Which level of measurement consist of categories only where data Cannot be arranged in an ordering scheme?

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:

1. Gender (Male/ Female):- One cannot say that Males are better than Females, or vice-versa.
2. Blood Groups (A/B/O/AB):- One cannot say that group A is superior to group O, for instance.
3. 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:

1. 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.
2. 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”.
3. 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:

1. The Kelvin scale: 100 K is twice as hot as 50 K; the difference between values is meaningful and can be ordered.
2. 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).
3. 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:

1. Number of children: 1, 2, 3, etc. are possible, but 1.5 children is not meaningful.
2. Number of votes: 100, 102, etc. are meaningful, not 110.2 votes.
3. 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:

1. 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.
2. Height: 10 m, 10.03 m, 10.0005 m are all meaningful.
3. Temperature: 100.0 F, 102.5 F, 99.8 F are all meaningful.
4. 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].   

http://en.wikibooks.org/wiki/Statistics/Different_Types_of_Data/Quantitative_and_Qualitative_Data

http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i11/bk7_11i1.htm

Click to access 03a_continuous_descriptive.slides.pdf

Which level of measurement Cannot have ordered categories?

What level of measurement involves data that may be arranged in some order?

What level of measurement classifies data into categories with no order or ranking?

What level of measurement is categories?