What are some more examples of how measurement level relates to statistical methodology?
As mentioned earlier, it is meaningless to claim that it was twice as warm today as yesterday because it was 40 degrees Fahrenheit today but only 20 degrees yesterday. Fahrenheit is not a ratio scale, and there is no meaningful sense in which 40 degrees is twice as warm as 20 degrees. It would be just as meaningless to compute the geometric mean or coefficient of variation of a set of temperatures in degrees Fahrenheit, since these statistics are not invariant or equivariant under change of origin. There are many other statistics that can be meaningfully applied only to data at a sufficiently strong level of measurement. Consider some measures of location: the mode requires a nominal or stronger scale, the median requires an ordinal or stronger scale, the arithmetic mean requires an interval or stronger scale, and the geometric mean or harmonic mean require a ratio or stronger scale.
As mentioned earlier, it is meaningless to claim that it was twice as warm today as yesterday because it was 40 degrees Fahrenheit today but only 20 degrees yesterday. Fahrenheit is not a ratio scale, and there is no meaningful sense in which 40 degrees is twice as warm as 20 degrees. It would be just as meaningless to compute the geometric mean or coefficient of variation of a set of temperatures in degrees Fahrenheit, since these statistics are not invariant or equivariant under change of origin. There are many other statistics that can be meaningfully applied only to data at a sufficiently strong level of measurement. Consider some measures of location: the mode requires a nominal or stronger scale, the median requires an ordinal or stronger scale, the arithmetic mean requires an interval or stronger scale, and the geometric mean or harmonic mean require a ratio or stronger scale. Consider some measures of variation: entropy requires a nominal or stronger scale, the standard deviati
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