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Data Scales

There are several scales of data. The scales of data from lowest to highest are: Nominal, Ordinal, Interval, Ratio.

Each data scale has certain characteristics. A data scale has the characteristics of the lower level scale, plus additional characteristics. For example, ordinal data has nominal characteristics and then some.

Nominal Data

Nominal data are data that are labels or names.

Nominal data will always be Qualitative in nature.

Examples:

  • A name (of a company, or person, or type of car, etc.)
  • A person's gender (Male or Female),
  • Political affiliation (democrat, republican, independent, etc.)
  • Marital status (single, divorced, widowed, cohabitating )
  • etc.

All of the above have been examples where the data can be represented non-numerically. But what if I record the gender of students in a class numerically, using 1=M, and 2=F?

Is this still nominal data? The answer is yes.

Remember that meaningful arithmetic operations (such as computing the average value) can only be performed on QUANTITATIVE data. So, let us see if I can compute the average gender, and if the result is meaningful.

If I have a class of 50 students comprised of 20 men and 30 women, the average would be: [20(1) + 30(2)]/50 = 80/50 = 1.6 on a scale of 1=M, 2=F.

So, I can compute the average, but is it meaningful? The answer is, no – it is not meaningful to say the average gender of a student is 1.6!

This is because gender is a label, a way to categorize individuals. That label, whether represented numerically with 1 and 2, or non-numerically with M and F, still represents a label and is qualitative in nature.

Other examples of numerically-represented nominal or qualitative data are: one's telephone number, zip-code, social security number, etc.

All of these are numbers but if I average the telephone numbers of all my students, the result would not be useful or meaningful.

Ordinal Data

The next level up in data scales is ordinal data. With ordinal scale, there is order within the data and a “direction” in values. Ordinal data can be recorded as numeric or non-numeric, but it is Qualitative in nature because the difference between data values is not fixed (is not discernible).

Examples of Ordinal scales:

  • Grades of Meat (Select, Choice, Premium: How much more tender or tasty is one grade than the one below it is not quantifiable).
  • Grades that could be earned (A, B, C, etc.) in a class: These grades represent a “range” of points earned in class. A student who falls in that range receives the letter grade. Therefore, the difference between an A and a B or even between two A’s could vary.
  • Managerial level (Upper, Middle, Lower)
  • Likert items on a survey where the choice of responses are on a continuum ranging between two extremes such as:
  • Always, Often, Sometimes, Never (could also be recorded numericallyas: 4, 3, 2, 1)
  • Excellent, Good, Average, Poor (could also be recorded numerically)
  • Extremely Satisfied, Satisfied, Dissatisfied, Extremely Dissatisfied (could also be recorded numerically).
  • Etc.

Ordinal data do not have discernible and concrete intervals between data values. For example, if 3 people answer the same job satisfaction question on a survey and one says Extremely Satisfied, another says Satisfied, and the third says Dissatisfied, it is not possible to determine what the difference is between the satisfaction level of respondent 1 and respondent 2, and between satisfaction level of respondent 2 and respondent 3. And if we do this with yet another set of 3 respondents, even between the two groups we cannot tell if the two people who gave the same answer (for example “Satisfied”) “actually” experience the “same” level of job satisfaction.

In other words, there is no fixed unit to measure “satisfaction”.

Interval Scale

Data that are on the interval scale have concrete and discernible intervals between data values (fixed unit of measure).

Examples:

  • SAT scores for two students are 1100 and 1200. One is 100 higher than the other. That difference is very measurable and fixed. But,ratio of the two is meaningless because the minimum SAT score is not zero.
  • Years that companies have existed: Company A was started in 1970 vs. B which was established in 2000. Obviously A has been around for 30 years longer than B. But ratio of 2000 to 1970 is not meaningful.
  • Temperature: Today is 10 degrees F, yesterday it was 5F. Temperature today is 5 degrees higher than yesterday, but you can’t say today is twice as hot.
  • Celsius is also an interval temperature scale. The zero in this scale is based on the freezing point of water. However, at zero Celsius all heat is not gone and temperature still exists.
  • Etc.

Interval scale data is always numeric and quantitative.

Ratio Scale

Ratio scale data are numeric and quantitative and computing ratio of two data values is meaningful. Ratio data have a natural zero meaning that at zero, there is none of it left! Height, weight, price, age, etc are all ratio scale.

Examples:

  • Weight of boxes of cereal: A weighs one pound, B weighs two pounds. B is twice as heavy as A.
  • Price of Stock: X is $50/share, Y is $10/share. X is 5 times as expensive as Y.
  • The Kelvin scale is Ratio. The zero on the Kelvin scale is equal to -273 degrees Celsius (or, -459 F) which equates to absolutely no temperature. The Kelvin scale is used for all scientific studies and research. Another ratio temperature scale is Rankin which has similar characteristics as the Kelvin Scale.
  • Etc.

Ratio scale data can only be numeric and quantitative.

I hope you find this helpful.

Dr. J.