Scales of measurement

Scale of measurement refer to ways in which variables/numbers are defined and categorized. Each scale of measurement has certain properties which in turn determines the appropriateness for use of certain statistical analyses. The four scales of measurement are nominal, ordinal, interval, and ratio.

Nominal

Categorical data and numbers that are simply used as identifiers or names represent a nominal scale of measurement.

“The measurement values are Categorical”

Only valid operation is \'=\'.  A measure of location is the MODE (most frequent value).

For example:

  • If I am maintaining student’s records and I\'m including gender as a variable, I will code Female as 1 and Male as 2 or visa versa when I enter my data into the computer. Thus, I am using the numbers 1 and 2 to represent categories of data.
  • The classification of defects by their type is also nominal data.
  • Human attention on certain project.

Ordinal

An ordinal scale of measurement represents an ordered series of relationships or rank order.

“The measurement values are Rankings”

Here Comparisons are possible using operations \'<\' and \'>\'. Non-parametric statistics can be used.  The usual measure of location is the MEDIAN (value with 50% of cases above & 50% below).

For example:

  • The assignment of defects to a severity level is ordinal data.

Interval

A scale which represents quantity and has equal units but for which zero represents simply an additional point of measurement is an interval scale. In addition, zero does not represent the absolute lowest value. Rather, it is point on the scale with numbers both above and below it (for example, -10 degrees Fahrenheit).

“The measurement values have equal distances corresponding to equal quantities of the attribute”

Addition and subtraction are allowed.  So the ordinary ARITHMETIC-MEAN can be calculated and most standard statistical techniques can be used.

For example:

  • The Fahrenheit scale is a clear example of the interval scale of measurement.
  • Cycloramic complexity has the minimum value of one, but each increment represents an additional path.

Ratio

The ratio scale of measurement is similar to the interval scale in that it also represents quantity and has equality of units. However, this scale also has an absolute zero (no numbers exist below the zero).

“The measurement values have equal distances corresponding to equal quantities of the attribute where the value of zero corresponds to none of the attribute”

Multiplication and division are allowed.  So the GEOMETRIC-MEAN can be calculated.

For example:

  • The size of a software component.
  • Bandwidth (Mbps) is in Ratio.
  • Staff Time required for completion of project.
  • Purchase cost.