Scales

Variables are often numbers, different types of variables (measurements) have to be distinguished. Following Stevens and Conover , four types of scales can be distinguished:
 

1. Nominal scale: this scale is based on a set of qualitative attributes. There is no criterion to order the items of a nominally scaled variable. Examples: species, sex, treatment groups in experimental designs.
2. Ordinal scale: this scale refers to measurements that can be ordered in terms of "greater", "less" or "equal". Observations need not be equidistant. Examples: percentile ranks, ranks in a race.
3. Interval scale: equally spaced units along the scale without a predefined zero point. Examples: temperature (in C, F, or R), water level.
4. Ratio scale: equally spaced units along the scale with true zero point. Examples: temperature in K, weight, driving speed

Please note that arithmetic operations are only meaningful for interval and ratio scales. Multiplication and division is meaningful only for ratio scales.