There are four scales of measurement: Nominal, Ordinal, Interval, Ratio.
These are considered under qualitative and quantitative data as under:
Qualitative data:
- Nominal scale:
In this scale, categories are nominated names [hence “nominal”]. There is no inherent order between categories. Put simply, one cannot say that a particular category is superior/ better than another.
Examples:
- Gender [Male/ Female]:- One cannot say that Males are better than Females, or vice-versa.
- Blood Groups [A/B/O/AB]:- One cannot say that group A is superior to group O, for instance.
- Religion [Hindu/ Muslim/ Christian/ Buddhist, etc.]:- Here, too, the categories cannot be arranged in a logical order. Each category can only be considered as equal to the other.
- Ordinal scale:
The various categories can be logically arranged in a meaningful order. However, the difference between the categories is not “meaningful”.
Examples:
- Ranks [1st/ 2nd/ 3rd, etc.]: The ranks can be arranged in either ascending or descending order without difficulty. However, the difference between ranks is not the same-the difference between the 1st rank and 2nd rank may be 20 units, but that between the 2nd and 3rd ranks may be 3 units. In addition, it is not possible to say that the 1st rank is x times better than the 2nd or 3rd rank purely on the basis of the ranks.
- Ranks [Good/ Better/ Best], [No pain/ Mild pain/ Moderate pain/ Severe pain]: Here, too, a meaningful arrangement [ordering] is possible, but the difference between the categories is subjective and not uniform. “Best” is not necessarily thrice as good as “Good”; or twice as good as “Better”.
- Likert scale [Strongly Disagree/ Disagree/ Neutral/ Agree/ Strongly Agree] : The ordering is flexible- the order can easily be reversed without affecting the interpretation- [Strongly Agree/ Agree/ Neutral/ Disagree/ Strongly Disagree]. Again, the difference between categories is not uniform.
Quantitative data:
- Interval scale:
The values [not categories] can be ordered and have a meaningful difference, but doubling is not meaningful. This is because of the absence of an “absolute zero”.
Example: The Celsius scale: The difference between 40 C and 50 C is the same as that between 20 C and 30 C [meaningful difference = equidistant]. Besides, 50 C is hotter than 40 C [order]. However, 20 C is not half as hot as 40 C and vice versa [doubling is not meaningful].
Meaningful difference: In the Celsius scale, the difference between each unit is the same anywhere on the scale- the difference between 49 C and 50 C is the same as the difference between any two consecutive values on the scale [ 1 unit].[Thus, [2-1]= [23-22]= [40-39]=[99-98]= 1].
- Ratio scale:
The values can be ordered, have a meaningful difference, and doubling is also meaningful. There is an “absolute zero”.
Examples:
- The Kelvin scale: 100 K is twice as hot as 50 K; the difference between values is meaningful and can be ordered.
- Weight: 100 kg is twice as heavy as 50 kg; the difference between 45 kg and 55 kg is the same as that between 105 kg and 100 kg; values can be arranged in an order [ascending/ descending].
- Height: 100 cm is taller than 50 cm; this difference is the same as that between 150 cm and 100 cm, or 200 cm and 150 cm; 100 cm is twice as tall as 50 cm; the values can be arranged in a particular manner [ascending/ descending].
In addition, quantitative data may also be classified as being either Discrete or Continuous.
Discrete:
The values can be specific numbers only. Fractions are meaningless. In some situations, mathematical functions are not possible, too.
Examples:
- Number of children: 1, 2, 3, etc. are possible, but 1.5 children is not meaningful.
- Number of votes: 100, 102, etc. are meaningful, not 110.2 votes.
- Driving license number/ Voter ID number/ PAN number: The number is a discrete value, but cannot be used for addition or subtraction, etc.
Continuous:
Any numerical value [including fractions] is possible and meaningful.
Examples:
- Weight: 1 kg, 1.0 kg, 1.000 kg, 1.00001 kg are all meaningful. The level of precision depends upon the equipment used to measure weight.
- Height: 10 m, 10.03 m, 10.0005 m are all meaningful.
- Temperature: 100.0 F, 102.5 F, 99.8 F are all meaningful.
- Time: 1.023 s, 1.00002 s, are meaningful. Mathematical functions [addition, subtraction, etc. are meaningful].
Most of the numerical data we use is continuous. As you might have noticed by now, the Ratio scale often involves continuous data [Temperature is an exception, unless the Kelvin scale is being used].