Scales of Measurement: Nominal, Ordinal, Interval, Ratio

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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

26 thoughts on “Scales of Measurement: Nominal, Ordinal, Interval, Ratio”

  3. park

    “In addition, quantitative data may also be classified as being either Discrete or Continuous.” with the example: “Driving license number/ Voter ID number/ PAN number”.

    However, these numbers are rather qualitative (nominal) and not quantitative.

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  4. Pingback: What Are Nominal And Ordinal Scales | Windranger5

  8. Venus M Brown

    That’s what I would think. They are for labeling or categorizing, therefor I would say they are nominal. Same with a social security number. They may have some meaningful order in the grand scheme of things, to those dealing with licences or ID’s, but for most people they are nothing more than a way to label or id you.

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    1. drroopesh Post author

      Dear Manju,

      Theoretically, yes.

      However, neither do I know of any software that does this, nor do I believe it is required.
      The concept is fairly straightforward, so I doubt someone would take the pains to create a program for this purpose.

      Regards,
      Dr. Roopesh

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  10. AnAnD

    Hello sir, can you explain what type of variable is the following:
    1. GCS score, APGAR score
    2. Time to recover from anaesthesis (expressed in seconds to hours)

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    1. drroopesh Post author

      Dear Anand,

      GCS score is nominal scale, since the numbers are assigned to labels, and are not meaningful by themselves. Ditto for Apgar score.

      Time to recover from anaesthesia (seconds to hours) would be ratio scale, since there is an absolute zero.

      I hope this helps.

      Regards,
      Dr. Roopesh

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      1. AnAnD

        Thank you sir for your timely reply. But I have a query. GCS APGAR scores can be arranged in an order, though there is no meangfull interval. So cant we call GCS APGAR scores as “ordinal” ??? Kindly clarify my doubt

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        1. drroopesh Post author

          Dear AnAnD,

          Thanks for pointing out my error. I had responded on the basis of the individual numerical values not being meaningful themselves, but forgot about the total score(s), and that those can be ordered.

          I stand corrected- they are ordinal, not nominal.

          Thanks and regards,

          Dr. Roopesh

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  12. Lisa

    I have a question….Would length of a program such as 0 to 3 months, 3 to 8 months or 9 months or greater be considered interval? I’m having a really hard time with this one. I’m 51 and taking an intro to statistics and actually enjoying it but I am having some difficulties. I think the absolute zeros are throwing me off.

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    1. drroopesh Post author

      Dear Lisa,

      It depends. If the length is in actual absolute numbers (3 months OR 6 months), then it is in ratio scale (absolute zero present), and you can compute mean duration.

      However, if the length is in terms of a range (0-3; 3-6; 6-9), then it is ordinal, since one can arrange the items in ascending or descending order, but cannot compute mean duration from just the range values (to compute mean one would need to know the frequencies as well).

      I hope this helps.

      Regards,
      Dr. Roopesh

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  16. Malith Abeywardena

    Hi I have a problem to which scale the number of children and income belongs to and why? In my opinion number of children should belong to ordinal scale not ratio because of the presence of absolute zero as number of children cannot be -ve value or interval scale cannot be used as as the number of children cannot be decimal numbers as 1.5, 2.5, 3.5 and all. Please kindly comment on this.

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    1. drroopesh Post author

      Dear Malith,

      As you rightly pointed out, the number of children cannot be a negative value. This is because there is a true zero. When the zero is not a true zero, negative values may be possible- like temperature in the Fahrenheit or Celsius scales. In scales where the zero is not a true zero, a ‘zero’ value does not mean absence of entity (Example: Zero degree Celsius does not mean absence of temperature, so negative temperatures are possible. However, in the Kelvin scale negative values are not possible.)

      Ordinal scale includes ranked data- 1st, 2nd, 3rd, etc.

      The number of children is an example of ratio scale because there is a true zero. Thus, one is able to say that 2 children is twice as many children as 1 child (this requires a true zero).

      Please note that both interval and ratio scales may include variables that are discrete or continuous. While continuous variables can take any numerical value (including decimal values), discrete variables can take only certain values (integers).

      Thus, number of children is an example of a discrete ratio scale.

      I hope this helps.

      Regards,
      Dr. Roopesh

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    1. drroopesh Post author

      Dear Bela,

      There are several examples of interval scale but I can’t think of any other than temperature that have negative values. Typically, any variable that can take negative values does not have an absolute (true) zero- If the zero were absolute ‘zero’ would imply the entity does not exist, so negative values would be meaningless. However, the absence of negative values does not mean that the scale has a true zero. Often, the label ‘zero’ is assigned arbitrarily- like in the pH scale, where ‘zero’ does not indicate absence of pH but maximum acidity. Whenever a ‘zero’ is assigned it is not ‘true’ or ‘absolute’. IQ scores are another example where a score of zero is possible- a newborn is assumed to have a mental age of zero so a person with anencephaly will have an IQ of zero (they don’t have a brain to speak of). If the score of zero were true/meaningful, a person with IQ 100 would be twice as smart as one with IQ 50- but that’s not true of IQ scores.

      I hope this clarifies your doubt.
      Regards,
      Dr. Roopesh

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