurement scales.

The most commonly and frequently used classification of scales of measurement was developed by a famous psychologist Stanley Smith Stevens who proposed following four types of scales of measurement:

**1)** Nominal scale of measurement

2) Ordinal scale of measurement

**3)** Interval scale of measurement

**4)** Ratio scale of measurementEach of these measurement scales are discussed below in detail.

Nominal scale of measurement is used to classify the categorical variables, i.e, the variables that define categories and names etc which cannot be ranked. This scale of measurement just satisfies the identity property of measurement. It is used to represent the variables that assign values in the form of descriptive category and do not have any numerical value or magnitude.

Basically, the nominal scale is the way of grouping or categorizing behaviors, in which the numbers are just labels and identifiers. It is also known as qualitative type sometimes. It classifies the subjects based on their names or categories or by some other qualitative classification. In this type, the numbers could be used to represent some variables but these numbers do not definitely have any numerical value. The variables that may fall in the category of nominal scale of measurement are - gender, ethnicity, citizenship, language, species, genre an many more.

**For Example:** Gender may be classified on the nominal scale
of measurement, since it has the types - "male" or "female", but not the
numerical values. Also, the variable “**religion**” does have responses such as “Muslim”, “Christian”, "Hindu", “Jewish” etc. So, it is measured on nominal scale.

The ordinal scale of measurement includes the variables that have the property of rank or order. Ordinal scale is actually more precise that the nominal one. The variables coming under this scale must have set of rankings. This scale of measurement possesses the properties related to identity as well as magnitude. Every value evaluated on ordinal scale has a unique meaning.

**For Example:** The order of some variable expressed as “low” “medium” and “high”. Similarly, if in a class, the obtained marks of each student are noted. Then, the variable that assigns
each student a number expressing their rank, is measured through ordinal scale. Here, we only know who obtained greater (or lower) marks to whom. But we definitely do not know by how much. We also do not know the actual marks obtained by anyone.

Interval scale of measurement includes categories in which the distances or intervals between the categories are to be compared. Interval scale keeps the rank characteristic just as ordinal scale. Along with that, the interval scale also shows the differences between the given data points. This scale of measurement states that the interval must be same.

**For Example:** A variable explaining that the difference
between the heights 5.5 feet and 6 feet is same as the difference between heights 4 feet and 4.5 feet.

Also, we can say that on interval scale the difference between 1 and 2 is equal to the difference between 6 and 7, 13 and 14, or 103 and 104.

Thus, the interval should be same. Hence, the interval scale of measurement possesses three properties - identity, magnitude and equal intervals. By using this scale, one is able to know which of the two values is greater or smaller. It also enables us to know by how much the values are greater or smaller. Ratio scale of measurement is almost same as interval-scale variable. Ratio-scale variable also includes a non-arbitrary zero value in it. It is the most powerful and precise of all the scales of measurement. The ratio scale has all the properties of interval scale, but it has a the most meaningful, zero point. Thus, one cannot have any negative value on the ratio scale. Here, along with the property of same intervals, we may be able to compare the scores by means of ratios. Therefore, we can say that ratio scale of measurement has all the four properties of measurement which are - identity, magnitude, equal intervals, and minimum value of zero.

**For Example:** A variable containing the score of 30 is 30 times bigger than 1. This may be expressed as 30:1.

In another example, when we measure something using a ruler, it gives us a measure on a ratio scale. A value that is 2 inches is said to be half of the length of something which is 4 inches. This is not evident on an interval scale. Also, zero in included in it meaning "no length". It is not possible to measure negative length too.

**Examples of Nominal Scale of Measurement:**

1) Symptoms of a disease - mild, moderate, severe.

**2)** Behavioral patterns - extroverts, introverts or ambivert.

**3)** Name of the person - John, Barbara, Samantha, Duke etc.

**4)** Nationality - Indian, American, African, European etc.

**Examples of Ordinal Scale of Measurement:**

**1)** Ranking in high school class.

**2) **Socioeconomic status (low, middle, high).

**3)** Rank in athletics.

**4)** Views about some political matter (Totally agree, mostly disagree, totally disagree).

**Examples of Interval Scale of Measurement:**

**1) **The score of IQ test (difference between someone's IQ of 110 and 98
is same as difference between 130 and 142).

**2)** Thermometer readings on Fahrenheit scale. The value zero does not mean "the
absence of heat."

**Examples of Ratio Scale of Measurement:**

**1) **Driving speed.

**2)** Measurement of weight.

**3)** Time taken for completing a task.

**4) **Record of number of errors made in a certain time period.

Therefore, we can say that the scales of measurement may be defined as the ways by which variables or numbers are classified into categories. Each scale of measurement possesses certain properties. These properties determine the appropriate use of certain statistical scale of measurement.

Every scale of measurement has few or all of the following properties explained below :

The most commonly and frequently used classification of scales of measurement was developed by a famous psychologist Stanley Smith Stevens who proposed following four types of scales of measurement:

2)

Nominal scale of measurement is used to classify the categorical variables, i.e, the variables that define categories and names etc which cannot be ranked. This scale of measurement just satisfies the identity property of measurement. It is used to represent the variables that assign values in the form of descriptive category and do not have any numerical value or magnitude.

Basically, the nominal scale is the way of grouping or categorizing behaviors, in which the numbers are just labels and identifiers. It is also known as qualitative type sometimes. It classifies the subjects based on their names or categories or by some other qualitative classification. In this type, the numbers could be used to represent some variables but these numbers do not definitely have any numerical value. The variables that may fall in the category of nominal scale of measurement are - gender, ethnicity, citizenship, language, species, genre an many more.

The ordinal scale of measurement includes the variables that have the property of rank or order. Ordinal scale is actually more precise that the nominal one. The variables coming under this scale must have set of rankings. This scale of measurement possesses the properties related to identity as well as magnitude. Every value evaluated on ordinal scale has a unique meaning.

Interval scale of measurement includes categories in which the distances or intervals between the categories are to be compared. Interval scale keeps the rank characteristic just as ordinal scale. Along with that, the interval scale also shows the differences between the given data points. This scale of measurement states that the interval must be same.

Also, we can say that on interval scale the difference between 1 and 2 is equal to the difference between 6 and 7, 13 and 14, or 103 and 104.

Thus, the interval should be same. Hence, the interval scale of measurement possesses three properties - identity, magnitude and equal intervals. By using this scale, one is able to know which of the two values is greater or smaller. It also enables us to know by how much the values are greater or smaller. Ratio scale of measurement is almost same as interval-scale variable. Ratio-scale variable also includes a non-arbitrary zero value in it. It is the most powerful and precise of all the scales of measurement. The ratio scale has all the properties of interval scale, but it has a the most meaningful, zero point. Thus, one cannot have any negative value on the ratio scale. Here, along with the property of same intervals, we may be able to compare the scores by means of ratios. Therefore, we can say that ratio scale of measurement has all the four properties of measurement which are - identity, magnitude, equal intervals, and minimum value of zero.

In another example, when we measure something using a ruler, it gives us a measure on a ratio scale. A value that is 2 inches is said to be half of the length of something which is 4 inches. This is not evident on an interval scale. Also, zero in included in it meaning "no length". It is not possible to measure negative length too.

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