Variables and scales of measurement

Before jumping into any statistical analysis it is important to understand the types of variables involved.

One of the classifications for variables is dependent and independent variables. Another classification is categorical and  continuous variables. Let us look at each of them in detail so as to get good understanding.

Dependent and independent variables

Consider an example, suppose we are analysing the influence of various factors on the success of a brand in the market. Here the success of the brand is outcome variable or dependent variable (as it depends on other factors in this study). Factors considered are independent variables.

Mathematically, y = f(x); here y is the dependent/outcome variable while x is the independent variable.

Dependent and independent variables
  • Dependent variable is the one which is the object of study. It is the end outcome.
  • Independent variable is one of the factors influencing the outcome (Dependent variable)

Categorical and continuous variables

In the above example, success of brand in the market could be measured in various ways.

Suppose if the one year sales of brand has exceeded USD 1 million, it could be termed ‘Successful’, anywhere from USD 500k to 1 million as ‘mediocre’ and less than USD 500k as ‘Not successful’.

As we can observe, here the variable ‘Success of brand in market’ is categorical in nature, that is, it is categorised as successful, mediocre or not successful.

  • Continuous variables are those which can take any value in a particular range. Suppose ‘income’ is one of the variables in our analysis. Virtually it can take any value between the maximum and minimum income figures.
  • Dichotomous variables are subset of categorical variables that can take only two values. For example, the variable ‘Possess a house’. Either an individual owns a house or not at a particular point of time. So there are only two options for this variable which makes it Dichotomous.
Examples of different types of variables

Scales of measurement

As discussed, there could be various types of variables involved in statistical analysis. It is important to have an understanding of the scale of measurement for each variable.

There are 4 scales of measurement

  • Nominal scale
  • Ordinal scale
  • Interval scale
  • Ratio scale

Nominal scale:

This scale is used for identification purpose only. No inference could be drawn quantitatively from such scale.

Example of Nominal scale – For example, there are three identical pens, one is red, one is green and other is blue. Here the classification of red pen, green pen and blue pen is simply nominal. It cannot be measured. Similarly gender, males, females and others is just a classification used for identification purpose only.

Ordinal scale:

This scale is used for identifying as well as to understand the relative importance of each value for a variable.

Example of Ordinal scale – Let us classify people into Rich, Middle class and Poor based on wealth. As this classification is based on wealth, we can definitely say that Wealth of rich > Wealth of middle class > Wealth of poor. In the example of nominal scale, we had classified pens based on color and colors cannot be compared unlike wealth.

Interval scale:

Interval scale is a quantitative one (that can be measured) and equal intervals in values represent equal differences in quality.

Example of Interval scale – Inclination is measured in degrees; difference between 30 deg and 60 deg is same as the difference between 90 deg and 120 deg in terms of inclination. Zero deg is just another measure and does not mean ‘nothing’. We have just set a particular position as zero deg for reference.

Similarly temperature, difference between -30 deg Celsius and -20 deg Celsius is same as the difference between 55 deg Celsius and 65 deg Celsius. Also, zero deg Celsius does not mean absolute zero or ‘nothing’ it just means another point in temperature.

Note: This scale inherently has the properties of Nominal and Ordinal scales.

Ratio scale:

This scale is a quantitative one and is used to measure a physical quantity such as weight, number of cars, no of football matches played etc. Also, in this scale equal intervals represent equal differences like in the case of interval scale. Here, zero means absolute zero and having ‘nothing’. Suppose no of cars is zero, it literally means there are no cars, that is, ‘nothing’.

Key difference between interval and ratio scale is that ratio scale can never go below zero.

Examples of scales of measurement in statistics