[Statistics Tutorial 4] Scales of Measurement

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The scales of measurements refer to the different methods of measuring variables.

There are 4 different scales of measurement: Nominal, Ordinal, Interval, and Ratio Scales

Consider these scales as the steps of a staircase as shown below:

Scales of Measurement

Scales of Measurement

 

The scales on the higher levels allow better statistical calculations and have some additional information than the scales on the lower stairs.

 

Also, every scale on the staircase can be viewed as an extension of the previous step. Example, an ordinal scale can be viewed as an extension of the nominal scale and so on. This will be more intuitive once we understand and define the 4 scales:

 

1. Nominal Scale:

  • This scale tells us which group a unit or individual belongs.
  • Participants are placed in categories. Hence, this scale is categorical in nature.
  • Differences between participants are measured in kind and not in degree. Hence, this scale is qualitative in nature.

 

Examples:

a) Gender–Male or Female?

b) Options–Yes or No?

c) Religion–Hindu or Christian or Muslim?

 

Note – It is clear from the above examples that it the options are not better or worse than each other. Example, we cannot say that “yes” is better than “no” or “male” is better than “female”.

The answers are not in any order.

 

2. Ordinal Scale:

  • The ordinal scale extends the information of the nominal scale to show order.
  • This is also qualitative and categorical in nature.

 

Examples:

a) Strongly agree, agree, neutral, disagree, and strongly disagree

b) Excellent, good, average, poor, very poor.

 

3. Interval Scale:

Extends ordinal scale to include a unit or measurement and talk about differences in degree of order and not just differences in order. Contains categories in which the actual distances, or intervals, between categories can be compared.

Examples:

 

a)  If we represent the values on the Likert Scale by numbers – 1, 2, 3, 4, and 5:

 

This is an interval scale with the start point 1 and end point 5. However, we can also change the assignment to the following without changing the meaning of the scale:

 

 

This means that the start point is arbitrary and there is no fixed starting point – and 0 does not always have to refer to strongly disagree.

However, the difference between any two values is still the same. i.e. – The difference between agree and neutral in the first table = the difference between agree and neutral in the second table = 1.

We can summarize to say that the interval is constant but the starting and terminating point is arbitrary.

b) The Fahrenheit scale for temperature:

Equal differences on this scale represent equal differences in temperature.

The difference between 30 degree and 20 degree will be the same as the difference between 20 degree and 10 degree. However, 0 degree would not mean absence of heat or no temperature.

Once again, we see that the interval is constant but the starting and terminating point is arbitrary.

Other examples are the Celsius scale & the IQ scale.

 

4. Ratio Scale:

Ratio scale is an extension of the interval scale and it adds a true zero or a fixed zero starting point to the interval scale. Hence, an interval scale with a fixed zero point is called a ratio scale.

Examples:

a)     Years of education – 0,1,2,3,4,5

Here, zero would mean no years of education.

b)    Temperature in Kelvin scale – 0 Kelvin is the point at which there is no heat.

 

Overview of Measurement Scales

 

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