Levels of Measurement (Nominal, Ordinal, Interval, Ratio) in Statistics

Image Source: Statistical Aid: A School of Statistics

Definition

In statistics, the statistical data whether qualitative or quantitative, are generated or obtain through some measurement or some observational process. Measurement is essentially the task of assigning numbers to observations according to certain rules. The way in which the numbers are assigned to observations determines the scale of measurement being used. There are four level of measurements in statistics. They are-

• Nominal Level
• Ordinal Level
• Interval Level
• Ratio Level

Nominal Level of Measurement

All qualitative measurements are nominal, regardless of whether the categories are designed by names (male, female) or numerals (bank account no., id no etc.). In nominal level of measurement, the categories differ from one another only in names. In other words, one category of a characteristic is not higher or lower, greater or smaller than the other category. For example, gender (male or female), religion (Muslim, Hindu or others), etc. The nominal level of measurement gives rise to nominal data. 

We must ensure that the categories of nominal level of measurement must be follow some important properties. They are-

• The categories are must be homogeneous.
• The categories are mutually exclusive and exhaustive.

Ordinal level of Measurement

In ordinal level of measurement there exist an ordered relationship among the categories. For example, we use less, more, higher, greater, lower etc. for define the categories such as costly, less profitable, more difficult etc. More precisely, the relationships are expressed in terms of the algebra of inequalities: a less than b (a<b) or is greater than b (a>b). So, the socio-economic status (low, medium, high), academic performance (poor, good, very good), agreement on some issue (strongly disagree, disagree, agree, strongly agree) are some practical variable of ordinal level of measurement. Ordinal level of measurement gives ordinal data. 

Ordinal level maintains some important properties as,

• The categories are distinct, mutually exclusive and exhaustive.
• The categories are possible to be ranked or ordered.
• The distance from one category to the other is not necessarily constant.

Interval Level of Measurement

The interval level of measurement includes all the properties of the nominal and ordinal level of measurement but it has an additional property that the difference (interval) between the values is known and constant size. In this measurement 0 is used as an arbitrary point. The interval measurement scale has some important properties. They are-

• The data classifications are mutually exclusive and exhaustive.
• The data can be meaningfully ranked or ordered.
• The difference between the categories is known and constant.

For example, in Gregorian calendar 0 is used to separate B.C. and A.D. We refer to the years before 0 as B.C. and to those after 0 as A.D. Incidentally 0 is a hypothetical date in the Gregorian calendar because there never was a year 0.

Another example, a thermometer measures temperature in degrees, which are of the same size at any point of the scale. The difference between 20⁰C and 21⁰C is the same as the difference between 12⁰C and 13⁰C. The temperature 12⁰C, 13⁰C, 20⁰C, 21⁰C can be ranked and the differences between the temperatures can easily be determined. When the temperature is 0⁰C, it means not the absence of heat but it is cold. In fact, 0⁰C is equal to 32⁰F.

Ratio level of Measurement

In ratio level, there is an ordered relationship among the categories where exist an absolute zero and follow the all properties of nominal level of measurement. All quantitative data fall under the ratio level of measurement. For example, wages, stock price, sales value, age, height, weight, etc. are the real life variable of ratio level measurement. If we say the sales value is 0, then there is no sale.

There exist some important properties in this level. They are-

• The categories are mutually exclusive and exhaustive.
• The categories can be ordered or ranked.
• The differences among the categories are constant.
• There exist an absolute zero point.

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