Scales of Measurement

Data can be classified as being on one of four scales: nominal, ordinal, interval or ratio. Each level of measurement has some important properties that are useful to know. Properties of Measurement Scales:

• Identity - Each value on the measurement scale has a unique meaning.
• Magnitude - Values on the measurement scale have an ordered relationship to one another. That is, some values are larger and some are smaller.
• Equal intervals - Scale units along the scale are equal to one another. For Example the difference between 1 and 2 would be equal to the difference between 11 and 12.
• A minimum value of zero - The scale has a true zero point, below which no values exist.

1. Nominal Scale - Nominal variables can be placed into categories. These don’t have a numeric value and so cannot be added, subtracted, divided or multiplied. These also have no order, and nominal scale of measurement only satisfies the identity property of measurement. For example, gender is an example of a variable that is measured on a nominal scale. Individuals may be classified as "male" or "female", but neither value represents more or less "gender" than the other. 2. Ordinal Scale - The ordinal scale contains things that you can place in order. It measures a variable in terms of magnitude, or rank. Ordinal scales tell us relative order, but give us no information regarding differences between the categories. The ordinal scale has the property of both identity and magnitude. For example, in a race If Ram takes first and Vidur takes second place, we do not know competition was close by how many seconds. 3. Interval Scale - An interval scale has ordered numbers with meaningful divisions, the magnitude between the consecutive intervals are equal. Interval scales do not have a true zero i.e In Celsius 0 degrees does not mean the absence of heat. Interval scales have the properties of:

• Identity
• Magnitude
• Equal distance

For example, temperature on Fahrenheit/Celsius thermometer i.e. 90° are hotter than 45° and the difference between 10° and 30° are the same as the difference between 60° degrees and 80°. 4. Ratio Scale - The ratio scale of measurement is similar to the interval scale in that it also represents quantity and has equality of units with one major difference: zero is meaningful (no numbers exist below the zero). The true zero allows us to know how many times greater one case is than another. Ratio scales have all of the characteristics of the nominal, ordinal and interval scales. The simplest example of a ratio scale is the measurement of length. Having zero length or zero money means that there is no length and no money but zero temperature is not an absolute zero. Properties of Ratio Scale:

• Identity
• Magnitude
• Equal distance
• Absolute/true zero

For example, in distance 10 miles is twice as long as 5 mile.