Data Science

by John D. Kelleher

apply ordering and subtraction operations to interval attributes, but other arithmetic operations (such as multiplication and division) are not appropriate. Ratio scales are similar to interval scales, but the scale of measurement possesses a true-zero origin. A value of zero indicates that none of the quantity is being measured. A consequence of a ratio scale having a true-zero origin is that we can describe a value on a ratio scale as being a multiple (or ratio) of another value. Temperature is a useful example for distinguishing between interval and ratio scales.2 A temperature measurement on the Celsius or Fahrenheit scale is an interval measurement because a 0 value on either of these scales does not indicate zero heat. So although we can compute differences between temperatures on these scales and compare these differences, we cannot say that a temperature of 20° Celsius is twice as warm as 10° Celsius. By contrast, a temperature measurement in Kelvins is on a ratio scale because 0 K (absolute zero) is the temperature at which all thermal motion ceases. Other common examples of ratio-scale measurements include money quantities, weight, height, and marks on an exam paper (scale 0–100).