Why quoting percentages of I.Q.'s betrays incompetence

© July 2010 Paul Cooijmans

Percentages only meaningful on a ratio scale

Computing a percentage is a form of the arithmetical manipulations called "division" and "multiplication". Such calculations only give meaningful results on a so-called "ratio scale"; that is, a scale that fulfils both of the following requirements:

  1. The scale has a true and absolute "zero" that really means zero, rather than a zero that is randomly assigned to one of many possible values;
  2. The scale is intervallic, that is, each unit step has the same size as every other unit step on the scale.

Examples of scales that meet these demands are distance, mass, time, and the Kelvin temperature scale. Scales that do not qualify are for instance the Celsius and Fahrenheit temperature scales; their zeros have been assigned to particular values and do not reflect true zeros.

The I.Q. scale has a zero that simply means "6 2/3 standard deviations below the mean". It is therefore not a true zero, and I.Q. is therefore not a ratio scale. The question whether or not it is an intervallic scale is not relevant at this point, as the absence of an absolute zero suffices to disqualify it as a ratio scale.

It follows that multiplication and division, and therewith the computation of percentages, do not give true and meaningful outcomes when applied to I.Q.'s. This insight is useful when encountering claims such as:

Such pseudoscientific ignorance betrays deep incompetence in the field the claimant is speaking about. Be assured that nothing from such a person or found in such a publication needs to be taken seriously.