Richter magnitude scale from it empirically as a quantity without units, just a number designed to conform to the formula_3 scale. A spectral analysis is required to obtain formula_12, whereas the other magnitudes are derived from a simple measurement of the amplitude of a specifically defined wave. All scales, except formula_5, saturate for large earthquakes, meaning they are based on the amplitudes of waves which have a wavelength shorter than the rupture length of the earthquakes. These short waves (high frequency waves) are too short a yardstick to measure the extent of the event. The resulting effective upper limit of measurement for formula_17
Rating scale at the ordinal level. Numbers indicate the relative position of items, but not the magnitude of difference. Attitude and opinion scales are usually ordinal; one example is a Likert response scale: Some data are measured at the interval level. Numbers indicate the magnitude of difference between items, but there is no absolute zero point. A good example is a Fahrenheit/Celsius temperature scale where the differences between numbers matter, but placement of zero does not. Some data are measured at the ratio level. Numbers indicate magnitude of difference and there is a fixed zero point. Ratios can be calculated. Examples include