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NOMINAL
A nominal scale classifies cases into mutually exclusive categories. The rules of assigning codes to categories are usually arbitrary, e.g. 1 for male and 2 for female, or 1 for female and 2 for male.
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ORDINAL
An ordinal scale arranges cases in a rank order of some underlying property. The magnitude of difference between any two consecutive ranks is unknown. Thus, we cannot ascertain that the difference between "rank 1" and "rank 2" is the same as the difference between "rank 2" and "rank 3" or not. For the same reason, the results of arithmetical operations on rank orders are dubious.
Example 1
In a university badminton club, there is a players ladder. Joe is ranked the first; Paul is ranked the second; John is ranked the third and Billy is ranked the fourth. We cannot tell whether Joe and Billy can beat Paul and John or not in a double tournament. If we know that Joe is far more better than the other three players and the three players are rather "close" in terms of skills, then we would know that Joe + Billy most probably will beat Paul + John. However, as usual an ordinal scale does not provide this type of information.
It is quite usual that ordinal scale data are added together to form some composite scale. By doing so, it violates the rule that ordinal data cannot be added together, and hence forming scale which is only partially ordinal.
Example 2
| Are you satisfied with | v. satisfied |
Satisfied |
Not satisfied |
v. dissatisfied |
| i) your work | 4 |
3 |
2 |
1 |
| ii) your family life | 4 |
3 |
2 |
1 |
| iii) your social life | 4 |
3 |
2 |
1 |
| iv) living environment | 4 |
3 |
2 |
1 |
A life satisfaction index is composed of the sum of the scores for the four areas of satisfaction-dissatisfaction. We cannot be sure that a person with a total score of 13 has a higher life satisfaction than the other with a score of 12. However, we may be more certain that the one with a score of 8 would have a higher life satisfaction than the one with a score of 4.
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INTERVAL SCALE
On an interval scale, the difference between any two points is of a known size, but there is no true zero on the scale. Commonly used examples are measures of temperature such as Fahrenheit and Celsius. Addition and subtraction are legitimate. Though it is legitimate to use multiplication and division, the meaning of multiple and quotient are dubious. For example, we cannot really say that 30 degree Celsius is twice as hot as 15 degree Celsius.
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RATIO SCALE
A ratio scale is similar to the interval scale, but with a true zero. e.g. weight, age, height, etc. Multiples and quotients are usually interpretable.
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NUMBERS VERSUS CONCEPTS
Numbers are assigned to the values of variables, which can be a nominal, ordinal, interval, or ratio scale. We have to ascertain the level of measurement before we can determine the appropriate types of statistics or analysis on these variables. Furthermore, social scientists are usually interested in concepts that are not directly measurable. For example, the researcher may be interested in "maturity", so he uses "age" as an indicator. "Age" is a ratio scale variable. But using "age" to indicate "maturity", the variable would be something even less than an ordinal scale. For interpretation of this kind, the use of statistics has to be very careful.